Numerical Algorithm For Dynamic Response Of Time-varying Structures And Thermal Vibration Analysis Of Composite Plate Structures

Hypersonic vehicle is subjected to severe aerodynamic and aerothermal loads during a high-speed flight in the atmosphere.Aerodynamic heating will lead to changes in the stiffness and damping property of hypersonic vehicle structures over time,while rapid fuel combustion will lead to changes in the mass property of hypersonic vehicle structures over time.These time-varying characteristics not only lead to changes in natural vibration characteristic of the structure,and sometimes may be the main reason for the excessive vibration of the structure.For this reason,it is rather important to accurately predict the vibration responses of linear time-varying structures.Furthermore,the thermal protection structure of the hypersonic vehicle is usually made of composite plate structures.The aerodynamic load will cause the vibration of the structure.The aerodynamic load will cause thermoelastic stresses and change the mechanical properties of the material,which will further affect the vibration characteristics and vibration response of these structures and will ultimately affect the performance of the hypersonic vehicle and may even lead to mission failure.For this reason,it is rather important to accurately predict the vibration characteristics of composite plate structures in thermal environments.This paper summarizes the research status of the numerical algorithm for dynamic response of linear time-varying structures and the thermal vibration analysis of composite plate structures,and focuses on developing the efficient and accurate numerical algorithm for dynamic response of linear time-varying structures and modeling method for thermal vibration analysis of composite plate structures.The main contents are as follows:(1)Primal and mixed form of Hamilton's law of variable mass systems is derived based on Meshchersky's fundamental equation,which are suitable for the variable mass system that mass is gained or lost at any velocity.The dynamical equation of linear timevarying structures is derived using Hamilton's principle of variable mass systems that obtained by simplifying the proposed Hamilton's law of variable mass systems.(2)Conditionally stable higher-order accurate time finite element methods for linear time-varying structures are developed based on the primal form of Hamilton's law of variable mass systems,where time-varying parameters are approximated by Hermite interpolation functions and linear interpolation functions,respectively.The compatibility and stability of the corresponding time finite element methods for linear time-invariant structures are analyzed by the theoretical method.The accuracy and effectiveness of time finite element methods for linear time-varying structures are verified and evaluated by several numerical examples.(3)Unconditionally stable higher-order accurate time discontinuous finite element methods for linear time-varying structures are developed based on the mixed form of Hamilton's law of variable mass systems,where time-varying parameters are approximated by Lagrangian interpolation functions.The compatibility and stability of the corresponding time discontinuous finite element methods for linear time-invariant structures are analyzed by the theoretical method.The accuracy and effectiveness of time discontinuous finite element methods for linear time-varying structures are verified and evaluated by several numerical examples.(4)An efficient transient response analysis method for linear time-varying structures is presented by combine the Newmark algorithm for linear time-varying structures with the multi-level substructuring method.The computational accuracy and efficiency of this method are analyzed by the theoretical method.Furthermore,the computational accuracy and efficiency of this method are also verified and evaluated through several numerical examples.(5)A piecewise shear deformation theory for composite plate structures is presented by integrating the advantages of the layerwise theory and equivalent single layer theory.A C0 continuous four-noded quadrilateral isoparametric plate element based on this theory is developed for free and forced vibration analysis of composite plate structures in thermal environments.The static and dynamic equations of composite plate structures are derived in a unified framework.The accuracy and effectiveness of piecewise shear deformation theory and its plate element are verified and evaluated by several numerical examples.(6)Thermal vibration analysis of the composite plate structure in the time-varying thermal environment is performed by combine the finite element model of composite plate structures based the piecewise shear deformation theory and the time discontinuous finite element method for linear time-varying structures based on the mixed form of Hamilton's law of variable mass systems.