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采用半解析法计算了横截面积、横截面的惯性矩沿轴线方向以幂函数规律变化的一类变截面梁的固有频率和振型,通过与有限元法的计算结果比较说明了半解析解的精确性。在此基础上,考虑牵连惯性力、相对惯性力、科氏力和离心惯性力的影响,推导了变截面梁受移动质量作用的横向弯曲振动方程,并采用Newmark法进行数值求解。以某梁式结构受移动质量作用为例,将其简化为横截面积和惯性矩沿轴线按任意次幂函数变化的变截面梁,结果表明:该方法能够正确、有效地处理此类问题。
The semi-analytical method was used to calculate the natural frequency and mode shape of a kind of variable cross-section beam whose cross-sectional area and moment of inertia of the cross-section changed by power function in the axial direction. Comparing with the finite element method, The accuracy of On this basis, considering the influence of the implicated inertial force, relative inertial force, Coriolis force and centrifugal inertial force, the transverse bending vibration equation of the variable cross-section beam subjected to moving mass is deduced, and the Newmark method is used to solve the problem. Taking the moving mass effect of a beam structure as an example, this method is simplified as a variable cross-section beam with cross-sectional area and moment of inertia varying along an arbitrary power function along the axis. The results show that this method can deal with such problems correctly and effectively.