In response to the urgent need for performance predictions of damaged aerospace structures, this study undertakes a comprehensive investigation into the flutter characteristics of damaged variable-stiffness composite laminate (VSCL) plates. The governing boundary value problem for the dynamics of damaged VSCL plates is formulated using first-order shear deformation theory (FSDT). Additionally, the first-order piston theory is utilized to model the aerodynamic pressure in supersonic airflow. A novel coupling methodology is developed through the integration of penalty function methods and irregular mapping techniques, which effectively establishes the interaction between damaged and undamaged plate elements. The vibration characteristics and aeroelastic responses are systematically analyzed using the Chebyshev differential quadrature method (CDQM). The validity of the proposed model is thoroughly demonstrated through comparative analyses with the existing literature and finite element simulations, confirming its computational accuracy and broad applicability. A notable characteristic of this research is its ability to accommodate arbitrary geometric configurations within damaged regions. The numerical results unequivocally demonstrate that accurately predicting the flutter characteristics of damaged VSCL plates constitutes an effective strategy for mitigating structural stability degradation. This approach provides valuable insights for aerospace structural design and maintenance.

In this paper, a full-domain stochastic response analysis is performed based on the meshless method to reveal the time–frequency dynamic characteristics, including the power spectral density (PSD) responses in the frequency domain and the evolving PSD distribution in the time domain for a sandwich trapezoidal plate–shell coupled system. The general governing equations are derived based on the first-order shear deformation theory (FSDT), linear piston theory and Hamilton’s principle, and the stochastic excitation is integrated into the meshless framework based on the pseudo-excitation method (PEM). By constructing the meshless shape function covering the entire structural domain from Chebyshev polynomials and discretizing the continuous domain into a series of nodes within a square definition domain, the points are assembled according to the sequence number and the equilibrium relationship on the coupling edge to obtain the overall vibration equations. The validity is demonstrated by matching the mode shapes, PSD responses, time history displacement and critical flutter boundaries with FEM simulation and reported data. Finally, the time–frequency characteristics of each substructure under global and single stochastic excitation, and the effect of aerodynamic pressure on full-domain stochastic vibration, are revealed.

This study comprehensively analyzes the free vibration and transient response for a sandwich piezoelectric laminated beam with elastic boundaries in a thermal environment. Quasi-3D shear deformation beam theory (Q3DBT) and Hamilton’s principle are used to obtain the thermo-electro-mechanical coupling equations, and the method of reverberation-ray matrix (MRRM) is utilized to integrate the phase and scattering relationship of the structure in a unified approach. Specifically, the scattering relationship established by the Mixed Rigid-Rod Model (MRRM) via dual coordinate systems describes the general dynamic model of the beam using generalized displacements and generalized forces at the two endpoints. This analytical solution is compared with the finite element numerical results based on Solid5 and Solid45 elements. The similarity of this approach lies in the fact that solid elements can account for the Poisson effect of thick beams, while the difference is that solid elements have a certain width; here, the error is minimized by adopting a single-element division in the width direction. Comparison of the numerical results under different geometric parameters and boundary conditions with the simulation software proves that MRRM has good accuracy and stability in analyzing the dynamic performance of sandwich piezoelectric laminated beams. On this basis, a spring-supported boundary technology is introduced to expand the flexibility of classical boundary conditions, and a detailed parameterization study is conducted on the material properties of the base layer, including the material parameters, geometric property, and the external temperature. The study in this article provides many new results for sandwich-type piezoelectric laminated structures to help further research.

This paper establishes a meshless thermal vibration model of a lattice sandwich panel, a type of thermal protection structure consisting of two thin upper and lower panels and a central hourglass-shaped truss core. The governing equations and compatible boundary conditions for the lattice structure are first derived using layered shear theory. Some discretizations using a meshless technique are then performed to obtain the general vibration equations of the system. A number of numerical comparisons are presented to verify the free and thermal vibration frequencies of the lattice panel. The effect of varying the core thickness and the range where buckling is likely to occur is investigated.