SOLUTION OF AN INVERSE VIBRATION PROBLEM USING A LINEAR LEAST-SQUARESERROR METHOD

A direct method is developed to estimate the force on one end of a bar in the one-dimensional inverse vibration problem. At the beginning of the study, the finite-difference method is employed to discretize the problem domain, and then a linear inverse model is constructed to ide ntify the force condition. The linear least-squares method is adopted for the linear model, and thus times for iterations can be limited to one and the uniqueness of the solutions cart be identified easily. Res ults from the example confirm that the proposed method is effective an d applicable in solving the one-dimensional inverse vibration problem. In the example problem, an impact force on one end of a bar is estima ted. The result shows that only one measured point is needed to estima te the axial force on one end of a bar, whether the measurement errors ave neglected or considered. (C) 1996 by Elsevier Science Inc.