Timoshenko梁在热冲击下的瞬态动力响应

TRANSIENT DYNAMIC RESPONSE OF TIMOSHENKO BEAMS UNDER THERMAL SHOCK

研究了矩形截面简支Timoshenko梁在热冲击载荷作用下的动力响应。首先由分离变量法求得了梁的温度响应,然后采用微分求积法(DQM)分别对位移形式的动力学方程及初边值条件在空间域和时间域进行离散。数值求解离散后的代数方程组,得到了梁在热冲击下的动态位移和应力响应。分析了相关物理和几何参数对动态位移响应和动态应力响应的影响,考察了数值结果的收敛性。数值结果表明,对该类问题采用DQ法求解具有简洁可靠、计算效率高的特点。

Transient dynamic response of Timoshenko beams with rectangular cross sections subjected to thermal shock was studied. The temperature rise response of the beam was obtained with the method of variables separation. Then, the dynamic equations associated with the boundary and initial conditions in terms of the beam displacements were discretized both in spatial and time domains by using differential quadrature method (DQM). Dynamic responses of the transverse displacement and the normal stresses of the beam under thermal shock were attained by solving the discrete algebraic equations numerically. Effects of the physical and geometrical parameters on the thermal shock responses were analyzed and convergence of the numerical result was also examined. Numerical results show that DQM is simple, effective and reliable in dealing with the thermal shock problem of elastic beams.