Research On Dynamic Characteristics Of Composite Piezoelectric Laminated Structures Subjected To Arbitrary Elastic Boundaries

Piezoelectric composites composed of piezoelectric materials and organic polymers,which have both stable piezoelectric properties of inorganic piezoelectric materials and excellent properties of piezoelectric macromolecule materials,have attracted much attention due to their excellent electrodynamic coupling properties.The piezoelectric and dielectric properties of piezoelectric composites depend on the material,component ratio,connection mode and other factors of single-phase,and the comprehensive properties are far better than those of each component materials,showing the overall characteristics of strong piezoelectric property,low dielectric coefficient,low brittleness and low density,etc.The appearance of piezoelectric composites has expanded the material domain space of laminated structure.Composite laminated piezoelectric structures have been widely applied in various military and civil fields due to their advantages of general composite laminated structures and intelligent components.In recent years,the research on laminated structure of piezoelectric composites has gradually become a frontier hotspot.Classical boundary conditions,such as free boundary,simply supported boundary and fixed supported boundary,are usually considered when studying the dynamic characteristics of composite piezoelectric laminated structures,but the mechanical properties under other boundary conditions such as arbitrary elastic boundary are rarely analyzed.This deviation from reality is difficult to provide sufficient theoretical support for engineering applications.In addition,most of the existing studies focus on the dynamic properties of beam,plate and shell structures under the condition of no elastic foundation.However,ignoring the impact of the foundation on the dynamic properties of the structure may result in a certain degree of deviation in the calculation results.These problems have not been included in the existing analytical methods for composite piezoelectric laminated materials,and there is a lack of reasonable and consistent analytical model,framework and process.Therefore,it is not only of great theoretical significance,but also of necessary reference for practical application to establish a more perfect and unified analysis model,develop a concise and efficient analysis method,and comprehensively and deeply investigate the dynamic characteristics under arbitrary elastic boundary and foundation support conditions for composite piezoelectric laminated structures.In this paper,based on the classical piezoelectric lamination theory(CPLT)and the high-order shear deformation piezoelectric lamination theory(HSDPLT),the dynamic characteristics of composite piezoelectric laminated beam,plate and shell structures are studied and analyzed by using Hamilton principle.The main research contents are as follows:First of all,based on the piezoelectric plane hypothesis,a unified analysis model of piezoelectric laminated beams with arbitrary elastic boundary and elastic foundation is established,and the inherent characteristics of such structures are deeply studied.Firstly,the global coordinate system and the local dual coordinates of the structure are established respectively by using the MRRM.According to the coordinate transformation relations,the phase and scattering relationship of the laminated piezoelectric beam under the condition of exact solution are derived,and the structural system equation is obtained.Secondly,the differential quadrature method(DQM)is used to discretely obtain the semi-analytic solution of the state equation of the laminated piezoelectric beam under non-simply supported conditions.The transfer equation of the whole structure is given in combination with the continuity condition between the layers of the structure,thus the system equation of the laminated piezoelectric beam is established.Finally,the variation trend of the inherent characteristics of the structure under different geometrical material parameters and elastic foundation parameters is discussed using finite element analysis method by an example,the influence rule of parameters is revealed,and the analysis results are verified by experiments.Secondly,based on different theories of laminated piezoelectric beams,a unified analysis model of composite piezoelectric laminated beams with arbitrary elastic boundary and elastic foundation conditions is established,a concise and effective analysis framework and process based on MRRM are constructed,and the inherent characteristics and transient behavior of such structures are investigated.Further,the external interference such as material parameters of orthogonal laying ratio and anisotropic ratio of structure,the geometric parameters of number of layers and laying angles,boundary conditions and elastic foundation parameters,is studied in detail by example analysis.The inherent characteristics of the structure and the influence rule of transient response are revealed,and the correctness and convergence of the relevant calculation results are verified by experiment.Thirdly,based on different theories of laminated piezoelectric plates,a unified analysis model of composite piezoelectric laminated rectangular plates with arbitrary elastic boundary and elastic foundation conditions is established,the analysis process based on MRRM is presented,and the inherent characteristics and transient behavior of such structures are deeply studied.Further,the effects of orthogonal laying ratio,anisotropic ratio and elastic foundation parameters on the inherent characteristics of the structure are discussed by an example,and the effects of orthogonal laying ratio,anisotropic ratio,number of layers and boundary spring stiffness on the transient behavior of the structure are revealed.Finally,based on the first order shear piezoelectric shell theory,a unified analysis model of composite piezoelectric laminated cylindrical shells with arbitrary elastic boundary and elastic foundation conditions is established,the analysis framework based on MRRM is presented,and the overall system equation of the structure is derived.Furthermore,the torsional vibration characteristics of the composite piezoelectric laminated cylindrical shells are deeply analyzed,the geometric,material and piezoelectric parameters of the structure are compared through numerical calculation and finite element simulation,and the influence rules of relevant parameters are revealed.In this paper,considering arbitrary elastic boundary and elastic foundation conditions,a unified dynamic analysis model is established and a unified analysis process is given,which enriches and improves the theoretical research framework of this kind of structure.On this basis,through detailed analysis of these composite piezoelectric laminated structures,the paper also fully reveals the inherent characteristics and transient behavior characteristics,as well as the influence rule of material structure parameters and external conditions,thus providing a reference for engineering applications.