桩基非线性轴向振动的多时间尺度分析  

MULTI-TIME SCALE ANALYSIS OF NONLINEAR AXIAL VIBRATION OF PILES

作　　者：胡春林[1] 程昌钧[1] 陈中学[2] 

机构地区：[1]上海大学上海市应用数学与力学研究所力学系,上海200072 [2]武汉理工大学土木工程与建筑学院,武汉430070

出　　处：《振动与冲击》2007年第5期54-59,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(50278051);上海市重点学科建设项目(Y0103)

摘　　要：假定桩基及桩周土的材料满足非线性弹性和线性粘弹性本构关系,给出了分析桩基轴向振动的非线性偏微分方程。用多时间尺度法推导出一端固定、另一端自由的桩基非线性轴向自由振动的n-阶主频率和位移的近似表达式,给出了数值算例,考察了参数的影响。研究结果表明:非线性系统的n-阶主频率不仅与线性系统的n-阶固有频率有关,而且也与振幅、阻尼系数和材料的非线性特征量有关;系统的响应中除含有主频率的谐波外,还含有2倍、3倍的主频率的高次谐波和二个或三个主频率的和或差的谐波存在。The nonlinear partial differential equation governing nonlinear axial vibration of piles is given under an assumption of both materials of a pile and soil around it obey nonlinear elastic and linear viscoelastic constitutive relations.The approximate expressions of the nth-order main frequency and the displacement of the nonlinear vibration system with one side fixed and other side being free are obtained by the method of multiple time scales.Numerical examples are given and the effect of parameters is considered.Research results show that the main frequencies of the nonlinear system is related to not only the natural frequencies of the corresponding linear vibration system,but also the amplitude,the damping coefficient and nonlinearity of materials.There are high order harmonic waves with double and triple of the main frequencies as well as sum and /or difference of 2 or 3 main frequencies besides the harmonic waves with the main frequencies in the response of the nonlinear system.

关 键 词：桩的非线性轴向自由振动 主频率和响应的近似表达式 多时间尺度法 参数的影响 

分 类 号：O322[理学—一般力学与力学基础] O343.5[理学—力学]