四边固定加劲板的非线性自由振动

NONLINEAR FREE VIBRATION OF STIFFENED PLATE WITH FOUR EDGES CLAMPED

针对工程中常用的加劲板,研究了非线性振动的求解方法与振动特性.将加劲板分为板与加劲肋两个部分考虑,其中板视为考虑几何非线性的大挠度板,加劲肋视为Euler梁.假定加劲板的位移,利用Lagrange方程结合系统能量和振型叠加推导了加劲板的动力平衡方程.运用椭圆函数及摄动法计算加劲板非线性振动的单模态解,多模态解则通过增量迭代法进行求解.最后,结合有限元软件ANSYS对一个四边固定且不可移动的加劲板进行分析,讨论解的收敛性,并分析两个方向设置不同数量加劲肋的情况下非线性自振频率与振幅的关系,得到了一些加劲板非线性振动特性.

One approach is presented to study the nonlinear free vibration characteristic of stiffened plates. The stiffened plate is divided into plate and stiffeners. The plate is considered to be geometrically nonlinear, and the stiffeners are taken as Euler beams. Assuming the displacement of the stiffened plate, Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. The single-mode results are obtained through Elliptic function and the perturbation method, and the multimode results are obtained through incremental-iterative methods. At last, a stiffened plate with four immovable clamped edges is studied through both the present approach and FE software ANSYS. The convergence of solution is analyzed, and the relationship between nonlinear natural frequency and its amplitude is discussed when the number of stiffeners in the two direction is different. Some nonlinear vibration characteristics of stiffened plate are obtained, which can provide references for engineering design.