Free vibration and physical parameter identification of non-uniform composite beams

A new low order analytical model is developed for the analysis of non-uniform composite beams, which approximates the dynamic behavior of the continuous system accurately and solves the associated direct and inverse problems. The analysis of some non-uniform composite beams is considered that are governed by Bernoulli–Euler beam equations. The mathematical model approximates the non-uniform composite beam, with another beam having piecewise constant material properties, leading to certain direct and inverse transcendental eigenvalue problems with transcendental matrix elements. Numerical methods are developed to solve such eigenvalue problems and several examples are solved. In solving direct problems, it is shown that the spectrum of non-uniform composite beams can be obtained with fair accuracy. Furthermore, it is also demonstrated that the physical parameters of piecewise composite beams can be reconstructed accurately from the spectral data obtained from vibration modal analysis experiments.