弹性边界约束加筋板结构振动特性与功率流分析

Analysis of Vibration Characteristics and Power Flow of a Stiffened Plate Structure with Elastic Boundary Restraints

从能量传输角度开展弹性边界约束条件下加筋薄板结构振动特性研究。加筋薄板结构振动系统横向振动位移采用边界光滑傅里叶级数展开,在加筋薄板端部引入平动约束弹簧与旋转约束弹簧,通过设置约束弹簧的刚度数值模拟任意边界条件。基于能量原理描述弹性边界约束加筋薄板结构振动系统的总势能、总动能与外激励做功项,结合瑞利-里兹方程得到系统的标准特征方程,弹性边界约束加筋薄板结构的振动响应特性可以通过求解标准特征方程得到。通过数值算例,验证本方法在求解弹性边界约束下加筋薄板结构振动特性的准确性,探究加强筋位置、高宽比以及边界约束弹簧刚度对系统振动特性、能量流响应的影响规律。本方法具有快速收敛、高效、高精度的特点,可为研究弹性边界约束加筋薄板结构动力学行为提供有效分析手段。

The vibration characteristic of the stiffened thin plate structure with elastic boundary constraints is studied by means of the energy method.The transverses vibration displacement of the structure is expressed by the boundary smoothed Fourier series.Translational restraint springs and rotational restraint springs are introduced at the boundary of the stiffened thin plate,and arbitrary boundary conditions can be simulated by adjusting the stiffness of the restraining springs.The total potential energy,total kinetic energy,and the external excitation work terms of the stiffened thin plate structure with elastic boundary constraints are presented according to the energy principle.Then,the vibration behavior of the stiffened thin plate structure with elastic boundary conditions are obtained by solving the standard characteristic equations with the Rayleigh-Ritz method.Via the numerical examples,the correctness and reliability of the current model in solving the vibration characteristics of the stiffened plate with elastic boundary conditions is verified.The influence of the rib position,the aspect ratio,and the boundary restraining stiffness on the plate vibration characteristic and power flow behavior are studied.Current method shows the advantage of fast convergence,high efficiency,and precision,which provides an effective analysis method for studying the dynamic behaviors of the stiffened thin plate structures with elastic boundary conditions.