Comparison of vibration and wave propagation approaches applied to assess damage influence on the behavior of Euler-Bernoulli beams

On numerical solution methods for flexural waves in stepped beams

This paper develops and examines a modified technique for identifying damage in slender structures. An algorithm, called modified sequential algebraic algorithm, is presented to solve the longitudinal acoustic wave propagation problem in inhomogeneous media. This method accurately predicts the echo generated by the inhomogeneities when the acoustic impedance variation profile in the damaged part of the structure is non-smooth. For these cases, the available algorithms fail to provide the actual regressive wave component. In the following, a stochastic optimization scheme, the differential evolution method, is applied to solve the inverse problem. Numerical examples with smooth and non-smooth impedance profiles are considered. It is shown that, for smooth profiles, both the available techniques and the modified algorithm succeed in identifying the actual damage. Nevertheless, in situations where a rough profile is to be reconstructed, only the modified algorithm succeeds. The technique is found to be robust with respect to additive noise in the signals.

A modified sequential algebraic algorithm applied to identify rough acoustic impedance profiles in slender structures.

The modified sequential algebraic algorithm (MSAA) is a routine developed to solve the longitudinal acoustic wave propagation problem in inhomogeneous media. This method accurately predicts the echo generated by the inhomogeneities, particularly when the acoustic impedance variation profile in the damaged part of the structure is non-smooth. Used for solving the inverse problem by a stochastic optimization approach, MSAA efficiently identifies rough profiles of impedance with low noise level in the input data. As noise level increases, the inverse problem turns out to be “ill-posed” and often yields inappropriate solutions. The purpose of this paper is to apply a regularization scheme and to use a hybrid optimization strategy to reduce the error in the damage estimation. In the numerical examples, 40 parameters are successfully identified for a signal to noise ratio of 20 dB. For all tested damage profiles, the regularization and hybridization procedures decreased the maximum absolute error to levels lowe...

Hybridization and regularization schemes applied to identify rough acoustic impedance profiles in slender structures with noisy data.

The propagation of elastic waves in a heterogeneous bar of variable cross-sectional area is investigated via use of the method of characteristics andthe Laplace transform technique. The Young's modulus and density are assumed to be representable as either power law or exponential distributions in the axial coordinate. The transform method is used to establish an infinite number of multi-parameter solutions in closed form for either a stress, velocity or displacement type boundary condition. The numerical characteristic computations show excellent agreement when compared to the transform solutions, and are then used to obtain additional solutions not attainable by the transform method. Detailed results and conclusions for a bar of ogival cross-section are given for a wide range of inhomogeneity.

S.C. Sanday

Papers

Elastic waves in heterogeneous bars of varying cross-section