【摘要】 以黏弹性力学理论为基础,首先推导出黏弹性地基上黏弹性梁振动的一般方程;然后忽略梁的黏性,但考虑地基的黏性,提出分析该地基梁的自由振动的方法,该方法适用于具有N个标准线性体通过串联或并联而构成的一般线性体地基,且具有通用性,可进一步用于分析地铁区间隧道类复杂结构由于列车行进引起的受迫振动等问题。在此基础上,推导出三参数标准线性体地基梁满足任意边界条件和任意初始条件的结果;最后给出数值算例,并对数值结果进行分析。算例表明,采用分离变量的级数解法,级数收敛很快,一般只要取前两项即足够满足工程要求。更多还原

【Abstract】 Based on the viscoelasticity theory,the general partially differential vibration equation is deduced for the viscoelastic beam on the viscoelastic foundation at first.Then,the method to analyze the free vibration of the foundation beam is put forward under circumstances neglected to the viscosity of the beam,but considering the viscosity of the foundation.This method adapts to the general linear foundation which is composed of N-standard linearity by means of series connection or/and parallel connection,and can be used more widely to analyze complicated structures,such as underground railway tunnel,whose compelled vibration induced by moving train.After this,the results are deduced in detail of an elastic beam on a 3-parameter standard linear foundation subjected to arbitrary boundary conditions and to arbitrary initial conditions.In the end,a numerical analyatic example is given to illustrate the validity of this method.The example shows that with the technique which separating one variable into two,the sequence converges so rapidly that,in ordinary cases,only two series should be taken to meet the requirements of a project.更多还原