动态刚度阵法在船体总振动计算中的应用

采用动态刚度阵法计算船体总振动的固有频率.该方法不但能简化计算模型,而且能获得较高精度的高阶固有频率.首先通过直接求解等直Timoshenko梁单元的运动微分方程,导出考虑剪切变形和转动惯量影响的平面梁单元动态刚度阵的解析表达形式;其次采用Wittrick-Williams算法结合二分法求解特征值;最后采用本方法计算299 500DWT超大型油船船体总振动的固有频率,并分别与一维梁有限元法和三维全船有限元法计算结果以及实测值进行比较,验证了方法的精确性和有效性.

Application of dynamic stiffness matrix method to compute the vibration of ship hull

Dynamic Stiffness Matrix Method is applied to compute vibration of ship hull.This method can not only simplify the computational model,but also get much higher frequencies accurately.Firstly,the analytical expressions of dynamic stiffness matrix of plane beam for transverse vibration with considering the shear distortion and rotary inertia of mass are presented by directly solving motion differential equations of a uniform Timoshenko beam.Secondly,the frequency characteristic equation is solved by the bisection method and Wittrick-Williams algorithm.Finally,the vibration of 299 500 DWT VLCC crude oil tanker ship hull is computed by this method.Compared with one-dimensional FEM model,three-dimensional FEM model and experiment,the numerical example demonstrates that the presented method is accurate and effective.