随机参数梁在考虑热弹耦合下的动力响应分析

以随机参数梁为研究对象，分析其在温度载荷和力载荷共同作用并考虑热弹耦合关系时的动力响应。建立了热弹耦合动力学有限元模型，给出了在时间域内差分离散、相互交替迭代的耦合计算方法。利用随机因子法推导了结构温度场和动力响应的数字特征表达式，其中温度场的求解利用θ 时间积分法，动力响应则利用Newmark-β 积分法。在求出结构各时间步温度场和动力响应数字特征的基础上，应用耦合算法获得了整个时间域内的结构响应数字特征。通过悬臂梁算例分析了热弹耦合项对动力响应的影响，并考察了诸随机参数分散性对结构动力响应分散性的影响。

DYNAMIC RESPONSE ANALYSIS OF STOCHASTIC BEAM STRUCTURES UNDER THERMOELASTIC COUPLING

To research the beam with random parameters, its dynamic response has been analyzed under both a thermal load and a force load when considering the effect of thermoelastic coupling. The dynamic model considering thermoelastic coupling is set up using the finite element method, then a coupling calculate method is proposed which make use of the finite difference method in the time domain and alternative iteration in each time step. The computational expressions for the numerical characteristics of the temperature field and dynamic response are derived by using the random factor method. Temperature field is worked out by applying the time integral method, while the dynamic response can be found through Newmark-βintegral method. Base on the numerical characteristics expressions of a temperature field and the dynamic response in each time step, the expressions in a whole time domain are obtained by using coupling algorithm. Finally, a cantilever beam is taken as an example and the influence of the dynamic response due to thermoelastic coupling and randomness of the parameters is presented.