Symplectic Method For Vibration And Buckling Of Composite Cylindrical Shells With Multi-field Coupling

Cylindrical shell structure is a kind of important load-bearing component,which is widely used in the design and manufacture of high-end equipment because of its advantages such as easy processing,less consumables,simple design and analysis,good mechanical properties and so on.In recent years,with the acceleration of China's modernization construction,the carrying capacity and service environment of high-end equipment are constantly improving.The 13th five year's national strategic emerging industry development plan clearly proposes to achieve new leap in China's manufacturing in eight industries,including aerospace equipment,marine engineering equipment,high-tech ships,advanced rail transit equipment,etc.In order to achieve this goal,the multi-field coupled composite material is widely used in the manufacturing of cylindrical shell structure,so that it can adapt to the increasingly complex extreme service environment.The dynamic performance analysis of this kind of multi-field coupled composite cylindrical shell is the premise and foundation of its design.However,the existing analytical research is limited by the solution system.The vibration and buckling governing equation with the generalized displacement functions(displacement,electric potential and magnetic potential)as the basic unknown quantities is a high-order partial differential equation,which can only be solved by the traditional inversed method or the semi-inversed method.The analytical solution is highly depended on pre-determined functions and has nothing to do with other parameters of the cylindrical shell.Thus,it is impossible to analyze the vibration and buckling behavior of this kind of cylindrical shell accurately.In order to solve the above problems,the vibration and buckling problems of the composite cylindrical shell under thermal,magnetic,electrical and elastic loads are studied.The Hamiltonian solution model of the free vibration and buckling problems of cylindrical shell is established and the corresponding analytical solution is derived.The influence of key design parameters on the frequency and critical buckling load is analyzed.A new direct solution method for the vibration and buckling problems of composite cylindrical shells with multi-field coupling is formed.This doctoral thesis mainly includes the following three aspects:(1)A unified Hamiltonian solution model for the vibration and buckling problems of elastic,piezoelectric and magneto-electro-elastic composite cylindrical shells is established.Based on the Hamiltonian variational principle,the basic equations of vibration and buckling in Lagrangian system are transformed into those in Hamiltonian system by using the basic variables which include the original variables,i.e.,generalized displacement functions(displacement,rotation angle,potential,magnetic potential,etc.)and the dual variables,i.e.,generalized internal force functions(axial force,bending moment,generalized electric displacement,generalized magnetic induction,etc.).The governing equations,which transform the higher-order governing differential equations into a set of lower-order ordinary differentia]equations,are obtained.Different from the traditional inversed method or semi-inversed methods,the Hamiltonian solution model based on symplectic method does not need to be solved by the pre-determined functions,and is not limited by the boundary conditions,the derivation process is rigorous and the solution process is rational.(2)The analytical solutions of the vibration and buckling of the composite cylindrical shell with thermal,magnetic,electrical and elastic loads are obtained.In Hamiltonian system,the free vibration and buckling of composite cylindrical shells with multi-field coupling loads are directly reduced to the eigenproblems in symplectic space.The frequency/critical buckling load and the corresponding vibration mode shape/buckling mode shape can be expressed by symplectic eigenvalues and eigensolutions,respectively.Therefore,the separation variable method can be directly applied to obtain the analytical solution of the free vibration and buckling with the form of series expansion of symplectic eigensolutions.It should be pointed out that the form of symplectic eigensolutions is depended on geometric parameters,material parameters and boundary conditions.Therefore,the analytical solutions of vibration and buckling problems of multi-field coupled composite cylindrical shells have several mathematical forms.The numerical results show that the solution of traditional inversed method or semi-inversed method is only one case of the solution of this paper.(3)The effects of design parameters such as geometrical parameters,material parameters,boundary conditions and multi-physical field loads on free vibration frequency and critical buckling load are analyzed.The control of vibration and buckling of multi-field coupled composite cylindrical shell by external magnetic,electrical,thermal and elastic coupling loads is proposed.The results show that the applied magnetic potential,voltage and temperature rise significantly affect the vibration and buckling characteristics of the composite cylindrical shell.The frequency and critical buckling load increase with the increase of magnetic potential,and decrease with the increase of voltage and temperature rise.The frequency and critical buckling load of multi-field coupled composite cylindrical shell have different sensitivity to the magnetic potential,voltage and temperature rise under different distribution profiles and distribution models.Reasonable selection of the above design parameters can realize the regulation of free vibration frequency and buckling load of this kind of cylindrical shell.