粘弹性智能结构非线性动力系统的建模及小波方法研究

项目名称： 粘弹性智能结构非线性动力系统的建模及小波方法研究

项目编号： No.11302081

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 王晓敏

作者单位： 华中农业大学

项目金额： 25万元

中文摘要： 粘弹性材料和结构以其良好的耗散性能和阻尼性能等优点在智能振动控制系统设计中受到高度重视，被广泛应用于航空、航天、建筑等大量现代工程和科学装置的振动控制中。由于这类材料自身的分数导数型本构关系特性及其随分数导数参数、结构非线性特征与系统力学行为相关性所导致的复杂性，使这类系统的设计应用受到严重制约。申请人在前期研究中发现小波在结构静动力学问题分析与微分方程求解中具有精度高、计算量小的特点。本项目在已有研究成果基础上，着重研究在考虑分数导数型本构关系下粘弹性智能结构非线性问题的力学模型及高精度定量分析方法。建立描述这类问题的分数阶导数力学模型，并应用小波这一新的数学工具，对与之相应的动力学方程进行求解，对系统力学行为与分数导数参数、非线性特征之间的关系进行定量分析，对系统模型进行数值仿真，从而为粘弹性结构的设计与可靠性分析提供理论依据，以达到为这类材料的智能振动控制应用建立有效的力学分析途径。

中文关键词： 粘弹性智能材料；梁板结构；非线性；分数阶导数；小波方法

英文摘要： Viscoelastic materials and structures with advantages of good dissipation properties and damping performance are highly valued in the design of smart vibration control system, and are widely used in the vibration control of a large number of modern engineering and scientific devices, such as, aviation, aerospace, construction and so on. Due to the complexity of such material with characteristics of the fractional order constitutive relations and the correlation between the mechanical behaviors of its system and the fractional derivative parameters or the nonlinear characteristics, the designs and applications of such systems are severely constrained. In preliminary studies, the applicant found that the wavelet analysis is efficient in quantitative analyzing the static and dynamic problems of the structures, and solving the fractional nonlinear differential equations with high precision and small amount of calculations. On the basis of existing research, the project focuses on the modeling and quantitative analysis method of the nonlinear problems of viscoelastic smart structure by considering the fractional derivative constitutive relations. Establish the mechanics model containing fractional order for describing this kind of problems, then, apply the wavelet which is a new mathematical tool to solve the corres

英文关键词： Viscoelastic smart materials；Beam and flat structure；Nonlinear；Fractional order；Wavelet method