Methods for estimating the natural frequencies of collapsed walls in stacked buildings under different boundary conditions

Abstract

This invention relates to the field of mechanical technology, specifically to a method for estimating the natural frequencies of collapsed walls in stacked buildings under different boundary conditions. The method involves constructing a simplified model of the collapsed wall and obtaining the vibration differential equations for the wall components; deriving the natural frequency expression for the collapsed wall under simply supported boundary conditions and the vibration differential equations, and establishing a formula for estimating the fundamental frequency of the collapsed wall under these conditions; deriving the calculation formula for the natural frequency of the collapsed wall under free boundary conditions and the vibration differential equations, and constructing an analytical formula for the fundamental frequency of the collapsed wall under these conditions; and combining the angular frequency analytical formula, the fundamental frequency estimation formula, and the fundamental frequency analytical formula to obtain the estimation results of the natural frequencies (fundamental frequencies) of the collapsed walls in stacked buildings under different boundary conditions. This invention provides technical support for estimating the natural frequencies of collapsed building components.

Description

Technical Field

[0001] This invention relates to the field of mechanical technology, specifically to a method for estimating the natural frequency of collapsed walls in stacked buildings under different boundary conditions. Background Technology

[0002] In building collapse accidents, the extremely poor structural stability of the collapsed walls not only severely hinders rescue efforts but also threatens the lives of firefighters. Currently, the demolition of collapsed building rubble mainly uses rapid demolition and safe demolition methods. In actual rescue operations, high-frequency vibrations are generated when breaking, digging, and cutting building components. When the vibration frequency of the excitation force is in the range of 0.7 to 1.3 times the natural frequency of the component, resonance will occur. Once the rescue operation resonates with the collapsed building components, it will severely damage the stability of the components and easily cause secondary collapse accidents.

[0003] Among common types of building collapses and burials, stacked building structures have unique structural characteristics. Their supports exist only in the vertical direction, making them highly susceptible to slippage during rescue operations, further increasing the difficulty and risk of rescue efforts. Therefore, it is particularly urgent and important to develop a method for estimating the natural frequencies of stacked building components (such as walls). Accurate estimation of the natural frequencies of these components can effectively avoid resonant frequency ranges, significantly reducing the probability of resonance and providing strong assurance for the safety of rescue operations.

[0004] Currently, there is limited research on estimating the natural frequencies of building components in building collapse scenarios. To accurately estimate the natural frequencies of collapsed components in stacked buildings under different boundary conditions, it is necessary to comprehensively consider both simply supported boundary conditions and free boundary conditions. Estimating and analyzing the natural frequencies of building walls will not only help to more comprehensively understand the vibration characteristics of collapsed building components, but also further reveal the influence of changes in the size of collapsed building components on their natural frequencies, providing more scientific and accurate support for building collapse rescue work. Summary of the Invention

[0005] To address the shortcomings of existing methods and their limitations in practical application, this invention aims to more accurately estimate the natural frequencies of collapsed components in stacked buildings under different boundary conditions. Based on scenarios such as simply supported and free boundaries, the natural frequencies of building walls are estimated and analyzed. Furthermore, the influence of changes in the dimensions of collapsed components on the natural frequencies of collapsed walls in stacked buildings is analyzed. In a first aspect, this invention provides a method for estimating the natural frequencies of collapsed walls in stacked buildings under different boundary conditions. The method includes the following steps: constructing a simplified model of the collapsed wall; obtaining the vibration differential equation of the building component wall based on the simplified model; setting simply supported boundary conditions; deriving the natural frequency expression of the collapsed wall under simply supported conditions based on the simply supported boundary conditions and the vibration differential equation; and establishing the natural frequency expression of the collapsed wall under simply supported conditions based on the natural frequency expression. The formula for estimating the fundamental frequency of a building wall is as follows: A four-sided free boundary condition is set, and the natural frequency calculation formula for the collapsed wall of a stacked building under the four-sided free condition is obtained based on the four-sided free boundary condition and the vibration differential equation. Based on the natural frequency calculation formula for the collapsed wall of the stacked building, the fundamental frequency analysis formula for the collapsed wall under the four-sided free condition is constructed. An angular frequency analysis formula is introduced, and the natural frequency (fundamental frequency) estimation results of the collapsed wall of a stacked building under different boundary conditions are obtained through the angular frequency analysis formula, the fundamental frequency estimation formula for the collapsed wall, and the fundamental frequency analysis formula for the collapsed wall.

[0006] This invention provides a method for estimating the natural frequencies of collapsed walls in stacked buildings. It combines model construction, boundary condition setting, equation derivation, and natural frequency calculation, making the method adaptable to different rescue scenarios and providing information reference for rescue work.

[0007] Optionally, the step of constructing a simplified model of a collapsed building wall and obtaining the vibration differential equation of the building component wall based on the simplified model includes: setting parameter information for an elastic rectangular thin plate; constructing a simplified model of a collapsed building wall based on the parameter information of the elastic rectangular thin plate; analyzing the equation parameter information based on the simplified model of the collapsed building wall; introducing thin plate small deflection theory information; and obtaining the vibration differential equation of the building component wall based on the equation parameter information and the thin plate small deflection theory information.

[0008] This invention constructs a simplified model of a collapsed building wall based on the parameter information of an elastic rectangular thin plate, abstracting the complex collapsed wall into an elastic rectangular thin plate model, making the model more practical and operable.

[0009] Optionally, the step of setting simply supported boundary conditions on four sides and deriving the natural frequency expression of the collapsed wall of a stacked building under simply supported boundary conditions and the vibration differential equation includes: setting the solution expression of the vibration differential equation under simply supported boundary conditions; substituting the solution expression of the vibration differential equation under simply supported boundary conditions into the vibration differential equation to obtain the solution equation for the vibration characteristics of the thin plate under simply supported boundary conditions; obtaining the natural frequency differential equation of the collapsed wall of a stacked building under simply supported boundary conditions based on the solution equation for the vibration characteristics of the thin plate; and obtaining the natural frequency expression of the collapsed wall of a stacked building under simply supported boundary conditions based on the natural frequency differential equation.

[0010] The derivation process of the method of this invention is logically rigorous and interconnected, with each step having a clear mathematical basis and physical meaning, which further ensures the accuracy and feasibility of the inherent frequency expression.

[0011] Optionally, obtaining the vibration differential equation of the collapsed wall of a stacked building under simply supported conditions based on the solution equation of the thin plate vibration characteristics includes: setting a thin plate vibration characteristic parameter function based on the solution equation of the thin plate vibration characteristics; and performing a transformation analysis on the solution equation of the thin plate vibration characteristics based on the thin plate vibration characteristic parameter function to obtain the natural frequency differential equation of the collapsed wall of the stacked building under simply supported conditions.

[0012] The natural frequency differential equation satisfies the following relationship:

[0013] ,

[0014] in, Let be the displacement function of the panel in the vertical direction. These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. Solve the equations for the vibration characteristics of the thin plate.

[0015] This invention fully considers the influence of various factors on vibration, ensuring that the natural frequency differential equation can accurately reflect the vibration characteristics of the collapsed wall of a stacked building under simply supported conditions.

[0016] Optionally, obtaining the natural frequency expression of the collapsed wall of a stacked building under the condition of simply supported quadrilaterals based on the natural frequency differential equation includes: setting the mode shape function based on bitrigonometric functions; substituting the mode shape function into the natural frequency differential equation for analysis to obtain the natural frequency expression of the collapsed wall of the stacked building under the condition of simply supported quadrilaterals; the natural frequency expression of the collapsed wall of the stacked building under the condition of simply supported quadrilaterals satisfies the following relationship:

[0017] ,

[0018] in, The natural frequency of the wall under simply supported conditions is given. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, During the vibration of the rectangular wall Half-wave number in the direction, Pi The length of the wall. During the vibration of the rectangular wall Half-wave number in the direction, The width of the wall. This is the foundation reaction modulus.

[0019] Under the simply supported boundary, the displacement and rotation of the wall edge are zero. The double trigonometric function of this invention can well satisfy the relevant boundary constraints, thus more accurately reflecting the actual shape of the wall during vibration, laying the foundation for the subsequent analysis and derivation of the natural frequency expression.

[0020] Optionally, the step of establishing the fundamental frequency estimation formula for the collapsed wall under the condition of simply supported four sides based on the natural frequency expression of the collapsed wall of the stacked building includes: introducing the bending stiffness of the wall; and establishing the fundamental frequency estimation formula for the collapsed wall under the condition of simply supported four sides based on the bending stiffness of the wall and the natural frequency expression of the collapsed wall of the stacked building.

[0021] The formula for estimating the fundamental frequency of a collapsed wall under simply supported conditions satisfies the following relationship:

[0022] ,

[0023] in, The results show the estimated natural frequencies of the wall under simply supported conditions. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. This is the foundation reaction modulus.

[0024] This invention is derived based on the expressions for the bending stiffness of walls and the natural frequency of collapsed walls in stacked buildings, which helps to ensure the correctness and reliability of the formulas.

[0025] Optionally, the step of setting four-sided free boundary conditions and obtaining the natural frequency calculation formula for the collapsed wall of a stacked building under four-sided free conditions based on the four-sided free boundary conditions and the vibration differential equation includes: deforming the vibration differential equation based on the four-sided free boundary conditions to obtain the natural frequency differential equation of the building component wall; constructing an approximate solution to the natural frequency differential equation according to the Galerkin method and obtaining an approximate mode shape function; obtaining the analysis equation for undetermined coefficients based on the natural frequency differential equation and the approximate mode shape function; and obtaining the natural frequency calculation formula for the collapsed wall of a stacked building under four-sided free conditions based on the solution equation for thin plate vibration characteristics and the analysis equation for undetermined coefficients.

[0026] This invention constructs an approximate solution to the differential equation of natural frequency based on the Galerkin method and obtains an approximate mode shape function. This allows for a more scientific and reasonable acquisition of the approximate mode shape function, providing a computational basis for subsequent solutions to the natural frequency.

[0027] Optionally, the natural frequency differential equation satisfies the following relationship:

[0028] ,

[0029] in, For the bending stiffness of the collapsing wall, It is an approximate mode shape function. For wall density, For wall thickness, For the natural frequency, This is the foundation reaction modulus.

[0030] The approximate mode shape function satisfies the following relationship:

[0031] ,

[0032] in, It is an approximate mode shape function. The first undetermined coefficient, The second undetermined coefficient, The parameter representing the influence of the half-wave number in the x-direction during the vibration of a rectangular wall is... The parameter representing the influence of the half-wave number in the y-direction during the vibration of a rectangular wall. These are the coordinate values ​​of the lateral displacement of the collapsed wall. Poisson's ratio, The length of the wall. These are the coordinate values ​​of the lateral displacement of the collapsed wall.

[0033] The formula for calculating the natural frequency of the collapsed wall of a stacked building under the condition of free quadrilaterals satisfies the following relationship:

[0034] ,

[0035] in, The result is the fundamental frequency calculation under the condition of a four-sided free boundary. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, It is a combined influencing factor of vibration mode and material Poisson's ratio. This is a balance factor between vibration correction and material properties. For the foundation reaction modulus, The compressive resilience modulus of the wall. Poisson's ratio, During the vibration of the rectangular wall Half-wave number in the direction, During the vibration of the rectangular wall Half-wave number in the direction.

[0036] The calculation results of this invention are closer to the actual natural frequency of the wall, reducing the calculation errors caused by model simplification or parameter neglect, and providing a more reliable information basis for decision analysis.

[0037] Optionally, constructing the fundamental frequency analysis formula for the collapsed wall under four-sided free conditions based on the natural frequency calculation formula of the collapsed wall of the stacked building includes: setting the fundamental frequency of the collapsed wall based on the four-sided free boundary conditions; and establishing the fundamental frequency analysis formula for the collapsed wall under four-sided free conditions based on the fundamental frequency of the collapsed wall and the natural frequency calculation formula of the collapsed wall of the stacked building. The fundamental frequency analysis formula of this invention comprehensively considers the influence of different boundary conditions, making the analysis results more consistent with the stress state and vibration characteristics of the collapsed wall in actual engineering, and enabling a more accurate analysis of the vibration behavior of the wall under four-sided free conditions.

[0038] Optionally, the step of constructing the fundamental frequency analysis formula for the collapsed wall under the condition of four-sided freedom based on the natural frequency calculation formula of the collapsed wall of the stacked building includes: the fundamental frequency analysis formula for the collapsed wall under the condition of four-sided freedom satisfies the following relationship:

[0039] ,

[0040] in, The results are the fundamental frequency analysis under the condition of four-sided free boundary. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. This refers to the foundation reaction modulus. This invention integrates wall geometric parameters, material properties, and boundary conditions into a single expression, avoiding redundant modeling of complex finite element models and providing a basis for analyzing the dynamic performance indicators of walls. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to the present invention.

[0042] Figure 2 This is a simplified model diagram of the collapsed wall structure of the present invention;

[0043] Figure 3 This is a schematic diagram showing the estimation results of the natural frequency (fundamental frequency) under the simply supported boundary conditions with a fixed thickness in this invention.

[0044] Figure 4 This is a schematic diagram showing the estimation results of the natural frequency (fundamental frequency) under the simply supported boundary conditions with a fixed length in this invention.

[0045] Figure 5 This is a schematic diagram showing the natural frequency (fundamental frequency) results under the four-sided free boundary conditions when the thickness is fixed according to the present invention;

[0046] Figure 6 This is a schematic diagram showing the estimation results of the natural frequency (fundamental frequency) under the four-sided free boundary conditions with a fixed length according to the present invention. Detailed Implementation

[0047] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0048] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0049] Please see Figure 1 To accurately estimate the natural frequencies of collapsed components in stacked buildings under different boundary conditions, and to deeply analyze the impact of changes in the dimensions of collapsed components on the natural frequencies of collapsed walls in stacked buildings, this invention helps to avoid resonant frequency ranges, reduce resonance, and ensure rescue safety during rescue operations. The invention provides a method for estimating the natural frequencies of collapsed walls in stacked buildings under different boundary conditions. This method includes the following steps:

[0050] S1. To effectively analyze the motion characteristics of collapsed building walls under stress and better apply them to practical scenarios such as fire rescue, this embodiment constructs a simplified model of collapsed building walls and derives the vibration differential equations of the building component walls based on this model. The specific implementation details are as follows:

[0051] The first step is to set the parameter information of the elastic rectangular thin plate and construct a simplified model of the collapsed building wall based on the parameter information of the elastic rectangular thin plate.

[0052] This embodiment considers that in building collapse scenarios, the layered building collapse model has the highest risk of slippage, and that during rescue operations, external loads mainly cause the building collapse frame to bend and deform vertically. Therefore, to better reflect the actual situation of fire rescue, this embodiment simplifies the building collapse wall into an elastic rectangular thin plate with length 'a', width 'b', thickness 'h', and density 'ρ'. A simplified building collapse wall model is constructed using the center of the simplified rectangular plate as the coordinate origin. Please refer to the schematic diagram of the model. Figure 2 Where xyz represents the model coordinate system, b represents the model width, and h represents the model thickness, this model can be used to simulate the motion characteristics of a building wall when it is subjected to load on the load-bearing surface, undergoing bending deformation and periodic vibration at the original equilibrium position. Compared with the theoretical boundary condition models in the existing technology, the simplified model of the collapsed building wall constructed in this embodiment is more targeted and can be better applied to actual rescue scenarios.

[0053] The second step involved analyzing and deriving the equation parameters based on the simplified model of the collapsed building wall. The specific parameter information is as follows:

[0054] Bending stiffness This refers to the bending stiffness of a collapsed wall, which reflects the wall's ability to resist bending deformation. The expression is: ,in, For the bending stiffness of the collapsing wall, The compressive resilience modulus of the wall. For wall thickness, It is Poisson's ratio.

[0055] Displacement function This refers to the vertical displacement of the panel using a function. The expression for this is as follows: ,in, Let be the displacement function of the panel in the vertical direction. These are the coordinate values ​​of the lateral displacement of the collapsed building wall. These are the coordinate values ​​of the lateral displacement of the collapsed building wall. For time.

[0056] Laplace operator It is mainly used to describe the operation of the second derivative in space, and its expression is as follows: ,in, For the Laplace operator, The second derivative with respect to the x-direction, Let be the second derivative with respect to the y-direction.

[0057] Foundation reaction modulus It is one of the key parameters in the model. Since the bottom of the collapsed wall needs support, the foundation response modulus can reflect the supporting effect of the foundation on the collapsed wall. If the influence of the foundation response modulus on the model is not considered, the model elements will be incomplete and thus unable to fully reflect the real situation.

[0058] The third step involves introducing theoretical information on small deflection of thin plates.

[0059] The thin-plate small deflection theory is an important theory for analyzing the mechanical behavior of thin plates under relatively small deflections. In this embodiment, the thin-plate small deflection theory is introduced to provide a theoretical basis for the subsequent derivation of the vibration differential equations of building component walls. This theory assumes that the deflection of the thin plate is much smaller than its thickness. Under this assumption, the mechanical analysis of the thin plate can be further simplified by ignoring some higher-order small quantities, thus obtaining a simpler and more practical simplified model of a collapsed building wall.

[0060] The fourth step is to obtain the vibration differential equation of the building component wall based on the equation parameter information and the thin plate small deflection theory information.

[0061] Based on the above equation parameter information and the thin plate small deflection theory, a vibration differential equation for the building component wall was established. This equation can describe the vibration characteristics of the building component wall under stress, and its expression is as follows:

[0062] ,

[0063] in, For the bending stiffness of the collapsing wall, For the Laplace operator, Let be the displacement function of the panel in the vertical direction. For the foundation reaction modulus, For wall density, For wall thickness, Let be the second reciprocal of the vertical displacement function of the panel with respect to time.

[0064] This embodiment constructs a simplified model of a collapsed building wall based on the above steps and derives the vibration differential equation of the building component wall, providing a theoretical basis for further research on the dynamic characteristics of collapsed building walls.

[0065] S2. Set the four-sided simply supported boundary conditions. Based on the above four-sided simply supported boundary conditions and vibration differential equations, derive the natural frequency expression of the collapsed wall of the stacked building under the four-sided simply supported condition. Based on the natural frequency expression of the collapsed wall of the stacked building, establish the fundamental frequency estimation formula of the collapsed wall under the four-sided simply supported condition. The implementation content is as follows:

[0066] To investigate the vibration characteristics of the collapsed walls of a stacked building under simply supported conditions, it is first necessary to derive the natural frequency expression of the collapsed walls under these conditions. The relevant steps are as follows:

[0067] The first step is to define the solution expression for the vibration differential equation under the condition of simple support on four sides.

[0068] In analyzing the vibration problem of a collapsed building wall, the separation of variables method was used in this embodiment to solve the vibration differential equation of the building component wall. For the specific boundary condition of simply supported on four sides, the displacement function of the wall in the vertical direction was set. That is, the solution of the vibration differential equation under the condition of simply supported on four sides satisfies the following relationship:

[0069] ,

[0070] in, Let be the displacement function of the panel in the vertical direction. Let be the displacement function of the wall in the vertical direction. Let x be the coordinate value of the lateral displacement of the collapsed wall, and let x be the coordinate value of the longitudinal displacement of the collapsed wall. A function of time t These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. For time, As the natural frequency, the complex time-varying displacement problem can be transformed into a function of the spatial displacement amplitude using the above setting. Solving this problem lays the foundation for subsequent analysis.

[0071] The second step is to substitute the solution expression of the vibration differential equation under the condition of simple support on four sides into the vibration differential equation to obtain the solution equation of the vibration characteristics of the thin plate under the condition of simple support on four sides.

[0072] Substituting the solution expression of the vibration differential equation under the condition of simply supported four sides into the vibration differential equation of the building component wall, and after a series of mathematical operations and simplifications, the solution equation for the vibration characteristics of the thin plate under the condition of simply supported four sides can be obtained, which satisfies the following relationship:

[0073] ,

[0074] in, Let be the displacement function of the panel in the vertical direction. These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. For the foundation reaction modulus, For the bending stiffness of the collapsing wall, The density of the collapsed wall For wall thickness, The natural frequency. The equation for solving the vibration characteristics of a thin plate can describe the displacement amplitude function when the thin plate vibrates under simply supported conditions. The relationships that should be satisfied.

[0075] The third step is to solve the equations based on the vibration characteristics of thin plates to obtain the natural frequency differential equations of the collapsed walls of a stacked building under simply supported conditions.

[0076] To simplify the equations for solving the vibration characteristics of thin plates, this embodiment is based on the equations for solving the vibration characteristics of thin plates.

[0077] The characteristic parameter function for the vibration of the thin plate is set, and it satisfies the following relationship:

[0078] ,

[0079] in, For the characteristic parameter function of thin plate vibration, For the foundation reaction modulus, The density of the collapsed wall For wall thickness, For the natural frequency, This represents the bending stiffness of the collapsed wall. This parametric function integrates multiple parameters in the equation, which facilitates subsequent equation transformation and derivation analysis.

[0080] Furthermore, by solving the equations for the vibration characteristics of thin plates based on the characteristic parameter functions of thin plate vibration, and through mathematical transformation and simplification, the natural frequency differential equations of the collapsed walls of a stacked building under simply supported conditions can be obtained.

[0081] The above natural frequency differential equation satisfies the following relationship:

[0082] ,

[0083] in, Let be the displacement function of the panel in the vertical direction. These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. The equations for solving the vibration characteristics of thin plates are provided. These equations help to further clarify the relationship between the vibration displacement amplitude function and characteristic parameters of thin plates under simply supported conditions, and provide a key basis for subsequent solutions to the natural frequencies.

[0084] The fourth step is to obtain the expression for the natural frequency of the collapsed wall of a stacked building under the condition of simply supported sides, based on the natural frequency differential equation.

[0085] Based on the characteristics of the simply supported boundary conditions, the embodiment uses bitrigonometric functions to represent the mode shape functions, which satisfy the following relationship:

[0086] ,

[0087] in, For mode shape function, During the vibration of the rectangular wall Half-wave number in the direction, During the vibration of the rectangular wall Half-wave number in the direction, For undetermined constants, These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. This represents the length of the collapsed wall. Let be the width of the collapsed wall. The mode shape function in the form of a bitrigonometric function can well satisfy the simply supported boundary conditions, i.e., when... and hour .

[0088] Substituting the above mode shape function into the natural frequency differential equation, and utilizing the orthogonality and other mathematical properties of trigonometric functions, through a series of mathematical derivations and simplifications, we can obtain the natural frequency expression for the collapsed wall of a stacked building under the condition of simply supported sides, which satisfies the following relationship:

[0089] ,

[0090] in, The natural frequency of the wall under simply supported conditions is given. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, During the vibration of the rectangular wall Half-wave number in the direction, Pi The length of the wall. During the vibration of the rectangular wall Half-wave number in the direction, The width of the wall. The above expression effectively reveals the relationship between the natural frequency and the geometric parameters, material parameters, and foundation parameters of the wall, providing technical support and theoretical basis for analyzing and predicting the vibration characteristics of collapsed walls in multi-tiered buildings under quadrilateral conditions.

[0091] Then, based on the expression of the natural frequency of the collapsed wall of the stacked building, a formula for estimating the fundamental frequency of the collapsed wall under the condition of simply supported four sides is established, which is helpful to quickly determine whether external loads will cause structural resonance.

[0092] The first step is to introduce the wall bending stiffness. Wall bending stiffness is an important parameter describing the wall's ability to resist bending deformation, and its calculation formula is as follows:

[0093] ,

[0094] in, For the bending stiffness of the collapsing wall, The compressive resilience modulus of the wall. For wall thickness, Poisson's ratio is the ratio of transverse strain to longitudinal strain in a wall under stress. The wall's compressive resilience modulus reflects its ability to return to its original shape after being compressed. This formula clearly shows that the wall's bending stiffness is directly proportional to the cube of the wall's compressive resilience modulus and wall thickness, and inversely proportional to 1 minus the square of Poisson's ratio.

[0095] The second step is to establish a formula for estimating the fundamental frequency of a collapsed wall under simply supported conditions, based on the wall bending stiffness and the natural frequency expression of the collapsed wall in a stacked building.

[0096] The expression for the natural frequencies of the collapsing walls of a stacked building under simply supported conditions is given by: Increase the bending stiffness of the wall Substituting the natural frequency expression of the collapsed walls of the above-mentioned layered building, after mathematical calculation and simplification, we can obtain:

[0097] ,

[0098] in, The natural frequency of the wall. The compressive resilience modulus of the wall. For wall thickness, For wall density, Poisson's ratio, During the vibration of the rectangular wall Half-wave number in the direction, The length of the wall. During the vibration of the rectangular wall Half-wave number in the direction, The width of the wall. The formula for the foundation response modulus takes into account the influence of wall material properties, geometric dimensions, and foundation conditions on the natural frequency.

[0099] According to vibration theory, continuous structural members have multiple natural frequencies. When the frequency of an applied dynamic load approaches any of the structure's natural frequencies, resonance may occur. To quickly predict whether a load will cause structural resonance, we can first determine whether the vibration frequency of the external load is close to the structure's lowest natural frequency.

[0100] In the vibration of a rectangular wall, when and When the frequency is such that the corresponding natural frequency is the lowest natural frequency of the structure, i.e., the fundamental frequency. Substituting into the above derived expression, we can obtain the formula for estimating the fundamental frequency of a collapsed wall under the condition of simply supported sides.

[0101] The formula for estimating the fundamental frequency of a collapsed wall under the above simply supported four-sided condition satisfies the following relationship:

[0102] ,

[0103] in, The results show the estimated natural frequencies of the wall under simply supported conditions. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. The fundamental frequency of the collapsed wall is the ground response modulus. This formula for estimating the fundamental frequency of a collapsed wall can quickly assess the resonance risk of a collapsed wall in a stacked building under simply supported conditions. By calculating the fundamental frequency and comparing it with the external load frequency, it is possible to preliminarily determine whether the structure will resonate, providing an important reference and analytical basis for structural safety assessment in engineering practice.

[0104] S3. Set up four-sided free boundary conditions. Based on the above four-sided free boundary conditions and vibration differential equations, obtain the calculation formula for the natural frequency of the collapsed wall of the stacked building under four-sided free conditions. Then, construct the fundamental frequency analysis formula for the collapsed wall under four-sided free conditions based on the calculation formula for the natural frequency of the collapsed wall of the stacked building. The implementation content is as follows:

[0105] First, a four-sided free boundary condition is set, and the natural frequency calculation formula of the collapsed wall of the stacked building under the four-sided free condition is obtained based on the four-sided free boundary condition and the vibration differential equation. This is helpful for subsequent wall vibration behavior analysis and structural safety assessment.

[0106] The first step is to deform the vibration differential equation based on the four-sided free boundary conditions to obtain the natural frequency differential equation of the building component wall.

[0107] The above natural frequency differential equation satisfies the following relationship:

[0108] ,

[0109] in, For the bending stiffness of the collapsing wall, It is an approximate mode shape function. For wall density, For wall thickness, For the natural frequency, This is the foundation reaction modulus.

[0110] The second step is to construct an approximate solution to the differential equation of the natural frequency based on the Galerkin method, and to obtain the approximate mode shape function.

[0111] In this embodiment, to solve the above vibration differential equation, the Galerkin method is used to select an approximate mode shape function, which satisfies the following relationship:

[0112] ,

[0113] in, It is an approximate mode shape function. The first undetermined coefficient, The second undetermined coefficient, The parameter representing the influence of the half-wave number in the x-direction during the vibration of a rectangular wall is... The parameter representing the influence of the half-wave number in the y-direction during the vibration of a rectangular wall. These are the coordinate values ​​of the lateral displacement of the collapsed wall. Poisson's ratio, The length of the wall. These are the coordinates of the lateral displacement of the collapsed wall.

[0114] The third step is to obtain the analysis equation for the undetermined coefficients based on the natural frequency differential equation and the approximate mode shape function.

[0115] The residual values ​​of the approximate deflection function, generated by the selection of the approximate mode shape function based on the Galerkin method, are eliminated so that the weighted integral of the residual values ​​over the entire wall area is zero, thereby obtaining the approximate deflection function residuals. and Two equations with undetermined coefficients, satisfying the following relationship:

[0116] ,

[0117] in, The first undetermined coefficient, The length of the wall. The width of the wall. For the characteristic parameter function of thin plate vibration, The second undetermined coefficient, Poisson's ratio, The parameter representing the influence of the half-wave number in the y-direction during the vibration of a rectangular wall. The parameter represents the influence of the half-wave number in the x-direction during the vibration of a rectangular wall.

[0118] At the same time, another information about and The equation is expressed as follows:

[0119] ,

[0120] in, The first undetermined coefficient, The length of the wall. The width of the wall. For Poisson's ratio, The parameters representing the influence of the half-wave number in the x-direction during the vibration of a rectangular wall are as follows. During the vibration of the rectangular wall Half-wave number in the direction, The length of the wall. Pi The parameter representing the influence of the half-wave number in the y-direction during the vibration of a rectangular wall. During the vibration of the rectangular wall Half-wave number in the direction, The width of the wall. Pi is the mathematical constant of a circle.

[0121] The fourth step is to obtain the formula for calculating the natural frequency of the collapsed wall of a stacked building under four-sided free conditions by solving the equations based on the vibration characteristics of the thin plate and the analysis equations for undetermined coefficients.

[0122] Because the characteristic parameter function of thin plate vibration satisfies the following relationship: In order to make the above angular frequency analysis formula It is not always 0, therefore, according to the differential equation of the natural frequency... and approximate mode shape function The determinant of the coefficient matrix of the equation is 0. Further calculations show that:

[0123] middle The combined influence factor of vibration mode and material Poisson's ratio satisfies the following relationship:

[0124] ,

[0125] middle The balance factor between vibration correction and material properties satisfies the following relationship:

[0126] ,

[0127] Immediately afterwards, Substitute into the characteristic parameter function of thin plate vibration From this, we can obtain the formula for calculating the natural frequency of the collapsing wall of a stacked building under the condition of four-sided freedom, and it satisfies the following relationship:

[0128] ,

[0129] in, The results are the natural frequencies calculated under the condition of a four-sided free boundary. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, It is a combined influencing factor of vibration mode and material Poisson's ratio. This is a balance factor between vibration correction and material properties. For the foundation reaction modulus, The compressive resilience modulus of the wall. Poisson's ratio, During the vibration of the rectangular wall Half-wave number in the direction, During the vibration of the rectangular wall Half-wave number in the direction.

[0130] Through the above analysis and derivation, we can obtain the calculation formula for the natural frequency of the collapsed wall of a stacked building under four-sided free conditions, which provides a theoretical basis and analytical formula for further analysis of the vibration characteristics and structural safety of the wall.

[0131] Then, based on the calculation formula of the natural frequency of the collapsed wall of the stacked building, the fundamental frequency analysis formula of the collapsed wall under the condition of free four sides is constructed.

[0132] The first step is to determine the natural frequencies of the collapsed building walls based on the four-sided free boundary condition. In this embodiment, the natural frequency analysis of the collapsed building walls under the four-sided free boundary condition is performed. Calculating the natural frequencies of the walls under this condition is the core objective, laying the foundation for the subsequent establishment of the analytical formula.

[0133] The second step, based on the calculation formula for the natural frequency of collapsed walls in a stacked building, and considering the characteristics of the four-sided free boundary conditions in the natural frequency of collapsed walls, derives the fundamental frequency analysis formula for collapsed walls under four-sided free conditions, which satisfies the following relationship:

[0134] ,

[0135] in, The results are the fundamental frequency analysis under the condition of four-sided free boundary. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. This represents the foundation response modulus. Through the above steps, the fundamental frequency of a collapsing building wall under four-sided free conditions can be calculated based on the fundamental frequency analysis formula, thereby effectively assessing the possibility of structural resonance caused by external loads.

[0136] S4. Introducing the angular frequency analysis formula: Through the above angular frequency analysis formula, the formula for estimating the fundamental frequency of collapsed walls, and the formula for analyzing the fundamental frequency of collapsed walls, the natural frequency (fundamental frequency) estimation results of collapsed walls in stacked buildings under different boundary conditions can be obtained. The implementation details are as follows:

[0137] In actual building collapse scenarios, the density of the collapsed building wall components... Compressive resilience modulus Poisson's ratio and foundation reaction modulus The parameters are relatively stable and can be queried based on relevant reliable data. Therefore, in this embodiment, by changing the structural dimensions, the variation law of the natural frequency (fundamental frequency) of the collapsed wall of the building under different boundary conditions can be estimated. This can provide technical support for quickly estimating the natural frequency (fundamental frequency) of the collapsed wall of the building during actual rescue operations, helping rescuers avoid unnecessary resonance risks. At the same time, the principle of resonance can be fully utilized to carry out demolition rescue, which has important practical application value.

[0138] In one optional embodiment, the analysis and calculation are performed, and the parameter values ​​are set to satisfy the following condition: wall density. Compressive resilience modulus Poisson's ratio Foundation reaction modulus Wall width Furthermore, five different values ​​for the length and thickness of the collapsed wall were selected for calculation and analysis, as detailed below:

[0139] The lengths of the collapsed walls are 5m, 10m, 15m, 20m, and 25m.

[0140] The thickness of the collapsed wall is taken as 0.10m, 0.15m, 0.20m, 0.25m, and 0.30m.

[0141] I. Analysis of Natural Frequency (Fundamental Frequency) Estimation Results under Four-sided Simply Supported Boundary Conditions

[0142] Under the boundary condition of simply supported sides, the fundamental frequency estimation formula for the collapsed wall under simply supported sides is used for calculation. Angular frequency analysis is introduced in the calculation process. The natural frequency (fundamental frequency) is estimated using the formula for estimating the fundamental frequency of a collapsed wall under simply supported conditions (presented in angular frequency form). Then, the calculation result is converted into frequency form based on the angular frequency analysis formula, finally yielding the estimated natural frequency (fundamental frequency). The estimated natural frequency (fundamental frequency) under simply supported conditions is also plotted as a curve. Please refer to [link to relevant documentation] for details. Figure 3 and Figure 4 .

[0143] Figure 3 This is the estimation result of the natural frequency (fundamental frequency) under the condition of simply supported four sides with a fixed thickness. Based on Figure 3 It can be seen that when the thickness of the collapsed wall remains constant, the influence of changes in length on the natural frequency (fundamental frequency) of the wall exhibits obvious stage characteristics. In the range where the wall length is less than 10m, the natural frequency (fundamental frequency) decreases significantly as the wall length gradually increases. However, when the wall length exceeds 10m, further changes in length have a relatively small impact on the natural frequency (fundamental frequency), and the natural frequency (fundamental frequency) tends to stabilize. This indicates that within a shorter length range, the length factor plays a dominant role in the natural frequency (fundamental frequency), while when the length reaches a certain level, the influence of other factors on the natural frequency (fundamental frequency) gradually becomes more prominent.

[0144] Figure 4 The natural frequency (fundamental frequency) estimation result under the condition of simply supported quadrilaterals with fixed length is based on... Figure 4 It can be seen that, with a fixed wall length in case of building collapse, the effect of changes in wall thickness on the wall's natural frequency also exhibits a phased effect. When the wall length is 5m, as the wall thickness increases, the natural frequency (fundamental frequency) first decreases significantly, reaches a minimum point, and then increases significantly, showing a trend of first decreasing and then increasing. When the wall length is greater than 10m, as the thickness increases, the natural frequency (fundamental frequency) first decreases significantly, especially within the thickness range of 0.1-0.2m, where the decrease in natural frequency (fundamental frequency) is more pronounced. This indicates that the influence of thickness on natural frequency (fundamental frequency) differs under different length conditions, and that at specific lengths, the effect of thickness on natural frequency (fundamental frequency) is more sensitive.

[0145] II. Analysis of Natural Frequency (Fundamental Frequency) Estimation Results under Quadrilateral Free Boundary Conditions

[0146] Under the condition of a four-sided free boundary, the fundamental frequency analysis and angular frequency analysis of the collapsed wall under four-sided free boundary conditions are used. The analysis and calculation process requires presenting the results of the fundamental frequency analysis of the collapsed wall under four-sided free conditions in the form of angular frequencies to obtain the final natural frequency (fundamental frequency) analysis value. In this embodiment, the analysis results are converted into frequency form using angular frequency analysis to obtain the estimated natural frequency (fundamental frequency). The estimated natural frequency (fundamental frequency) under four-sided free boundary conditions is also plotted as a curve diagram. Please refer to [link to relevant documentation] for details. Figure 5 and Figure 6 .

[0147] Figure 5 The natural frequency (fundamental frequency) estimation result under the condition of free boundary on four sides with fixed thickness is obtained from... Figure 5 It can be seen that, when the wall thickness is fixed during building collapse, the effect of changes in length on the wall's natural frequency (fundamental frequency) is similar to that under simply supported boundary conditions, exhibiting a phased characteristic. When the length is less than 10m, the natural frequency (fundamental frequency) decreases significantly with increasing length; when the length exceeds 10m, the effect of length changes on the natural frequency (fundamental frequency) is relatively small, and the change in natural frequency (fundamental frequency) tends to be gradual. This indicates that, under four-sided free boundary conditions, the influence of length on the natural frequency (fundamental frequency) has a certain similarity to that under four-sided simply supported boundary conditions within a specific length range.

[0148] Figure 6 The natural frequency (fundamental frequency) estimation results are based on the condition of a free boundary with four sides and a fixed length. Figure 6 It can be seen that when the length of the collapsed wall is fixed, the effect of changes in thickness on the wall's natural frequency (fundamental frequency) also exhibits a phased effect. When the wall length is 5m, the natural frequency (fundamental frequency) first decreases significantly and then increases significantly with increasing thickness; when the wall length is greater than 10m, the natural frequency (fundamental frequency) first decreases significantly with increasing thickness. Compared with the simply supported boundary condition, the influence of thickness on the natural frequency (fundamental frequency) under the free boundary condition is similar in overall trend, but there are certain differences in specific values ​​and amplitudes of change.

[0149] III. A comprehensive comparative analysis of the natural frequency (fundamental frequency) analysis results of building collapse walls under different boundary conditions is conducted.

[0150] By comparing the natural frequency (fundamental frequency) estimation results under four-sided free boundary conditions and four-sided simply supported boundary conditions, it can be seen that the change in structural dimensions has a more significant impact on the natural frequency (fundamental frequency) under four-sided free boundary conditions. This means that the vibration characteristics of a collapsed building wall differ significantly under different boundary conditions. In actual rescue operations, it is necessary to fully consider the influence of boundary conditions on the wall's natural frequency (fundamental frequency) in order to more accurately assess the vibration risk of the structure and formulate a scientifically sound rescue plan.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for estimating the natural frequency of a stacked building collapse wall under different boundary conditions, characterized by, Includes the following steps: A simplified model of a collapsed building wall is constructed, and the vibration differential equation of the building component wall is obtained based on the simplified model of the collapsed building wall; Set up four-sided simply supported boundary conditions, and derive the natural frequency expression of the collapsed wall of the stacked building under the four-sided simply supported condition based on the four-sided simply supported boundary conditions and the vibration differential equation. Based on the natural frequency expression of the collapsed wall of the stacked building, establish the fundamental frequency estimation formula of the collapsed wall under the four-sided simply supported condition. Set up four-sided free boundary conditions, and obtain the natural frequency calculation formula of the collapsed wall of the stacked building under the four-sided free conditions based on the four-sided free boundary conditions and the vibration differential equation. Construct the fundamental frequency analysis formula of the collapsed wall under the four-sided free conditions based on the natural frequency calculation formula of the collapsed wall of the stacked building. By introducing an angular frequency analysis formula, the natural frequency estimation results of the collapsed wall of a stacked building under different boundary conditions are obtained through the angular frequency analysis formula, the fundamental frequency estimation formula of the collapsed wall, and the fundamental frequency analysis formula of the collapsed wall. The natural frequency estimates are obtained under both simply supported and free boundary conditions with four sides using the aforementioned angular frequency analysis formula. The angular frequency analysis expression satisfies the following relationship: ， wherein is the eigenfrequency estimate, is the fundamental frequency analysis result for a four-sided free boundary condition, is the ratio of the circumference to the diameter.

2. The method of claim 1, wherein, The construction of a simplified model of a collapsed building wall, and the obtaining of the vibration differential equations of the building component wall based on the simplified model, include: Set the parameter information for the flexible rectangular thin plate; A simplified model of a collapsed building wall is constructed based on the parameter information of the elastic rectangular thin plate. Based on the simplified model analysis equation parameter information of the collapsed building wall; Introducing theoretical information on small deflection of thin plates; The vibration differential equation of the building component wall is obtained based on the equation parameter information and the thin plate small deflection theory information.

3. The method of claim 1, wherein the method is characterized by, The derivation of the natural frequency expression of the collapsed wall of a stacked building under the simply supported boundary conditions, based on the simply supported boundary conditions and the vibration differential equation, includes: Set the solution expression for the vibration differential equation under the condition of simple support on four sides; Substituting the solution expression of the vibration differential equation under the simply supported four-sided condition into the vibration differential equation, we obtain the solution equation for the vibration characteristics of the thin plate under the simply supported four-sided condition. Based on the vibration characteristics of the thin plate, the natural frequency differential equation of the collapsed wall of the stacked building under the condition of simple support on four sides is obtained by solving the equation. Based on the natural frequency differential equation, the expression for the natural frequency of the collapsed wall of a stacked building under the condition of simply supported sides is obtained.

4. The method of claim 3, wherein the method is characterized by, The natural frequency differential equations of the collapsed wall of a stacked building under simply supported conditions obtained by solving the equations based on the vibration characteristics of the thin plate include: Based on the equations for solving the vibration characteristics of the thin plate, the characteristic parameter function for the vibration of the thin plate is set. Based on the vibration characteristic parameter function of the thin plate, the vibration differential equation is transformed and analyzed using the method of separation of variables to obtain the natural frequency differential equation of the collapsed wall of the stacked building under the condition of simple support on four sides. The natural frequency differential equation satisfies the following relationship: ， in, Let be the displacement function of the panel in the vertical direction. These are the coordinate values ​​of the lateral displacement of the collapsed wall. These are the coordinate values ​​of the longitudinal displacement of the collapsed wall. Solve the equations for the vibration characteristics of the thin plate.

5. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 3, characterized in that, The expression for the natural frequency of the collapsed wall of a stacked building under the condition of simple support on four sides, obtained from the natural frequency differential equation, includes: Setting the mode shape function based on double trigonometric functions; Substitute the mode shape function into the natural frequency differential equation for analysis to obtain the natural frequency expression of the collapsed wall of the stacked building under the condition of simply supported four sides. The natural frequency expression of the collapsed wall of the stacked building under the condition of simple support on four sides satisfies the following relationship: ， in, The natural frequency of the wall under simply supported conditions is given. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, During the vibration of the rectangular wall Half-wave number in the direction, Pi The length of the wall. During the vibration of the rectangular wall Half-wave number in the direction, The width of the wall. This is the foundation reaction modulus.

6. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 3, characterized in that, The formula for estimating the fundamental frequency of a collapsed wall under simply supported conditions, based on the natural frequency expression of the collapsed wall of the stacked building, includes: Introduce wall bending stiffness; Based on the bending stiffness of the wall and the natural frequency expression of the collapsed wall of the stacked building, a formula for estimating the fundamental frequency of the collapsed wall under the condition of simply supported sides is established. The formula for estimating the fundamental frequency of a collapsed wall under simply supported conditions satisfies the following relationship: ， in, The results are the fundamental frequency estimation of the wall under the condition of simple support on four sides. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. This is the foundation reaction modulus.

7. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 1, characterized in that, The method of setting four-sided free boundary conditions, and obtaining the calculation formula for the natural frequency of the collapsed wall of the stacked building under the four-sided free condition based on the four-sided free boundary conditions and the vibration differential equation includes: The vibration differential equation is deformed based on the four-sided free boundary condition to obtain the natural frequency differential equation of the building component wall. An approximate solution to the differential equation of natural frequency is constructed based on the Galerkin method, and an approximate mode shape function is obtained; The analysis equation for undetermined coefficients is obtained based on the natural frequency differential equation and the approximate mode shape function; Based on the characteristic parameter function of thin plate vibration and the analysis equation of undetermined coefficients, the formula for calculating the natural frequency of the collapsed wall of a stacked building under four-sided free conditions is obtained.

8. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 7, characterized in that, The natural frequency differential equation satisfies the following relationship: ， in, For the bending stiffness of the collapsing wall, It is an approximate mode shape function. For wall density, For wall thickness, For the natural frequency, It is the foundation reaction modulus; The approximate mode shape function satisfies the following relationship: ， in, It is an approximate mode shape function. The first undetermined coefficient, The second undetermined coefficient, The parameter representing the influence of the half-wave number in the x-direction during the vibration of a rectangular wall is... The parameter representing the influence of the half-wave number in the y-direction during the vibration of a rectangular wall. These are the coordinate values ​​of the lateral displacement of the collapsed wall. Poisson's ratio, The length of the wall. These are the coordinate values ​​of the lateral displacement of the collapsed wall. The formula for calculating the natural frequency of the collapsed wall of a stacked building under the condition of free quadrilaterals satisfies the following relationship: ， in, The results are the natural frequencies calculated under the condition of a four-sided free boundary. For the bending stiffness of the collapsing wall, For wall density, For wall thickness, It is a combined influencing factor of vibration mode and material Poisson's ratio. This is a balance factor between vibration correction and material properties. For the foundation reaction modulus, The compressive resilience modulus of the wall. Poisson's ratio, During the vibration of the rectangular wall Half-wave number in the direction, During the vibration of the rectangular wall Half-wave number in the direction.

9. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 7, characterized in that, The construction of the fundamental frequency analysis formula for the collapsed wall under four-sided free conditions based on the natural frequency calculation formula of the collapsed wall of the stacked building includes: The fundamental frequency of the building's collapsing wall is determined based on the four-sided free boundary conditions; Based on the fundamental frequency of the collapsed wall of the building and the natural frequency of the collapsed wall of the stacked building, an analysis formula for the fundamental frequency of the collapsed wall under the condition of free movement of four sides is established.

10. The method for estimating the natural frequency of collapsed walls in a stacked building under different boundary conditions according to claim 9, characterized in that, The construction of the fundamental frequency analysis formula for the collapsed wall under four-sided free conditions based on the natural frequency calculation formula of the collapsed wall of the stacked building includes: The fundamental frequency analysis formula for the collapsed wall under the four-sided free condition satisfies the following relationship: ， in, The results are the fundamental frequency analysis under the condition of four-sided free boundary. The compressive resilience modulus of the wall. For wall thickness, Pi For wall density, Poisson's ratio, The length of the wall. The width of the wall. This is the foundation reaction modulus.

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