A method for identifying dynamic load of a closed structure containing non-light fluid

Abstract

The application discloses a closed structure dynamic load identification method containing non-light fluid, and the identification method comprises the following steps: establishing a finite element model to obtain a detection point, obtaining vibration displacement response data of the detection point, and constructing a displacement response column vector W; obtaining position data of the detection point and a modal truncation order, and solving a modal coefficient matrix C; converting the vibration displacement response data of the detection point into vibration speed response data of the detection point, and establishing a relationship between sound pressure and the vibration speed response data at the detection point, so as to solve a reaction sound pressure of the non-light fluid on a stimulated wall surface of the closed structure; and substituting the modal coefficient matrix C and the reaction sound pressure of the stimulated wall surface of the closed structure into a thin plate motion equation, so as to obtain the dynamic load at the detection point. The dynamic load identification method can accurately identify the action position of the dynamic load and the corresponding amplitude, so that the influence of the reaction force of the non-light fluid on the closed structure is fully considered.

Description

Technical Field

[0001] This invention relates to the field of structural dynamic load identification methods, and in particular to a method for identifying dynamic loads on closed structures containing non-lightweight fluids. Background Technology

[0002] Engineering structures are developing towards larger scale, greater complexity, and greater intelligence, making effective dynamic load information crucial for solving structural dynamics problems. In practice, due to the randomness of load application locations, uneven structural surfaces, and the lack of suitable sensing methods, dynamic loads acting on structures are often difficult or even impossible to measure directly. Therefore, methods for indirectly identifying dynamic loads by measuring the structure's dynamic response (such as displacement, velocity, or acceleration) have received widespread attention from scholars both domestically and internationally and have remained a research hotspot in the field of dynamics. After years of research, dynamic load identification methods have been summarized from different perspectives, including frequency domain methods, time domain methods, and regularization methods.

[0003] In the transportation, aerospace, civil, and nuclear industries, some enclosed structures can experience structural damage, severe vibrations, and liquid leakage when subjected to excessively high dynamic loads in actual engineering projects. These enclosed structures include liquid fuel tanks for aircraft or rockets, rectangular storage tanks for offshore oil and gas platforms, and some large steel rectangular water purification devices. Therefore, accurately and effectively acquiring the load data of sealed structures is crucial for optimizing structural design, analyzing vibration sources, and evaluating the performance of vibration reduction and isolation devices. For example, recording load data from liquid fuel tanks during aircraft and rocket operation can effectively provide a reference for the reliability design of the structure; similarly, identifying the dynamic load data in the design of vibration damping platforms for rectangular storage tanks can effectively assess the performance of vibration reduction and isolation devices. Since these enclosed structures inevitably contain non-lightweight fluids during use, the interaction of these fluids with the enclosed structure significantly affects the effectiveness and accuracy of the dynamic load, thus impacting the safety and reliability design of the enclosed structure. Summary of the Invention

[0004] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes a method for identifying dynamic loads on closed structures containing non-light fluids. This method considers the influence of the forces of non-light fluids on the sealed structure, providing an important approach for the analysis and study of vibration problems in structures containing non-light fluid media.

[0005] According to a first aspect of the present invention, a method for identifying dynamic loads on a closed structure containing a non-lightweight fluid is provided, the method comprising:

[0006] A corresponding finite element model is established based on the stimulated wall of the closed structure to obtain the detection points;

[0007] Obtain the vibration displacement response data of the detection point and construct the displacement response column vector W;

[0008] Obtain the location data and modal truncation order of the detection points, and solve for the modal shape φ of the closed structure. mn (x,y), based on the displacement response column vector W and the modal shape φ mn The modal coefficient matrix C is obtained by solving the modal shape matrix Φ composed of (x,y).

[0009] The vibration displacement response data of the detection point is converted into vibration velocity response data of the detection point, and the relationship between the sound pressure at the detection point and the vibration velocity response data is established in order to solve for the reaction sound pressure of the non-light fluid on the stimulated wall surface of the closed structure.

[0010] Substituting the modal coefficient matrix C and the reaction sound pressure at the stimulated wall of the closed structure into the motion equation of the thin plate, the dynamic load at the detection point is obtained, thereby completing the identification of the dynamic load of the closed structure containing non-light fluid.

[0011] According to some embodiments of the present invention, the step of establishing a corresponding finite element model based on the stimulated wall of the closed structure and obtaining detection points includes: uniformly dividing the stimulated wall of the closed structure into x rows and y columns, and taking the M grid points that intersect between the x rows and y columns as detection points of vibration displacement response on the stimulated wall, wherein the number of detection points M = x * y.

[0012] In some embodiments of the present invention, in the step of acquiring the vibration displacement response data of the detection point to construct a displacement response column vector, the constructed displacement response column vector is:

[0013] W = [w(0,0) w(0,1)…w(x,y)] T (1)

[0014] According to some embodiments of the present invention, the location data and modal truncation order of the detection point are obtained, and the modal shape φ of the closed structure is solved. mn (x,y), based on the displacement response column vector W and the modal shape φ mn The steps for obtaining the modal coefficient matrix C by solving the modal shape matrix Φ composed of (x,y) specifically include:

[0015] The normal displacement w(x,y,l) at the detection point z This can be expanded as follows:

[0016]

[0017] in: The mode shapes of wall vibration; C mn These are the modal coefficients.

[0018] From equation (2), we can obtain the following matrix equation.

[0019] W=ΦC (3)

[0020] Where: W is the displacement response column vector; Φ is the vector formed by φ mn The modal shape matrix is ​​composed of (x, y); C is the modal coefficient C mn The matrix formed.

[0021] The modal coefficient matrix C can be obtained by inverting the modal shape matrix Φ using equation (3).

[0022] According to some embodiments of the present invention, the step of inverting the modal shape matrix employs a regularization method, wherein,

[0023] If the number of detection points M is greater than or equal to the modal coefficient C mn The number of modal coefficients is then determined using the Tikhonov regularization method, and the resulting modal coefficient matrix C is:

[0024] C=(Φ H Φ+λ 2 I) -1 Φ H W (4)

[0025] Where: the superscript "H" indicates the conjugate transpose of the matrix; I is the identity matrix; λ is the regularization parameter, which can be automatically selected by methods such as the L-curve method or the GCV method.

[0026] According to some embodiments of the present invention, the step of inverting the modal shape matrix employs a regularization method, wherein if the number of detection points M is less than the modal coefficients C... mn If the number of modal coefficients is determined, then the modal coefficient matrix C is solved using sparse regularization.

[0027] According to some embodiments of the present invention, the step of converting the vibration displacement response data of the detection point into vibration velocity response data of the detection point includes:

[0028] From equation (2), the normal vibration velocity on the excited wall surface can be further obtained as:

[0029]

[0030] Where the dimensions of the closed structure in the x, y, and z directions are lx, ly, and lz, respectively, then the sound pressure p(x,y,z) at any point in the closed structure can be expressed as:

[0031]

[0032] in: Sound wave number; ω is angular frequency; c0 is speed of sound.

[0033] From equation (6), according to Euler's formula, the normal vibration velocity in the z-direction of the closed structure can be obtained as follows:

[0034]

[0035] Where ρ0 is the fluid density.

[0036] According to some embodiments of the present invention, the step of establishing the relationship between the sound pressure at the detection point and the vibration velocity response data to solve for the reaction sound pressure of the non-light fluid on the stimulated wall of the closed structure includes: Boundary condition 1: Assuming that only the sound pressure at z = l z The wall vibrates at a certain point, and its normal velocity is v. z (x,y,l z ).

[0037] Boundary condition 2: Assume that the walls of the closed structure, except for the stimulated surface, are rigid, therefore v z (x,y,0)=0. Substituting boundary condition 1 and boundary condition 2 into equation (7), we get:

[0038]

[0039]

[0040] From equations (8) and (9), we can see that:

[0041] -A rs +B rs =0 (10)

[0042]

[0043] Combining equations (5) and (11), we can obtain:

[0044]

[0045] Multiply both sides of equation (12) by ψ pq (x,y), and integrating on the stimulated wall, we get:

[0046]

[0047] Based on the orthogonality of modal shapes, the left side of equation (13) can be simplified to:

[0048]

[0049] The integral on the right-hand side of equation (13) can be simplified to:

[0050]

[0051] Among them, G mp and G nq The expression is as follows:

[0052]

[0053]

[0054] By combining equations (13) to (15), we can obtain:

[0055]

[0056] Substitute equations (10) and (16) into equation (6), and take z = l z The reaction sound pressure of the internal non-light fluid acting on the stimulated wall surface of the sealed structure can be obtained as follows:

[0057]

[0058] According to some embodiments of the present invention, in the step of substituting the modal coefficient matrix C and the reaction sound pressure at the stimulated wall of the closed structure into the equation of motion of the thin plate: the displacement response column vector W is transformed into modal coordinates according to modal theory and substituted into the equation of motion of the plate, simplifying it into the modal coordinate equation of motion of the plate; wherein, the relationship between the vibration of the stimulated wall of the closed structure and its dynamic load is expressed by the equation of motion of the thin plate as:

[0059]

[0060] Where: F(x,y,l) z ) represents the dynamic load; ρ s h and ρ are the density and thickness of the box wall, respectively; p(x,y,l) represents the bending stiffness of the box wall; E and υ represent the Young's modulus and Poisson's ratio of the box wall, respectively; z ) is the reaction sound pressure of a non-light fluid, and its expression is shown in equation (17).

[0061] Substituting equation (2) into equation (18), we get:

[0062]

[0063] in:

[0064] Beneficial effects:

[0065] The dynamic load identification method of this application can accurately identify the location and amplitude of the dynamic load, thereby fully considering the influence of the reaction force of non-light fluid on the closed structure. It can accurately obtain the peak value of the dynamic load on some closed structures in actual engineering, and thus effectively be used for the optimization design of the structure, analysis of the source of structural vibration and evaluation of the performance of vibration reduction and isolation devices, avoiding problems such as structural damage, severe structural vibration, and liquid leakage, and improving the reliability and safety of the structure. Attached Figure Description

[0066] Figure 1 This is a simplified box model and coordinate system diagram of the simulation experiment example of the present invention;

[0067] Figure 2 This is a simulation experiment example of the present invention, showing the sound pressure diagram of the fluid reaction on the box wall at 2200Hz when the inside of the box is a light fluid (air).

[0068] Figure 3 The sound pressure diagram of the fluid reaction on the box wall at 2200Hz, when the inside of the box is a non-lightweight fluid (water), is used as a simulation example of the present invention.

[0069] Figure 4 The results of dynamic load identification of the enclosure at 2200Hz without fluid reaction are shown in the simulation experiment example of this invention when the fluid inside the enclosure is non-lightweight (water).

[0070] Figure 5 The results of dynamic load identification of the enclosure at 2200Hz, when the inside of the enclosure is a non-lightweight fluid (water), including fluid reaction, are presented in the simulation experiment example of this invention. Detailed Implementation

[0071] The embodiments of the present invention are described in detail below. The embodiments described with reference to the accompanying drawings are exemplary. The embodiments of the present invention are described in detail below.

[0072] An embodiment of the present invention provides a method for identifying dynamic loads on a closed structure containing a non-lightweight fluid, the method comprising the following steps:

[0073] Step 1: Establish a corresponding finite element model based on the stimulated wall of the closed structure to obtain the detection points. The stimulated wall of the closed structure is uniformly divided into x rows and y columns, and the M grid points that intersect between the x rows and y columns are taken as the detection points of the vibration displacement response on the stimulated wall. The number of detection points is M = x * y.

[0074] Step 2: Obtain the vibration displacement response data of the detection points and construct the displacement response column vector W, where the displacement response column vector W is:

[0075] W = [w(0,0) w(0,1)…w(x,y)]T (1)

[0076] Step 3: Obtain the location data and modal cutoff order of the detection points, and solve for the modal shape φ of the closed structure. mn (x,y), based on the displacement response column vector W and the modal shape φ mn The modal coefficient matrix C is obtained by solving the modal shape matrix Φ composed of (x,y); specifically...

[0077] Based on the fact that the boundary condition of the vibrating excited wall is simply supported, the normal displacement w(x,y,l) at the detection point can be expressed as... z This can be expanded as follows:

[0078]

[0079] in: The mode shapes of wall vibration; C mn These are the modal coefficients.

[0080] From equation (2), we can obtain the following matrix equation:

[0081] W=ΦC (3)

[0082] Where: W is the displacement response column vector; Φ is the vector formed by φ mn The modal shape matrix is ​​composed of (x, y); C is the modal coefficient C mn The matrix formed.

[0083] Then, by inverting the mode shape matrix Φ, the mode coefficient matrix C can be obtained from equation (3).

[0084] However, due to the ill-posedness of the modal shape matrix Φ inversion process, errors in the measurement data will be amplified. Therefore, a regularization method is needed to solve the problem. Specifically,

[0085] If the number of detection points M is greater than or equal to the modal coefficient C mn When the number of loads is large, the Tikhonov regularization method is used to solve the problem, thereby achieving higher load identification accuracy; at this time, the modal coefficient matrix C is:

[0086] C=(Φ H Φ+λ 2 I) -1 Φ H W (4)

[0087] Where: the superscript "H" indicates the conjugate transpose of the matrix; I is the identity matrix; λ is the regularization parameter, which can be automatically selected by methods such as the L-curve method or the GCV method.

[0088] If the number of detection points M is less than the modal coefficient C mnWhen the number of detection channels is small, it is impossible to obtain a sufficient number of displacement responses. In this case, the distribution of detection points for the displacement response can be optimized, and the modal coefficient matrix C is solved using sparse regularization.

[0089] Step 4: Convert the vibration displacement response data of the detection point into vibration velocity response data of the detection point, and establish the relationship between the sound pressure and vibration velocity response data at the detection point in order to solve for the reaction sound pressure of the non-light fluid on the stimulated wall of the closed structure.

[0090] Specifically, the normal vibration velocity on the excited wall surface can be further obtained from equation (2):

[0091]

[0092] Where the dimensions of the closed structure in the x, y, and z directions are lx, ly, and lz, respectively, then the sound pressure p(x,y,z) at any point in the closed structure can be expressed as:

[0093]

[0094] in: Sound wave number; ω is angular frequency; c0 is speed of sound.

[0095] From equation (6), according to Euler's formula, the normal vibration velocity in the z-direction of the closed structure can be obtained as follows:

[0096]

[0097] Where ρ0 is the fluid density.

[0098] Furthermore, through the unknown coefficient A in the sound pressure formula rs and B rs The vibration velocity response at each detection point is used to express the result, and then the obtained coefficient A is... rs and B rs Substituting into the formula for the sound pressure at the stimulated wall, we can solve for the reaction sound pressure of the non-light fluid within the closed structure on each detection point of the stimulated wall. Specifically...

[0099] Boundary condition 1: Assume that only the area at z = l z The wall vibrates at a point, and its normal velocity is vz(x,y,l). z );

[0100] Boundary condition 2: Assume that the walls of the closed structure, except for the stimulated surface, are rigid, therefore v z (x,y,0)=0;

[0101] Substituting boundary condition 1 and boundary condition 2 into equation (7), we get:

[0102]

[0103]

[0104] From equations (8) and (9), we can see that:

[0105] -A rs +B rs =0 (10)

[0106]

[0107] Combining equations (5) and (11), we can obtain:

[0108]

[0109] Multiply both sides of equation (12) by ψ pq (x,y), and integrating on the stimulated wall, we get:

[0110]

[0111] Based on the orthogonality of modal shapes, the left side of equation (13) can be simplified to:

[0112]

[0113] The integral on the right-hand side of equation (13) can be simplified to:

[0114]

[0115] Among them, G mp and G nq The expression is as follows:

[0116]

[0117]

[0118] By combining equations (13) to (15), we can obtain:

[0119]

[0120] Substitute equations (10) and (16) into equation (6), and take z = l z The reaction sound pressure of the internal non-light fluid acting on the stimulated wall surface of the sealed structure can be obtained as follows:

[0121]

[0122] Step 5: Substitute the obtained modal coefficient matrix C and the reaction sound pressure at the stimulated wall of the closed structure into the motion equation of the thin plate to obtain the dynamic load at the detection point, so as to complete the identification of the dynamic load of the closed structure containing non-light fluid.

[0123] Specifically, the displacement response column vector W, based on modal theory, is transformed into modal coordinates and substituted into the plate's equation of motion, simplifying it into the plate's modal coordinate equation of motion, thus reducing computational difficulty. Specifically, the relationship between the vibration of the excited wall surface of the closed structure and its dynamic load is expressed by the thin plate equation of motion as follows:

[0124]

[0125] Where: F(x,y,l) z ) represents the dynamic load; ρ s h and ρ are the density and thickness of the box wall, respectively; p(x,y,l) represents the bending stiffness of the box wall; E and υ represent the Young's modulus and Poisson's ratio of the box wall, respectively; z ) is the reaction sound pressure of a non-light fluid, and its expression is shown in equation (17).

[0126] Substituting equation (2) into equation (18), we get:

[0127]

[0128] in:

[0129] Furthermore, the dynamic load F(x,y,l) is identified. z After obtaining the specific values ​​for F(x,y,l), it is important to note that: the F(x,y,l) obtained here... z The stress is measured in Pa. Therefore, it needs to be multiplied by the area of ​​the discrete element to be converted into the actual force (in N).

[0130] Since existing load identification technologies generally study independent structures, they ignore the influence of fluid reaction forces on load identification. Therefore, when the density of the fluid medium is low, the magnitude of the fluid reaction force is very small and its influence on the load identification results can be ignored. However, when the density of the fluid medium is high, the magnitude of the fluid reaction force is close to the magnitude of the actual dynamic load. Ignoring its influence will not only lead to a large error in the identified dynamic load amplitude, but will also identify false dynamic load distributions outside the actual load application location.

[0131] Therefore, the dynamic load identification method of this application can accurately identify the location and corresponding amplitude of the dynamic load, thereby fully considering the influence of the reaction force of non-light fluid on the closed structure. It can accurately obtain the peak value of the dynamic load on some closed structures in actual engineering, and thus effectively be used for the optimization design of the structure, analysis of the source of structural vibration and evaluation of the performance of vibration reduction and isolation devices, avoiding problems such as structural damage, severe structural vibration, and liquid leakage, and improving the reliability and safety of the structure.

[0132] To further verify the dynamic load identification method for closed structures containing non-light fluids designed in this invention, which can accurately identify the location and amplitude of the dynamic load, the following simulation process was performed:

[0133] For ease of simulation, the closed structure containing a non-light fluid can be simplified as follows: Figure 1 The object of study shown is a rectangular box containing a non-lightweight fluid and surrounded by air (whose reaction is negligible). One of its walls is an elastic thin plate that vibrates. It should be noted that although a rectangular box is used as the simulation object here, the derivation process can be extended to structures of other shapes.

[0134] like Figure 1 As shown, the parameters of the box structure are: lx=ly=lz=1m, h=0.005m, ρs=7850Kg / m3, E=2.061011Pa, υ=0.3; the parameters of the fluid medium inside the box are: c0=1500m / s, ρ0=1000Kg / m3 or c0=343m / s, ρ0=1.29Kg / m3, that is, the study was conducted on two fluid media, water and air respectively.

[0135] The excitation load used is two simple harmonic point forces located at (0.46, 0.46) m and (0.54, 0.54) m, each with an amplitude of 500 N.

[0136] To simulate the actual dynamic response measurement process, COMSOL software was used to calculate the displacement vibration response of 51×51 points on the excited wall surface, considering fluid-structure interaction. These points are uniformly distributed along the x and y directions with a spacing of 0.02m.

[0137] Using the simulated displacement vibration response as input, the modal coefficients of the displacement response are first calculated. Then, these modal coefficients are substituted into the calculation to obtain the reaction sound pressure of the fluid on the vibrating wall. This sound pressure is multiplied by the area of ​​the discrete element (here, 0.02m × 0.02m) to obtain the reaction force of the flow field. At 2200Hz, the calculated reaction force is as follows: Figure 2 and Figure 3 As shown:

[0138] Depend on Figure 2 As can be seen, when the fluid medium is air, the force amplitude of the fluid reaction is only 0.4N, which has a negligible impact compared to the input load of 500N. Therefore, when the fluid inside the box is light, the reaction force generated by the fluid can be ignored.

[0139] Depend on Figure 3 As can be seen, when the fluid medium is water, the amplitude of the reaction force reaches 100N, which is close to the magnitude of the given load amplitude (500N). Therefore, it cannot be ignored, otherwise it will affect the load identification result.

[0140] Furthermore, substituting the reaction force and modal coefficients into equation (19) yields the input load. At 2200Hz, the identification result is as follows: Figure 4 and Figure 5 As shown:

[0141] from Figure 4 and Figure 5 As can be seen, the identified load peak coordinates are 0.46m and 0.54m in the x-direction and 0.46m and 0.54m in the y-direction. Figure 4 The peak loads identified were 566.5 N and 565.5 N, respectively. Figure 5 The identified peak loads were 518.5 N and 517.5 N, respectively.

[0142] The results above show that even without the reaction force of the fluid, the load application location can still be accurately identified, but the amplitude error of the identified load is relatively large. However, when the reaction force of the fluid is included, not only is the application location accurately identified, but the amplitude error is also smaller.

[0143] In addition, in comparison Figure 4 and Figure 5 It can be observed that outside the load application location, when there is no fluid reaction force, the identification results show significant fluctuations, that is, a relatively obvious load is identified in places where there is no excitation load.

[0144] Conversely, when the reaction force of the fluid is included, the surface is relatively flat and close to zero, except for the fluctuation error at the edge of the structure, which is more in line with the actual situation.

[0145] Therefore, the results of the above numerical simulation show that when the fluid inside the box is not lightweight, the reaction of the fluid on the vibrating structure has a significant impact on the load identification effect and cannot be ignored. Moreover, the dynamic load identification method with fluid reaction proposed in this invention can effectively identify the excitation load acting on the structure.

[0146] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0147] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example.

[0148] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for identifying dynamic loads on a closed structure containing a non-lightweight fluid, characterized in that, The method includes: A corresponding finite element model is established based on the stimulated wall of the closed structure to obtain the detection points; Obtain the vibration displacement response data of the detection points and construct a displacement response column vector. ; Obtain the location data and modal truncation order of the detection points, and solve for the modal shapes of the closed structure. Based on the displacement response column vector and by modal vibration modes The modal shape matrix is ​​composed of The modal coefficient matrix is ​​obtained by solving. Wherein, the normal displacement at the detection point It can be expanded as follows: （2） in: These are the mode shapes of wall vibration. These are the modal coefficients; From equation (2), we can obtain the following matrix equation. （3） in: This is the column vector of displacement response; For the reason The modal shape matrix is ​​composed of; For modal coefficients The matrix formed; Through the modal shape matrix The modal coefficient matrix can be obtained by inverting equation (3). ; The vibration displacement response data of the detection point is converted into vibration velocity response data of the detection point, and the relationship between the sound pressure at the detection point and the vibration velocity response data is established to solve for the reaction sound pressure of the non-light fluid on the stimulated wall surface of the closed structure. The normal vibration velocity on the stimulated wall surface can be further obtained from equation (2): （5） Let the dimensions of the closed structure in the x, y, and z directions be lx, ly, and lz, respectively. Then, the sound pressure at any point in the closed structure... It can be represented as: （6） in: ; ; Sound wave number; Angular frequency; Speed ​​of sound; and The unknown coefficients to be solved; From equation (6), according to Euler's formula, we can obtain the closed structure... The normal velocity in the direction is （7） in, For fluid density; Boundary condition 1: Assume that only those located at The wall at point [location] vibrates, and its normal velocity is [value]. ; Boundary condition 2: Assume that the walls of the closed structure, except for the stimulated surface, are rigid. ; Substituting boundary condition 1 and boundary condition 2 into equation (7), we get: （8） （9） From equations (8) and (9), we can see that: （10） （11） By combining equations (5) and (11), we can obtain: （12） Multiply both sides of equation (12) Integrating over the stimulated wall, we obtain: （13） Based on the orthogonality of modal shapes, the left side of equation (13) can be simplified to: （14） The integral on the right-hand side of equation (13) can be simplified to: （15） in, and The expression is as follows: ； ； By combining equations (13) to (15), we can obtain: （16） Substitute equations (10) and (16) into equation (6), and take... The reaction sound pressure of the internal non-light fluid acting on the stimulated wall surface of the sealed structure can be obtained as follows: （17）； The modal coefficient matrix Substituting the reaction sound pressure at the stimulated wall of the closed structure into the equation of motion of the thin plate, the dynamic load at the detection point is obtained, thereby completing the identification of the dynamic load of the closed structure containing non-light fluid.

2. The method for identifying dynamic loads on a closed structure containing a non-lightweight fluid according to claim 1, characterized in that, The steps for establishing a corresponding finite element model based on the stimulated wall of the closed structure and obtaining detection points include: uniformly dividing the stimulated wall of the closed structure into x rows and y columns, and taking the M grid points that intersect between the x rows and y columns as detection points for the vibration displacement response on the stimulated wall, wherein the number of detection points M = x * y.

3. The method for identifying dynamic loads on a closed structure containing a non-lightweight fluid according to claim 1, characterized in that, The vibration displacement response data of the detection points are obtained to construct a displacement response column vector. In the steps, the displacement response column vector is constructed. for: （1）。 4. The method for identifying dynamic loads on a closed structure containing a non-lightweight fluid according to claim 1, characterized in that, The step of inverting the modal shape matrix employs a regularization method, wherein... If the number of detection points M is greater than or equal to the modal coefficient The number of modal coefficients is then determined using the Tikhonov regularization method. for: （4） Among them: superscript " " denotes the conjugate transpose of a matrix; It is the identity matrix; This is a regularization parameter, which can be automatically selected using the L-curve method or the GCV method.

5. The method for identifying dynamic loads on a closed structure containing a non-lightweight fluid according to claim 1, characterized in that, The step of inverting the modal shape matrix employs a regularization method, wherein if the number of detection points M is less than the modal coefficients... The number of modal coefficients is then the modal coefficient matrix. The solution is obtained by using sparse regularization.

6. The method for identifying dynamic loads on a closed structure containing a non-lightweight fluid according to claim 1, characterized in that, The modal coefficient matrix In the step of substituting the reaction sound pressure at the stimulated wall of the closed structure into the equation of motion of the thin plate: the displacement response column vector Based on modal theory, modal coordinate transformation is introduced and substituted into the plate's motion equations, simplifying them into the plate's modal coordinate motion equations; wherein, the relationship between the vibration of the excited wall surface of the closed structure and its dynamic load is expressed by the thin plate motion equations as follows: （18） in: For dynamic loads; and These are the density and thickness of the box wall, respectively; The bending stiffness of the box wall; and These are Young's modulus and Poisson's ratio of the box wall, respectively; It is the reaction sound pressure of non-light fluid, and its expression is shown in equation (17); Substituting equation (2) into equation (18), we get: （19） in: ; .

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