【作者】 赵磊；

【导师】 舒海生；

【作者基本信息】 哈尔滨工程大学 ， 机械工程， 2021， 博士

【摘要】 压电复合材料由压电材料和有机高分子聚合物构成,兼有无机压电材料稳定的压电性和高分子压电材料的优良性能,因其良好的力-电耦合性能受到了人们的广泛关注。压电复合材料的压电、介电性能取决于单相材料的材质、组分比和连通方式等因素,综合性能远优于各组分材料,整体表现出强压电性、低介电系数、低脆性、低密度等特点,压电复合材料的出现,拓展了层合结构的材料域空间。复合材料压电层合结构因同时具有一般复合材料层合结构及智能构件的优点,在各种军用及民用领域都已有较为广泛的应用前景,近年来针对复合材料压电层合结构的研究已经逐步发展为一项前沿热点。研究人员在考察复合材料压电层合结构的动力学特性时,通常考虑的是自由边界、简支边界或固支边界等常见的经典边界条件,对任意弹性边界条件下此类结构的动力学特性的研究和认识还很有限。同时,已有研究大多针对的是梁、板、壳类结构在自由状态情况下的动力学性能,而在实际工程中此类结构经常会受到各种弹性地基的支撑作用,忽略地基对结构动力学性能的影响可能导致分析结果与实际情况不符。对于复合材料压电层合结构来说,现有此类结构的分析方法尚未将这些问题包括进来,缺乏合理而一致的分析模型、框架和流程。因此,针对复合材料压电层合结构,研究建立更为完善的统一的分析模型,发展简洁高效的分析手段,全面而深入地考察任意弹性边界与地基支撑条件下的动力学特性,不仅具有重要的理论意义,同时也可为实际应用问题提供必要的参考。本文针对上述问题,借助经典压电层合理论(CPLT)及高阶剪切变形压电层合理论(HSDPLT),结合Hamilton原理对复合材料压电层合梁、板、壳类结构的动力学特性进行了研究与分析。具体研究工作如下:1)针对压电层合梁模型,基于压电平面假设理论,建立了任意弹性边界和弹性地基条件下的统一分析模型,深入研究了此类结构的固有特性。首先,利用回传射线矩阵法(MRRM)分别建立了结构的总体坐标系和局部对偶坐标系,根据坐标系间的变换关系推导了压电层合梁结构在精确解情况下的相位关系和散射关系,进而得到了结构系统方程;其次,对于非简支条件情况下的压电层合梁结构,采用微分求积法(DQM)将结构状态方程进行离散得到了其半解析解,并结合结构层间连续性条件给出了整体结构传递方程,从而建立了压电层合结构的系统方程;最后,通过算例并结合有限元分析方法探讨了不同几何材料参数和弹性地基参数下结构的固有特性变化趋势,揭示了参数影响规律,并通过实验对分析结果进行了验证。2)针对复合材料压电层合梁结构,基于不同的压电层合梁理论,建立了考虑任意弹性边界和弹性地基的统一分析模型,并利用MRRM构建了简洁有效的分析框架和流程,考察了此类结构的固有特性和瞬态行为。通过算例分析对结构正交铺设比和各向异性比等材料参数、铺设层数和铺设角度等几何参数以及边界条件和弹性地基参数等外界干扰进行了细致的研究,揭示了结构的固有特性与瞬态响应的变化规律,并通过实验验证了相关计算结果的正确性与收敛性。3)针对复合材料压电层合矩形板结构,基于不同的压电层合板理论,建立了类似的统一分析模型与分析流程,深入研究了此类结构的固有特性和瞬态行为。讨论了正交铺设比、正交各向异性比以及弹性地基参数对结构固有特性的影响,并揭示了正交铺设比、正交各向异性比、铺层层数以及边界弹簧刚度等对结构瞬态行为的影响。4)针对复合材料压电层合圆柱板壳结构,基于一阶剪切压电柱壳理论,构建了带有任意弹性边界和弹性地基的统一分析模型,推导得到了结构的总体系统方程。进一步,针对复合材料压电层合圆环结构这一特殊情形,深入分析了此类结构的扭振特性,通过数值计算与有限元仿真对结构几何参数、材料参数和压电参数进行了细致的对比分析,揭示了相关的参数影响规律。综上,本文针对复合材料压电层合梁、板、壳类结构,将任意弹性边界条件和弹性地基等考虑进来,建立了统一的动力学分析模型,给出了统一的分析流程,从而充实和完善了此类结构的理论研究框架。在此基础上,通过对这些复合材料压电层合结构物的细致分析,本文还较为全面地揭示了固有特性和瞬态行为特性,以及材料结构参数及外部条件的影响规律,从而为工程应用提供了参考。更多还原

【Abstract】 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.更多还原