A method for analyzing the stability of a hot gas elastic system across a saddle transition

Abstract

The application discloses a kind of hot aerodynamic elastic system across saddle transition dynamics stability analysis method, comprising: S1, construct nonlinearly heated wallboard aeroelastic system analysis model, obtain the buckling modal configuration and vibration modal configuration of linearized system;S2, construct the reduced-order analysis model of nonlinearly heated wallboard aeroelastic system, for analyzing the stability characteristics of system initial equilibrium position;S3, construct the potential energy surface of heated wallboard structure, for analyzing the balance point species, quantity and position of wallboard under different temperatures;S4, consider aerodynamic elastic effect and load aerodynamic load to construct the linearized across saddle transition dynamics analysis model of hot aeroelastic system, for analyzing the across saddle transition dynamics characteristics of multi-stable non-conservative dynamic system saddle point local jump behavior.The application realizes high-fidelity prediction to the nonlinear thermal aeroelastic behavior of wallboard structure, provides key theoretical tool for the thermal strength reliable design and accurate evaluation of wallboard structure.

Description

Technical Field

[0001] This invention relates to the field of theoretical analysis and prediction of nonlinear aeroelastic behavior in supersonic / hypersonic airflow, and particularly to a method for analyzing the stability of cross-saddle transition dynamics of a multistable nonconservative thermo-aeroelastic system. Background Technology

[0002] The skin panel structure of an aircraft plays a crucial role in ensuring the integrity of the airframe. Its nonlinear thermo-aeroelasticity in supersonic / hypersonic airflow is a cutting-edge research topic in fluid-structure interaction dynamics. Under aero-thermal loads, the panel structure not only experiences material property degradation but also critical thermal buckling instability (at which point thermally induced in-plane compressive load becomes the main indicator for static strength design). This results in the heated panel structure exhibiting multiple post-thermal buckling stable equilibrium configurations and multi-stable characteristics. Under dynamic loads meeting certain energy threshold conditions, it can undergo ergodic / non-ergodic escape / saddle transition / reentry behaviors between multiple potential wells. The saddle transition process between potential wells corresponds to nonlinear jump dynamics, causing the structure to experience extremely large reversal stresses, severely compromising its structural strength performance.

[0003] Existing traditional stability algorithms are mostly based on approximate global dynamic behavior analysis using linearly derived system modal information from the potential well of thermally buckled panel structures. They rarely explore the core physical essence of the "heterogeneous" saddle transition behavior under dynamic loads satisfying predetermined energy threshold conditions. Therefore, traditional theoretical methods have poor applicability, becoming a bottleneck restricting the reliable design and accurate evaluation of the thermal strength of panel structures. It is necessary to rely on saddle transition dynamics theory, based on the heterogeneous physical essence of saddle behavior in multi-stable systems, to achieve accurate understanding, prediction, and control of the structural evolution behavior in each phase space of multi-stable systems. Summary of the Invention

[0004] To address the problem that traditional stability calculation methods cannot accurately predict the dynamic behavior of multistable panel structure nonlinear thermo-aeroelastic systems across all traps, saddle transitions, and reentry in fine-grained aircraft designs, this invention proposes a saddle transition dynamic stability analysis method for thermo-aeroelastic systems. This method is applicable to the predictive analysis of saddle jump transition dynamic behavior in multistable nonconservative cyclic dynamic systems, thus solving the aforementioned problem.

[0005] This application discloses a method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle transition, comprising the following steps: S1. Construct an analytical model of the aeroelastic system of a multistable nonlinear heated wall panel, and obtain the buckling mode configuration and vibration mode configuration of the linearized system by solving the eigenvalue problem; S2. Based on the buckling mode configuration and vibration mode configuration, a reduced-order analysis model of the nonlinear heated wall panel aeroelastic system is constructed to analyze the stability characteristics of the system at the initial equilibrium position. S3. Construct the potential energy surface of the heated wall panel structure to analyze the types, number, and locations of equilibrium points of the wall panel at different temperatures; S4. Considering aeroelastic effects and applying aerodynamic loads, construct a linearized cross-saddle transition dynamics analysis model of the thermo-aeroelastic system to analyze the cross-saddle transition dynamics characteristics of the jump behavior of the local system at the saddle point.

[0006] Preferably, the multi-steady-state aeroelastic motion model of the heated wall panel includes a motion model of the heated wall panel, the expression of which is as follows:

[0007] in, For density, For thickness, This refers to the out-of-plane displacement of the wall panel structure. This represents the chordal displacement of the wall panel. For time variables, The additional in-plane forces are caused by the nonlinear effects of large geometric deformation. For thermally induced in-plane compressive load, For the bending stiffness of the wall panel, It is a pneumatic load.

[0008] Preferably, the buckling mode configuration is obtained by substituting the displacement boundary constraints into the buckling equilibrium differential equation and solving it.

[0009] Preferably, the vibration mode configuration is obtained by substituting the displacement boundary constraints into the linear vibration control equation and solving it.

[0010] Preferably, the reduced-order analysis model is obtained through a modal reduction method.

[0011] Preferably, the stability characteristics of the initial equilibrium position of the analysis system include: Based on the system order reduction analysis model, a two-degree-of-freedom system order reduction model is obtained, which is defined as follows: , , For first-order degree of freedom displacement, For second-order degree-of-freedom displacement, For viscous damping on the first degree of freedom, Viscous damping on the second degree of freedom; Assume the two-order modal coordinate displacements are in harmonic form: , This represents the dynamic small-amplitude displacements of each order after the system is reduced in order; The instability boundary conditions can be obtained by applying the Routh-Hurwitz criterion, which specifies... It is the ratio of the damping coefficients of the two modes.

[0012] Preferably, the potential energy surface of the heated wall panel is constructed based on the reduced-order model of the system with two degrees of freedom. By analyzing the potential energy surface, the spatial positions of the potential well, saddle point and potential barrier on the potential energy surface of the system under different temperature rise parameters and flow field dynamic pressure parameters are confirmed. These three cases on the potential energy surface correspond to different types of equilibrium points of the wall panel. After discovering the correspondence between the saddle point and the equilibrium position, the relationship is extended to the nonconservative case. The nonlinear static aeroelastic equilibrium control equations of the two-degree-of-freedom reduced-order model of the system are solved to obtain the spatial positions of the potential well, saddle point and potential barrier on the potential energy surface corresponding to the non-zero and zero solutions of the static aeroelastic deformation of the structure.

[0013] Preferably, based on the linearized saddle transition dynamics analysis model, the system eigenvalues ​​and their corresponding eigenvectors are solved, and corresponding nonlinear dynamics analysis is carried out accordingly.

[0014] The beneficial effects of this invention are: This invention elucidates the deep-seated heterogeneity mechanism of nonlinear thermo-aeroelasticity of plates, enabling high-fidelity prediction and analysis of the nonlinear thermo-aeroelastic behavior of hypersonic / hypersonic vehicle panel structures. It solves a bottleneck problem hindering the reliable design and accurate evaluation of the thermal strength of panel structures. Furthermore, this invention is also applicable to the predictive analysis of the transsaddle transition dynamics of other multistable, nonconservative cyclic dynamic systems. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method for analyzing the stability of a thermo-aeroelastic system across a saddle transition dynamics according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a heated wall panel in a supersonic airflow according to an embodiment of the present invention; Figure 3 The diagram shows the stable / unstable regions of the heated wall panel structure in this embodiment of the invention, obtained based on the Routh-Hurwitz criterion. Detailed Implementation

[0016] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments.

[0017] This application discloses a method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle transition, the process of which is as follows: Figure 1 As shown, it includes the following steps: S1. Construct an analytical model of the aeroelastic system of the multi-steady nonlinear heated wall panel, and obtain the buckling mode configuration and vibration mode configuration of the linearized aeroelastic system of the heated wall panel by solving the eigenvalue problem.

[0018] The aeroelastic system analysis model does not refer to a specific structure, but rather to a system in which aerodynamic forces, elastic forces, and inertial forces interact. The heated wall panel motion model is part of an aeroelastic system analysis model. In this embodiment, a two-dimensional isotropic material wall panel in a supersonic airflow is selected as the research object, with a supersonic flow field acting on its upper surface, as shown in the schematic diagram. Figure 2 As shown. Let the chord direction of the wall panel be... Based on the motion characteristics of the heated wall panel under the influence of aerodynamic forces and temperature rise, the motion model of the heated wall panel is constructed as follows:

[0019] in, For density, For thickness, This refers to the out-of-plane displacement of the wall panel structure. This represents the chordal displacement of the wall panel. For time variables, The additional in-plane forces are caused by the nonlinear effects of large geometric deformation. For thermally induced in-plane compressive load, For the bending stiffness of the wall panel, It is a pneumatic load.

[0020] The structural parameters of the heated wall panel include: length ,thickness ,density Poisson's ratio and elastic modulus Supersonic flow field parameters include: velocity. airflow density and Mach number .and , Assuming the heat load caused by the supersonic airflow heating effect is uniformly distributed in steady-state space, the temperature rise parameter is... This generates a thermally induced in-plane compressive load. Using piston theory, the range is... Internal aerodynamic load Represented as:

[0021] in, For dynamic pressure, These are the Prandtl-Glauert coefficients. The velocity is the supersonic flow field velocity.

[0022] Aerodynamic load The dimensionless model is as follows:

[0023] in, , , , , , , , The parameters mentioned above are used to perform dimensionless transformation and simplify equations, and have no practical meaning.

[0024] The buckling modal configuration is obtained by solving the buckling equilibrium differential equation of the system. The buckling modal configuration can be obtained by substituting the displacement boundary constraints into the buckling equilibrium differential equation.

[0025] The vibration mode configuration is obtained by solving the linear vibration control equation of the system. The vibration mode configuration can be obtained by substituting the displacement boundary constraints into the linear vibration control equation.

[0026] S2. Based on the buckling mode configuration and vibration mode configuration, a reduced-order analysis model of the nonlinear heated wall panel aeroelastic system is constructed to analyze the stability characteristics of the system at the initial equilibrium position.

[0027] The reduced-order analysis model of the nonlinear heated wall panel aeroelastic system is obtained through modal reduction method, which realizes the stability analysis of the initial equilibrium position of the heated wall panel structure and obtains the reduced-order analysis model of the system through modal reduction method.

[0028] Regulation , , , For the first Displacement on the first degree of freedom, For the selected degrees of freedom, For dimensionless parameters related to the dynamic pressure of the flow field, For the first Viscous damping on the step.

[0029] Based on the system order reduction analysis model, a two-degree-of-freedom system order reduction model is obtained, which is defined as follows: , , For first-order degree of freedom displacement, For second-order degree-of-freedom displacement, For viscous damping on the first degree of freedom, It is a viscous damping on the second degree of freedom.

[0030] The instability boundary conditions can be obtained by applying the Routh-Hurwitz criterion. (This is the ratio of the two modal damping coefficients).

[0031] Assume the two-order modal coordinate displacements are in harmonic form: , This represents the dynamic small-amplitude displacements of each order after the system has been reduced in order. The instability boundary conditions can be obtained by applying the Routh-Hurwitz criterion. It is the ratio of the damping coefficients of the two modes.

[0032] In setting ( In the case of Routh-Hurwitz criterion, the stable / unstable regions of the heated wall panel structure are obtained as follows: Figure 3 The figure shows one stable region and three adjacent regions: 1) the stable region of the heated wall panel structure (AECF), where the wall panel is stable at its initial equilibrium position; 2) the flutter region (AEH); 3) the buckling region (FCBG); and 4) the transition region (CEB), where the wall panel exists in different equilibrium states. The geometric relationships between the lines (curves) in the figure are as follows: the horizontal lines CEH and AEBD are tangent to the curve FCBG at points C and B, respectively, with point B being the intersection of line BI and curve FCBG. Subsequent research in this paper will primarily focus on the wall panel buckling region FCBG (the thick solid line in the figure).

[0033] S3. Construct the potential energy surface of the heated wall panel structure to analyze the types, number, and location of equilibrium points of the wall panel at different temperatures.

[0034] The potential energy surface of the heated wall panel is constructed based on the two-degree-of-freedom reduced-order model of the system. Through the analysis of the potential energy surface of the heated wall panel structure, the spatial locations of the potential well, saddle point and potential barrier on the potential energy surface of the system under different temperature rise parameters (characterizing thermal load) and flow field dynamic pressure parameters (characterizing aerodynamic load) are confirmed. These three cases on the potential energy surface correspond to different types of equilibrium points of the wall panel, which are obtained by solving the potential energy function and Hessian matrix of the heated wall panel.

[0035] After discovering the correspondence between the saddle point and the equilibrium position, the relationship is extended to the nonconservative case. The nonlinear static aeroelastic equilibrium control equations of the two-degree-of-freedom reduced-order model of the system are solved to obtain the spatial positions of the potential well, saddle point and potential barrier on the potential energy surface corresponding to the non-zero and zero solutions of the static aeroelastic deformation of the structure.

[0036] S4. Considering aeroelastic effects and applying aerodynamic loads, construct a linearized cross-saddle transition dynamics analysis model of the thermo-aeroelastic system to analyze the cross-saddle transition dynamics characteristics of the jump behavior of the local system at the saddle point.

[0037] A linearized transition dynamic analysis model for the system across the saddle is constructed, the system eigenvalues ​​and their corresponding eigenvectors are solved, and corresponding nonlinear dynamic analysis is carried out based on this model.

[0038] In summary, based on the model of S1-S4, this application embodiment calculates the eigenvalues ​​and eigenvectors of the system when it exhibits cross-saddle behavior within the buckling region of system instability, and analyzes the eigenvalues ​​and eigenvectors to confirm the type and characteristics of the corresponding modes.

[0039] Based on the structural parameters of the wall panel and the parameters of the supersonic flow field in which it is located, its equations of motion are constructed, and the differential governing equations are solved through boundary conditions to confirm its buckling / vibration modes. Based on the obtained buckling / vibration modes, a reduced-order analysis model of the multi-stable heated wall panel aeroelastic system is obtained through mode reduction. The first two modes of the reduced-order analysis model are selected, and the Routh-Hurwitz criterion is applied to analyze the stability of the system's initial equilibrium position under different temperature rise parameters and flow field dynamic pressure parameters. Based on the two-degree-of-freedom reduced-order analysis model of the system, a potential energy surface of the heated wall panel is constructed, and the surface characteristics under different temperature rise parameters and the corresponding types, numbers, and positions of the wall panel's equilibrium points are analyzed. Based on the analysis of the potential energy surface of the heated wall panel and the static aeroelastic mechanical properties under different temperature rise parameters and flow field dynamic pressure parameters, the saddle point position of the system is obtained. At the saddle point position, a linearized cross-saddle transition dynamic analysis model is constructed to analyze the cross-saddle transition dynamic characteristics of the local system at the saddle point.

[0040] This embodiment draws upon transition dynamics theory, describing the characteristics of the system's potential well and saddle point, and constructing a linearized cross-saddle transition dynamics analysis model of the system locally at the saddle point. It analyzes the buckling / vibration modes of the linearized system, revealing the cross-saddle transition dynamic characteristics and evolutionary connection mechanism of the system's two motion modes during nonlinear jump behavior. This provides a predictive analysis of the nonlinear thermo-aeroelastic behavior of hypersonic / hypersonic vehicle panel structures. It should be noted that this application is also applicable to the predictive analysis of cross-saddle jump transition dynamics behavior of other multistable, nonconservative cyclic dynamic systems.

[0041] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle transition, characterized in that, Predictive analysis of the transition dynamics of a saddle jump applicable to multistable, nonconservative cyclic dynamic systems includes the following steps: S1. Construct an analytical model of the aeroelastic system of a multistable nonlinear heated wall panel, and obtain the buckling mode configuration and vibration mode configuration of the linearized system by solving the eigenvalue problem; S2. Based on the buckling mode configuration and vibration mode configuration, a reduced-order analysis model of the nonlinear heated wall panel aeroelastic system is constructed to analyze the stability characteristics of the system at the initial equilibrium position. S3. Construct the potential energy surface of the heated wall panel structure to analyze the types, number, and locations of equilibrium points of the wall panel at different temperatures; S4. Considering aeroelastic effects and applying aerodynamic loads, construct a linearized cross-saddle transition dynamics analysis model of the thermo-aeroelastic system to analyze the cross-saddle transition dynamics characteristics of the jump behavior of the local system at the saddle point.

2. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 1, characterized in that, The multi-stable aeroelastic motion model of the heated wall panel includes a motion model of the heated wall panel, the expression of which is as follows: in, For density, For thickness, This refers to the out-of-plane displacement of the wall panel structure. This represents the chordal displacement of the wall panel. For time variables, The additional in-plane forces are caused by the nonlinear effects of large geometric deformation. For thermally induced in-plane compressive load, For the bending stiffness of the wall panel, It is a pneumatic load.

3. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 2, characterized in that, The buckling mode configuration is obtained by substituting the displacement boundary constraints into the buckling equilibrium differential equation and solving it.

4. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 3, characterized in that, The vibration mode configuration is obtained by substituting the displacement boundary constraints into the linear vibration control equation and solving it.

5. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 4, characterized in that, The reduced-order analysis model is obtained through modal reduction.

6. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 5, characterized in that, The stability characteristics of the initial equilibrium position of the analysis system include: Based on the system order reduction analysis model, a two-degree-of-freedom system order reduction model is obtained, which is defined as follows: , , For first-order degree of freedom displacement, For second-order degree-of-freedom displacement, For viscous damping on the first degree of freedom, Viscous damping on the second degree of freedom; Assume the two-order modal coordinate displacements are in harmonic form: , This represents the dynamic small-amplitude displacements of each order after the system is reduced in order; The Routh-Hurwitz criterion is applied to obtain the instability boundary conditions.

7. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 6, characterized in that, The potential energy surface of the heated wall panel is constructed based on the reduced-order two-degree-of-freedom model of the system. By analyzing the potential energy surface, the spatial locations of potential wells, saddle points and potential barriers under different temperature rise and dynamic pressure parameters are identified, corresponding to the type of equilibrium point of the wall panel. The relationship between saddle point and equilibrium position is extended to nonconservative systems. By solving the nonlinear hydrodynamic equilibrium control equations, the potential well, saddle point and potential barrier positions corresponding to the non-zero solution and the zero solution are obtained.

8. The method for analyzing the dynamic stability of a thermo-aeroelastic system across a saddle according to claim 7, characterized in that, Based on the linearized saddle transition dynamics analysis model, the system eigenvalues ​​and their corresponding eigenvectors are solved, and nonlinear dynamics analysis is carried out accordingly.

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