两种波浪理论下铰接塔平台的非线性运动特性分析  

ANALYSIS OF NONLINEAR DYNAMIC BEHAVIORS OF AN ARTICULATED TOWER PLATFORM UNDER TWO WAVE THEORIES

作　　者：沈纪苹[1] 杨骁[2] 

机构地区：[1]上海市应用数学和力学研究所,上海200072 [2]上海大学土木工程系,上海200072

出　　处：《工程力学》2011年第6期242-248,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10872124/A020601);上海市重点学科建设项目(Y0103);上海市自然科学基金项目(06ZR14037)

摘　　要：将铰接塔平台简化为底端具有线扭转弹簧支撑,顶端附有集中质量块的水中柔性梁。采用连续介质力学方法,在小变形假设下,应用大挠度理论建立了梁的非线性耦合运动控制方程和边界条件。基于Airy线性波理论和二阶Stokes波理论,应用Morison方程计算梁在水中所受的水动力。运用有限差分法和Runge-Kutta法得到了方程数值解,分析了两种波浪理论下梁的非线性振动特性,讨论了二阶Stokes波的非线性项对运动特性的影响,并对大挠度理论下非线性结构与横截面转角近似下非线性结构及线性结构进行了比较。An articulated tower platform is modeled as a flexible beam supported by a linear-elastic torsional spring at the base and with a point mass at the free end.Using the method of continuum mechanics and on the basis of small deformation and large deflection,nonlinearly coupled equations of motion and boundary conditions are derived.The fluid forces are modeled using a semi-empirical Morison equation under Airy wave theory and second-order Stokes wave theory.The nonlinear vibrations under two wave theories are analyzed through a finite difference approach and the Runge-Kutta method.The influences of nonlinearity of the second-order Stokes wave theory on the vibrations are studied,and the results of the nonlinear structures with accurate angles and with approximate angles and the linear structures are compared.

关 键 词：柔性梁 大挠度 非线性耦合 二阶Stokes波理论 有限差分法 主共振 超谐共振 

分 类 号：O322[理学—一般力学与力学基础] TV312[理学—力学]