力电耦合软固体与结构中的线性和非线性波动

项目名称： 力电耦合软固体与结构中的线性和非线性波动

项目编号： No.11272281

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 陈伟球

作者单位： 浙江大学

项目金额： 88万元

中文摘要： 本项目拟系统研究有限偏场作用下各向异性力电耦合软固体和结构中的波动现象。首先根据非线性连续介质力学方法，建立偏场作用下各向异性力电耦合软固体的一般线性和非线性波动理论，研究自由能函数多项式展开的具体形式，考察不可压缩、不可伸张等约束对本构表达式的影响。其次，针对杆、梁、板、壳等典型结构，采用级数展开和摄动分析等手段建立高精度的简化结构波动理论。最后，利用所建立的波动理论模型，考察典型线性波（包括表面波、界面波以及其他类型的导波）以及一维非线性波的传播特性，发展有效的分析与求解方法。拟综合考察有限偏场、力电耦合、各向异性、材料非均匀、周期结构、界面特性、尺寸效应等对波动特性的影响，探讨软固体与结构中波传播的调控方法，为软声波器件设计和超声弹性成像等应用提供理论支撑。

中文关键词： 软材料；力电耦合；波动；偏场；非线性分析

英文摘要： The aim of this project is to systematically study various wave propagation phenomena in anisotropic soft electroelastic solids and structures under finite biasing fields. First, basing on the nonlinear continuum mechanics methods, we will establish the general linear and nonlinear theories for wave motion in anisotropic soft electroelastic solids. Attentions will be paid to the polynomial form of free energy function, and the effects of material incompressibility and inextensibility on the expressions of the constitutive relations. Second, for typical structures such as rods, beams, plates and shells, we will construct high-precise, simplifying, structural wave theories by the methods of series expansion and perturbation. With the developed theories, we will investigate the propagation characteristics of some typical linear waves (e.g. surface waves, interface waves, and other guided waves) and of certain one-dimensional nonlinear waves. Effective analysis methods and solution procedures also will be developed. The effects on the wave propagation characteristics of finite biasing field, electroelastic coupling, material anisotropy, material inhomogeneity, periodic structure, interface property, and size-dependence will be studied comprehensively, to explore the methods for tuning waves in soft solids and struct

英文关键词： soft material；electroelastic coupling；wave propagation；biasing field；nonlinear analysis