简支梁及其电测传感器在移动横载下的动响应

DYNAMIC RESPONSES OF THE ELECTRICAL MEASURING SENSOR AND THE SIMPLY-SUPPORTED BEAM WITH TRANSVERSE MOVING LOAD

粱在移动横向集中载荷作用下的动力学响应在桥梁的强度和刚度设计及强度和刚度校核中都是非常重要的实际问题。电测传感器测量技术无疑是检测结构应力的非常成熟的方法之一,合理设计电测传感器往往是建立在理论分析基础之上的,但给出问题的理论解却是有一定的困难。首先建立了问题的定解数学模型;由问题的线性特点将问题分解为两个子问题;而后利用分离变量法和固有函数法分别给出了两个子问题的解析解,通过一个算例得到了粱的挠度响应、应力响应和某点处电测传感器的电容随时间的变化,说明了动力效应的重要影响,方法可推广用于粱上移动弹性系统的动力响应问题研究,给出的理论分析解对于开发设计新型电测传感器有一定的参考指导意义。

The dynamic responses of the beam under the function of the moving loads are very important practical problem in the strength and stiffness designs and the strength and stiffness checks. The measuring technology of the sensors is no doubt one of the ripe methods in the detections of the structural stresses, The reasonable designs of the electrical measuring sensors are often based on the theoretical analyses, but the theoretical solution of this kinds of problems are often hard to be given. In this paper, the definite mathematical model was proposed before hand; and the model can be divided into two sub-problems considering of the linearity of the problem, then the method of separation of variables and the inherent function method were used to give the theoretical solutions respectively, an numerical example were introduced to give the deflection responses and the stress responses of the simply-supported beam and the dynamic responses of the capacitor of the sensor in order to illustrate the important effects of the dynamic effects. This method can be extended to study the dynamic responses of the beam with an elastic system moving on it. , the given theoretical conclusions have some references to the designs of new electrical sensors.