典型边界条件下加筋矩形板的横向振动特性分析

Analysis of transverse vibration characteristics for stiffened rectangular plates with classical boundary conditions

采用能量法研究典型边界条件下加筋矩形板的横向振动特性。将矩形板、加强筋沿交界面切开,分别采用薄板弯曲理论和欧拉梁理论建立其横向振动的总能量方程,利用第一类切比雪夫多项式构造矩形板的位移试函数,由Rayleigh-Ritz法得加筋矩形板的横向振动特征方程。数值计算结果表明,该方法收敛性好,与有限元软件ANSYS和已有文献的对比显示了高精度,并可以得到任意阶次的固有频率,具有计算简单的特点;最后分析了加强筋位置和加强筋高度对加筋方板无量纲自振频率的影响。

The transverse vibration characteristics of stiffened rectangular plates with classical boundary conditions were studied using the energy method.The stiffened rectangular plate was divided into two parts along the interface of the plate and stiffeners.The total energy equation for the transverse vibration of the stiffened plate was established based on the flexural theory for the thin plate and the Euler beam theory for the stiffeners.The first kind of Chebyshev polynomials was used to construct the displacement functions for the stiffened rectangular plate.The eigenvalue equations of the stiffened rectangular plate were derived by using the Rayleigh-Ritz method.Numerical results indicated good convergence of the present method.High accuracy was demonstrated by comparing with the available results in literature and those from the finite element software ANSYS.Any number of frequencies can be obtained with simple calculation.The effects of the position and height of the stiffener on the non-dimensional natural frequency of the stiffened square plates were studied.