用GDQ空-时半解析法分析圆弧拱强迫振动

从圆弧拱的强迫振动控制方程出发,在空间域采用广义微分求积法,将广义微分求积法中的节点参数在时域内取为响应的时间级数,通过时域配点求解该六阶偏微分方程得到全域内的响应位移场,分析了圆弧拱的平面内强迫振动问题。运用Matlab语言编制圆弧拱强迫振动时程分析的计算程序,并进行了相应的算例分析,数值计算结果表明该方法对于求圆弧拱的强迫振动问题具有较高的精度和效率。

Forced Vibration Analysis of a Circular Arch by GDQ Space-time Semi-analytical Method

Starting with the forced vibration governing equations for a uniform cross-section circular arch with the consideration of tangential inertia effect,the solution of displacement response of the arch is obtained.In this solution,the generalized differential quadrature method in space domain is adopted.The response at each node is expressed as time series in time domain.Then,a set of sixth-order partial differential equations is obtained and solved by means of collocation method in the time domain.Finally,solution of the displacement response field is obtained.The in-plane forced vibration problem of the circular arch with appropriately prescribed boundary constraint conditions is analyzed.A program is written in Matlab code for solving this problem.And some numerical examples are given.The results indicate that this method has the advantages of higher accuracy and efficiency for forced vibration analysis of circular arches.