单向加劲矩形板面内振动特性分析

Analysis of In-Plane Vibration Characteristics for Rectangular Plate Stiffened in Single Direction

采用能量法研究典型边界条件下加劲矩形板的面内自由振动特性。将矩形板、加强筋沿交界面切开,分别采用平面应力理论和欧拉梁理论建立其面内振动的总能量方程,利用第一类Chebyshev多项式构造矩形板的位移试函数,由Rayleigh-Ritz法得加劲矩形板的面内振动特征方程。数值结果表明,本文方法收敛性好,并用本文解验证了有限元软件ANSYS结果的精度。本方法具有计算简单的特点,可以得到任意阶次的固有频率。最后分析了加强筋宽度与板宽比值(b0/b)对加劲板无量纲固有频率的影响。

Dynamic characteristics of in-plane vibration of stiffened plates with classical boundary conditions were studied by the energy method.The stiffened rectangular plate was divided into two parts along the interface of the plate and the stiffeners.The total energy equation of the in-plane vibration of the stiffened plate was established by applying the plane stress theory for the plate and the Euler beam theory to the stiffeners.The first kind of Chebyshev polynomials was used to construct the displacement functions of the stiffened rectangular plate.The eigenvalue equations of the stiffened rectangular plate were derived by using the Rayleigh-Ritz method.Numerical results showed good convergence of the present method.High accuracy of the results obtained from the finite element software ANSYS was demonstrated by comparing with the present results.Any number of frequencies can be obtained if required.The effects of stiffener-width-to-plate-width ratio on the non-dimensional natural frequency of the stiffened square plates were studied.