海洋顺应式结构的非线性自由振动分析

NONLINEAR FREE VIBRATION OF A COMPLIANT STRUCTURE

将海洋平台中顺应式结构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,在小变形和大转角的假定下,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。在Morison方程的基础上研究了流体力的作用效应。运用有限差分法和Runge-Kutta法得到了方程数值解,分析了梁在真空中和在水中无阻尼、有阻尼的自由振动,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。

A compliant structure in the ocean environment is modeled as a 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, accurate angle and large deflection, nonlinearly coupled equations of motion and boundary conditions are derived. The fluid forces are modeled using a semi-empirical Morison equation. The free response in vacuum and the free response in still water without and with damping are analyzed through finite difference approach and Runge-Kutta method. The results of the nonlinear structures with both accurate angles and approximate angles and the linear structures are compared, respectively.