Winkler-Pasternak弹性地基梁自由振动的二维弹性分析

基于二维线弹性理论,应用Hamilton原理,获得Winkler-Pasternak弹性地基梁自由振动的控制微分方程,应用微分求积法(DQM)数值研究了梁自由振动的无量纲频率特性。计算结果与已有的结果(Bernoulli-Euler梁和Timoshenko梁)比较表明,本文的分析方法对弹性地基长梁和短梁自由振动的研究都有效。最后考虑了几何参数对梁频率的影响,以及不同边界条件下地基系数对频率的影响和收敛性。

Two-dimensional elastic analysis for f ree vibration of beams set on winkler-pasternak elastic foundations

Based on the two‐dimension linear elasticity theory and applied the Hamilton's principle ,the governing differential equations of free vibration for beam set on Winkler‐Pasternak elastic foundation are derived .Using differential quadrature method (DQM ) ,the free vibration dimensionless frequencies of beams are investigated numerically .With application of DQM in this paper ,it illustrated that the method was validated and accurate for Bernoulli‐Euler beams as well as for Timoshenko beams by comparison of previously reported results .Finally ,the effect of the geometrical parameter on the non‐dimensional frequency parameter of the beams ,the influence and the convergence for dimensionless frequency owing to elastic coefficients of foundation under different boundary conditions are considered .