On the basis of the general problem formulation for an inhomogeneous isotropic body, the problems of steady-state longitudinal-radial and torsional vibrations of a cylinder are considered. The Lamé parameters and the density are variable in radial coordinate. The inverse coefficient problem on determining the laws of variation of cylinder’s properties from the data on the amplitude–frequency characteristics specified at different frequency ranges is studied. The numerical solution is constructed by using a three-stage iterative process based on the derived systems of the Fredholm integral equations of the first kind with smooth kernels with respect to the unknown corrections; the A.N. Tikhonov regularization method is employed to solve these equations. The reconstruction examples for monotonic laws are presented.

在非均质各向同性物体的一般问题公式的基础上，考虑了圆柱的稳态纵向径向和扭转振动问题。Lamé参数和密度在径向坐标中可变。研究了根据在不同频率范围内指定的幅频特性数据确定汽缸特性变化规律的反系数问题。基于三阶迭代过程，基于第一类具有光滑核的Fredholm积分方程的推导系统，对未知校正进行了数值求解。AN Tikhonov正则化方法用于求解这些方程。给出了单调律的重建实例。