黏弹性地基上变截面Timoshenko梁稳态谐振动分析

Analysis of the Steady-state Harmonic Vibration of TimoshenkoBeam with Varying Cross Sections on Viscoelastic Foundation

运用微分求积法研究了黏弹性地基上变截面Timoshenko梁横向稳态谐振动响应,分析了地基参数对梁位移和内力的影响。首先,基于Timoshenko梁理论,建立了黏弹性地基上变截面Timoshenko梁横向稳态谐振动的复变系数常微分方程组,然后基于微分求积法原理将梁的复变系数常微分方程组的两点边值问题转化为一组含复变系数的线性代数方程组求解问题。研究通过算例验证了所提方法分析梁横向稳态谐振动响应问题的可行性和精确性,同时,以黏弹性地基上变截面Timoshenko悬臂梁为例,定性分析了地基弹性系数、地基剪切系数及地基阻尼系数对Timoshenko梁位移与内力的影响。

The transverse steady-state harmonic vibration response of Timoshenko beam with varying cross-section on viscoelastic foundation is studied by using differential quadrature method and analyzing the influence of foundation parameters on displacements and internal forces of the beam.Firstly,based on the theory of Timoshenko beam,a set of ordinary differential equations with complex variable coefficients for transverse steady harmonic vibration of a variable cross-section Timoshenko beam on viscoelastic foundation is established.Then,based on the differential quadrature method,the two-point boundary value problem of ordinary differential equations with complex variable coefficients of beams is transformed into a set of linear algebraic equations with complex variable coefficients.The feasibility and accuracy of the method to analyze the transverse steady-state harmonic vibration response of the beam are verified by an example.Meanwhile,taking the varying cross-section Timoshenko cantilever beam on viscoelastic foundation as an example,the influence of the elastic coefficient,shear coefficient and damping coefficient about foundations on displacement and internal force of Timoshenko beam is qualitatively analyzed.