A dynamic response prediction method for thin-walled structures considering modal matching

Abstract

The present invention discloses a method for predicting the dynamic response of thin-walled structures taking into account modal matching, which belongs to the field of dynamic strength of aircraft skin structures. The present invention defines the characteristic parameters of the load mode and the structural resonance mode according to the comparative relationship between the wavelength and the structural characteristic length, constructs a load integral term expression taking into account the matching conditions of the load space mode and the vibration mode, and substitutes the wavelength ratio Kn into the calculation of the structural dynamic response. The dynamic load spatial correlation and the structural coupling law are characterized by Kn, thereby realizing the prediction of the dynamic response of thin-walled structures taking into account the matching of the load space mode and the vibration mode. The present invention can not only calculate the time-frequency characteristics of the structural dynamic response, but also obtain the structural dynamic response characteristics under different matching conditions of the dynamic load space mode and the structural characteristic mode; through dynamic response modeling analysis, the vibration law and mechanism of the dynamic load space correlation can be more effectively explained, and the optimal modal matching conditions can be met by adjusting the Kn value to suppress the vibration of the thin-walled structure.

Description

Technical Field

[0001] The present invention belongs to the field of dynamic strength of aircraft skin structures, and in particular relates to a method for predicting dynamic response of thin-walled structures taking into account the matching of load space modes and vibration modes. Background Art

[0002] During high-speed flight of an aircraft, high-speed airflow creates a strong dynamic load environment on the aircraft surface. This strong dynamic load environment acts on the aircraft skin structure, inducing violent vibrations in the skin structure, which in turn endangers the structural safety and reliability of the aircraft. The dynamic load transmitted through the aircraft skin structure to the aircraft instrument cabin will also generate a strong noise environment, further affecting the working stability of the sound-sensitive equipment in the cabin. With the continuous development of aerospace aircraft technology, aircraft flight performance indicators are gradually improving. The requirements of high speed and high maneuverability have made the dynamic load environment faced by aircraft more severe, thus posing a more severe test to the development of aircraft. Conducting research on the dynamic strength assessment of high-speed aircraft, developing high-precision dynamic load environment modeling and its vibration response coupling analysis method, and solving key technical problems in the structural safety design of aircraft are basic requirements for the development of a new generation of aerospace aircraft.

[0003] Finite element and statistical energy methods are commonly used numerical methods for calculating flow-induced vibration. Li Yueming's team at Xi'an Jiaotong University used the finite element method to study the acoustic mechanisms and characteristics of metal, sandwich, and composite structures. Yu Kaiping's team at Harbin Institute of Technology used the finite element method to analyze the modal and response characteristics of composite sandwich structures under thermal loads. Sha Yundong's team at Shenyang Aerospace University used the finite element method to study the mechanisms and laws of thermoacoustic fatigue in thin-walled structures. Chen Haibo's team at the University of Science and Technology of China conducted research on the mechanisms of structural acoustic vibration in the broadband domain and established a broadband flow-induced vibration prediction technique based on a hybrid finite element and statistical energy method. The finite element method is more effective for complex structures, while modal analysis can be used to study the dynamic response of simpler structures. DeRosa used both modal analysis and finite element methods to study the acoustic response characteristics of flat plate structures under turbulent boundary layer noise excitation. Researcher Liu Bilong at the Institute of Acoustics used the modal analysis method to study the mechanisms and laws governing the effects of different reinforcement conditions on the acoustic response and acoustic radiation of flat plate structures. Based on the analytical solution of the acoustic vibration response of a simply supported plate, Joshi further developed the optimization design technology for structural sound radiation control under the condition of reinforced plates.

[0004] However, existing studies on flow / acoustic vibration analyze the effects of different wall dynamic load environments on structural vibration and sound radiation from a time-frequency perspective, and cannot fully reflect the spatial correlation characteristics of dynamic loads and the structural coupling mechanism. In fact, the spatial correlation of dynamic loads caused by complex flows is the key point that distinguishes flow loads from conventional concentrated forces. Structural vibrations exhibit certain spatial modal characteristics, and flow-actuated loads also have certain spatial modal characteristics. Under the action of different dynamic load modes, the response laws of the structural vibration modes are also different, that is, the different matching of dynamic load modes and structural vibration modes causes different dynamic responses of the structure. Obviously, the existing structural dynamic response time-frequency modeling and analysis methods do not take into account the matching characteristics of the two different modes, resulting in low accuracy in the prediction of the dynamic response of current aircraft, which cannot meet the needs of refined structural design of the new generation of aircraft. Summary of the Invention

[0005] In view of the problem that the existing dynamic response modeling and analysis methods are only suitable for analyzing the time-frequency characteristics of structural dynamic response and cannot effectively reflect the spatial correlation of flow-actuated loads and the structural coupling mechanism, the main purpose of the present invention is to provide a thin-walled structure dynamic response prediction method considering modal matching. This method can not only predict the time-frequency characteristics of the structural dynamic response, but also obtain the dynamic response characteristics under different matching conditions of the dynamic load spatial mode and the structural characteristic mode, and obtain the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration. According to the Kn value, the vibration of the aircraft structure is suppressed, and the flight stability and service life of the aircraft are improved.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses a method for predicting the dynamic response of a thin-walled structure considering modal matching, comprising the following steps:

[0008] Step 1: Definition of characteristic parameters: Define the dynamic load N according to the comparison between wavelength and structural characteristic length. f and structural characteristic mode N s The characteristic number of U is respectively based on the disturbance migration speed U in the wall turbulent boundary layer. c and the analysis frequency f define the dynamic load modal wavelength λ f , according to the structural size a and the structural characteristic modal characteristic number N s Define the wavelength λ of the structural resonant mode s ; Define the wavelength ratio K based on the dynamic load modal wavelength and the structural resonance modal wavelength n . By wavelength ratio K n Characterize the matching status of load space mode and vibration mode. The subsequent steps 2 to 4 will be the wavelength ratio K n By bringing it into the calculation of structural dynamic response, the structural dynamic response law under different matching conditions is obtained.

[0009] The specific method for selecting and defining the characteristic parameters is as follows:

[0010] The dynamic load and the structural characteristic number are determined by their wavelength and the length of the model along the flow direction. f is the disturbance migration velocity U in the turbulent boundary layer. c and analysis frequency f, and its expression is:

[0011]

[0012] The wavelength λ of the structural resonance mode s It is composed of the structural size a and the structural characteristic modal characteristic number N s Jointly decided, the calculation formula is expressed as:

[0013]

[0014] Dynamic load modal wavelength and structural resonance modal wavelength define the wavelength ratio K n for:

[0015]

[0016] Step 2. Calculation of key parameters: Based on the dynamic load power spectrum, the geometric dimensions of the aircraft thin-wall model, the structural damping and density, the characteristic frequency of the analysis mode and other parameters, the impedance of the structure at the resonant frequency, the structural vibration response coefficient, the mode integral term and the load integral term are calculated respectively. The characteristic parameters that affect the matching conditions of the load space mode and the vibration mode are brought into the calculation of the load integral term in order to analyze K n The law of action on structural dynamic response.

[0017] According to the structure thickness h, density ρ, damping η, analysis frequency ω j Calculate the structural impedance Z j (ω:

[0018]

[0019] From the dynamic load power spectrum S pp (ω, structural vibration shape ψ j (x A ,y A ), structural impedance Z j (ω), the geometric dimensions a and b of the thin-walled structure model, and the expression of the structural dynamic response coefficient ∈ is obtained:

[0020]

[0021] Mode integral term Expressed as:

[0022]

[0023] Load integral term Expressed as:

[0024]

[0025] Substituting the characteristic parameters defined in step 1 into the above formula and simplifying it, we can obtain the load integral term expression that takes into account the matching conditions of the load space mode and the vibration mode:

[0026]

[0027] Step 3: Calculate the structural dynamic response: Calculate the structural dynamic response by combining the characteristic parameters defined in step 1 and the key parameters calculated in step 2, and draw the velocity spectrum response curve (Kn-Sv) based on the calculation results of the structural dynamic response.

[0028] Combining the characteristic parameters defined in step 1 and equations (5), (6), and (8) constructed in step 2, the above expressions are combined to express the structural displacement response as follows:

[0029]

[0030] The structural velocity response is calculated from the structural displacement response:

[0031]

[0032] The velocity spectrum response curve is drawn based on the calculation results of formula (10).

[0033] Step 4: According to the prediction in step 3, the structural velocity spectrum response curve (Kn-Sv) is obtained, the dynamic response law under different matching conditions of dynamic load mode and structural vibration mode is analyzed, and the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration is obtained.

[0034] The method further includes step 5, wherein the structural topology is optimized or partially optimized according to the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration obtained in step 4, so that the wavelength ratio of the dynamic load mode and the structural characteristic mode is equal to Kn, thereby reducing the structural dynamic response and stress level and extending the service life of the structure.

[0035] Beneficial effects:

[0036] 1. The present invention discloses a method for predicting and analyzing the dynamic response of thin-walled structures by considering the matching of load spatial modes and vibration modes. By defining characteristic parameters of load modes and structural resonance modes, and characterizing the matching conditions of load spatial modes and vibration modes by wavelength ratio Kn, an expression for load integral term considering the matching conditions of load spatial modes and vibration modes is constructed, and the wavelength ratio Kn is substituted into the calculation of the structural dynamic response. This method can not only calculate the time-frequency characteristics of the structural dynamic response, but also obtain the structural dynamic response characteristics under different matching conditions of dynamic load spatial modes and structural characteristic modes. Through dynamic response modeling and analysis, the vibration laws and mechanisms caused by dynamic load spatial correlation can be more effectively elucidated, the dynamic response and dynamic strength of aircraft structures can be suppressed, and the service life of the structure can be extended.

[0037] 2. The present invention discloses an analytical method for predicting the dynamic response of thin-walled structures taking into account the matching of load spatial modes and vibration modes. The method is suitable for predicting the dynamic response of thin-walled structures under the action of high-speed airflow. By characterizing the spatial correlation of dynamic loads and the law of structural coupling, the dynamic response prediction of thin-walled structures taking into account the matching of load spatial modes and vibration modes is realized, thereby improving the prediction accuracy of the dynamic response of thin-walled structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram for defining the modal characteristic number.

[0039] Figure 2 It is a schematic diagram of the flat plate model and its main dimensions.

[0040] Figure 3 It is a structural dynamic response prediction curve considering the matching of load space mode and vibration mode.

[0041] Figure 4 It is the structural velocity response curve obtained by time-frequency method.

[0042] Figure 5 This is a flow chart of a method for predicting dynamic responses of thin-walled structures considering modal matching disclosed by the present invention. DETAILED DESCRIPTION

[0043] The following embodiments are further described in conjunction with the accompanying drawings and examples. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0044] The dynamic load environment generated by high-speed airflow on the surface of the aircraft is an important reason for inducing structural vibration and thus reducing the service life of the structure. Compared with traditional concentrated forces, flow-driven loads show obvious spatial distribution characteristics. Carrying out research on dynamic load spatial correlation-induced vibration and developing structural dynamic response modeling and analysis methods that consider the dynamic load spatial correlation and structural resonance mode matching mechanism are of great value for aircraft dynamic response prediction and dynamic strength design. This embodiment takes a flat plate structure as an example to carry out a prediction study on the dynamic response of a flat plate structure under high-speed dynamic loads, such as Figure 5 As shown, this embodiment discloses a method for predicting the dynamic response of a thin-walled structure considering modal matching, and the specific implementation steps are as follows:

[0045] Step 1: Definition of characteristic parameters: Define the dynamic load N according to the comparison between wavelength and structural characteristic length. f and structural characteristic mode N s The characteristic number of U is respectively based on the disturbance migration speed U in the wall turbulent boundary layer. c and the analysis frequency f define the dynamic load modal wavelength λ f , according to the structural size a and the structural characteristic modal characteristic number N s Define the wavelength λ of the structural resonant mode s ; Define the wavelength ratio K based on the dynamic load modal wavelength and the structural resonance modal wavelength n .

[0046] The definitions of dynamic loads and structural characteristic numbers are given in Figure 1 The wavelength of the dynamic load mode, the wavelength of the structural resonance mode and the wavelength ratio of the dynamic load mode and the structural resonance mode wavelength can be calculated using formulas (1), (2) and (3) respectively. The structural dynamic response prediction analytical method of the present invention is illustrated by taking a simply supported plate as the calculation model. The research model and main dimensions are shown in Figure 2 , taking the first-order mode as an example, the corresponding analysis frequency is f = 43 Hz.

[0047] Step 2: Calculation of key parameters: Based on the dynamic load power spectrum, the geometric dimensions of the research model, the structural damping and density, the characteristic frequency of the analysis mode and other parameters, the impedance of the structure at the resonant frequency, the structural vibration response coefficient ∈, the mode integral term and load integral

[0048] The structural impedance, structural vibration response coefficient, mode integral term, and load integral term are calculated according to formulas (4), (5), (6), and (8). The plate model material is aluminum, and the structural damping is 0.02.

[0049] Step 3: Calculate the structural dynamic response: Calculate the structural dynamic response by combining the characteristic parameters defined in step 1 and the key parameters calculated in step 2, and draw the velocity spectrum response curve (Kn-Sv) based on the calculation results.

[0050] Based on the characteristic parameters defined in step 1 and the key parameters calculated in step 2, the velocity responses corresponding to different wavelength ratios are calculated using formulas (9) and (10). The velocity spectrum response curves drawn based on the calculation results are shown in Figure 3 .

[0051] Step 4: According to the prediction in step 3, the structural velocity spectrum response curve (Kn-Sv) is obtained, the dynamic response law under different matching conditions of dynamic load mode and structural vibration mode is analyzed, and the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration is obtained.

[0052] Figure 4 is the structural velocity response curve obtained by conventional time-frequency method. Figure 4 The results show the speed response of the structure at different frequencies, and the structural vibration control can be targeted to analyze the frequency band with more severe vibration. Figure 4 The calculation results cannot effectively reflect the influence of the spatial correlation of flow loads on structural vibration. The spatial correlation of dynamic loads is the key parameter that distinguishes flow-induced loads from concentrated forces. If the structural dynamic response modeling method cannot reflect the influence of flow spatial correlation, it cannot accurately reveal the coupling mechanism between flow-induced loads and structures, and has obvious deficiencies and errors. Figure 3 The structural dynamic response curve calculated by the present invention can effectively reveal the structural response characteristics induced by different dynamic load spatial distributions, improve the prediction accuracy of the structural dynamic response, improve the dynamic strength and flight stability of the aircraft structure, and extend the service life of the aircraft structure.

[0053] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the dynamic response of thin-walled structures considering modal matching, characterized by: The following steps are included: Step 1: Definition of characteristic parameters: Define the dynamic load N according to the comparison between wavelength and structural characteristic length. f and structural characteristic mode N s The number of features; According to the disturbance migration speed U in the wall turbulent boundary layer c and the analysis frequency f define the dynamic load modal wavelength λ f , according to the structural size a and the structural characteristic modal characteristic number N s Define the wavelength λ of the structural resonant mode s ; Define the wavelength ratio K based on the dynamic load modal wavelength and the structural resonance modal wavelength n ; Through wavelength ratio K n Characterize the matching status of load space mode and vibration mode. The subsequent steps 2 to 4 will be the wavelength ratio K n Bring it into the calculation of structural dynamic response to obtain the structural dynamic response law under different matching conditions; Step 2. Calculation of key parameters: According to the dynamic load power spectrum, the geometric dimensions of the aircraft thin-wall model, the structural damping and density, and the characteristic frequency of the analysis mode, the impedance of the structure at the resonant frequency, the structural vibration response coefficient, the mode integral term, and the load integral term are calculated respectively. The characteristic parameters that affect the matching conditions of the load space mode and the vibration mode are brought into the calculation of the load integral term in order to analyze the wavelength ratio K. n The law of action on the dynamic response of the structure; Step 3: Calculate the structural dynamic response: Calculate the structural dynamic response by combining the characteristic parameters defined in step 1 and the key parameters calculated in step 2, and draw the velocity spectrum response curve Kn-Sv based on the calculation results of the structural dynamic response; Step 4: According to the prediction in step 3, the structural velocity spectrum response curve Kn-Sv is obtained, the dynamic response law under different matching conditions of dynamic load mode and structural vibration mode is analyzed, and the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration is obtained.

2. The method for predicting dynamic response of thin-walled structures considering modal matching according to claim 1, characterized in that: The method further includes step five, wherein the structural topology is optimized or partially optimized according to the Kn value corresponding to the optimal modal matching condition for suppressing structural vibration obtained in step four, so that the wavelength ratio of the dynamic load mode and the structural characteristic mode is equal to Kn, thereby reducing the structural dynamic response and stress level and extending the service life of the structure.

3. The method for predicting dynamic response of thin-walled structures considering modal matching according to claim 1 or 2, characterized in that: In step one, The specific method for selecting and defining the characteristic parameters is as follows: The dynamic load and structural characteristic number are determined by their wavelength and the length of the model along the flow direction; the dynamic load modal wavelength λ f is the disturbance migration velocity U in the turbulent boundary layer. c and analysis frequency f, and its expression is: The wavelength λ of the structural resonance mode s It is composed of the structural size a and the structural characteristic modal characteristic number N s Jointly decided, the calculation formula is expressed as: Dynamic load modal wavelength and structural resonance modal wavelength define the wavelength ratio K n for: 。 4. The method for predicting dynamic response of thin-walled structures considering modal matching according to claim 3, characterized in that: In step 2, According to the structure thickness h, density ρ, damping η, analysis frequency ω j Calculate the structural impedance Z j (ω): From the dynamic load power spectrum S pp (ω), structural vibration shape ψ j (x A ,y A ), structural impedance Z j (ω), the geometric dimensions a and b of the thin-walled structure model, and the expression of the structural dynamic response coefficient ∈ are obtained: Mode integral term Expressed as: Load integral term Expressed as: Substituting the characteristic parameters defined in step 1 into the above formula and simplifying it, we can obtain the load integral term expression that takes into account the matching conditions of the load space mode and the vibration mode: 。 5. The method for predicting dynamic response of thin-walled structures considering modal matching according to claim 4, characterized in that: In step three, Combining the characteristic parameters defined in step 1 and equations (5), (6), and (8) constructed in step 2, the above expressions are combined to express the structural displacement response as follows: The structural velocity response is calculated from the structural displacement response: The velocity spectrum response curve is drawn based on the calculation results of formula (10).

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