黏弹性三参数地基梁横向自由振动

摘要

Extending the complex modal approximate analysis to the vibration of foundation beams,transverse vibrations of three-parameter viscoelastic Pasternak foundation beams were studied.Complex frequency equations and modal function expressions were obtained for beams with clamped-clamped, clamped-pinned and free-free ends. Numerical methods were employed to approximately solve the transcendental equations,and differential quadrature scheme was applied to verify the approximate results.The effect of boundary conditions,stiffnesses and viscoelastic coefficients on natural frequencies and modal functions were analyzed and described by numerical examples.The numerical results obtained by using the differential quadrature and the complex mode methods are in good agreement.%将复模态方法推广至地基梁系统的振动分析中，研究了三参数描述的黏弹性Pasternak地基梁的横向振动特征，得到不同边界条件下的频率方程的近似解析式以及模态函数表达式。采用数值方法近似求解复模态分析得到的超越方程，并运用微分求积方法数值加以验证。通过具体算例，分析了边界条件、刚度系数以及地基黏性系数等对固有频率和模态函数的影响。研究结果表明，微分求积法的数值解与复模态的近似解析解吻合的很好。