粘弹性Timoshenko梁非线性动力学行为的微分求积分析

Differental quadrature method for nonlinear dynamical behavior of a viscoelastic Timoshenko beam

对有限变形条件下,Timoshenko粘弹性梁非线性分析的数学模型应用推广的微分求积方法进行空域的离散,得到了简洁的矩阵形式的非线性数值逼近公式,时域上引进新的变量,得到了简支粘弹性梁运动的简化模型。然后利用非线性动力学中数值方法,分析了粘弹性Timoshenko梁的动力学行为。同时,为表明该方法的可靠性和有效性,研究了DQ解的收敛性和精确性。并考察了梁的材料、几何等参数对非线性粘弹性梁的动力学特性的影响。

By the extended differential quadrature(DQ)method,the motion equations governing the dynamical behavior of a visco-elastic beam with finite deformations were discretized,and the nonlinear governing equations could be converted into an explicit matrix form in spatial domain.The dynamic behaviors of the visco-elastic beam were numerically analyzed by introducing new variables in time domain.The classical methods in nonlinear dynamics were applied to reveal dynamical phenomena of the visco-elastic beam.The convergence and comparison of solutions were studied.The results showed that the DQ method presented here is very reliable and effective;at the same time,the influences of geometric and material parameters on dynamic behaviors are investigated.