The Solution Of Static And Dynamic Multi-Variables Inverse Problem For A Beam With Elastic And Damping Boundary

A numerical model to solve multi-variables inverse problem for a beam with elastic supports is presented by FEM facilitating to the sensitivity analysis of displacements with respect to parameters of elastic support and constitutive relationship. The Levenberg-Marquardt algorithm is employed in the process solving the inverse problem, either elastic support or constitutive parameters can be identified singly or simultaneously. A self-adaptive precise algorithm in time domain is exerted to dynamics equation. By expanding variables in discrete time intervals, problems with time and space coulpled can be transformed into a series space problems which can be solved recursively.The responses of beam under static and dynamic force are presented, with analyzing the responses and vibration mode in various elastic supports. The identification of elastic supports and unknown Young's modulus are achieved. The impacts of data noise and the locations of measuring points on the solutions are taken into account; numerical verification provides a satisfactory result.This paper provide a new approach to identify elastic supports, its application in practice is looked forward to.