简谐荷载作用下粘弹性梁振动的非线性动力学模型及其简化  

A nonlinear dynamic model of vibration for viscoelastic beam under simple harmonic load and its simplification

作　　者：陈姗[1] 琚宏昌[2] 

机构地区：[1]广西科技大学土木建筑工程学院,广西柳州545006 [2]广西科技大学鹿山学院土木工程系,广西柳州545616

出　　处：《广西科技大学学报》2014年第4期30-33,39,共5页Journal of Guangxi University of Science and Technology

基　　金：国家自然科学基金项目(51168006);广西自然科学基金(面上项目)(2011GXNSFA018024);广西柳州市应用技术研究与开发计划项目(2010020603)资助

摘　　要：为了研究简谐荷载作用下粘弹性梁振动的非线性动力学行为,建立了相应的粘弹性梁横向振动非线性动力学模型.考虑粘弹性材料采用微分型本构关系,针对简谐荷载作用下的两端简支梁,给出了基于牛顿第二定律和欧拉-伯努利(Euler-Bemoulli)假定的横向振动非线性动力学模型—非线性偏微分方程.同时,引入微分求积法(DQM)将其方程进行空间域的离散,得到了粘弹性简支梁横向振动的常微分方程简化模型.In order to study the nonlinear dynamic behavior of vibration of viscoelastic beams under simple harmonic load,this paper establishes the corresponding nonlinear dynamic model of transverse vibration of a viscoelastic beam.Considering that viscoelastic material obeys the differential type constitutive relation for the simply supported beam under simple harmonic load,the nonlinear dynamic model of transverse vibrationnonlinear partial differential equation based on the Newton's second law and the Euler-Bernoulli assumption is given.At the same time,by introducing the differential quadrature method(DQM),the equations are discreted airspace;we can gain the simplified model of ordinary differential equations of transverse vibration of viscoelastic simply supported beam.

关 键 词：粘弹性梁 简谐荷载 偏微分方程 本构关系 微分求积法 

分 类 号：TU323.3[建筑科学—结构工程]