Abstract
A wavelet based approach is proposed in this paper for analysis and optimization of the dynamical response of a multilayered medium subject to a moving load with respect to the material properties and thickness of supporting half-space. The investigated model consists of a load moving along a beam resting on a surface of a multilayered medium with infinite thickness and layers with different physical properties. The theoretical model is described by the Euler-Bernoulli equation for the beam and the Navier's elastodynamic equation of motion for a viscoelastic half-space. The moving load is modelled by a finite series of distributed harmonic loads. A special method based on a wavelet expansion of functions in the transform domain is adopted for calculation of displacements in the physical domain. The interaction between the beam and the multilayered medium is analyzed in order to obtain the vibration response at the surface and the critical velocities associated. The choice of the specific values of the design parameters for each layer, which minimize the vibration response of the multilayered medium, can be seen as a structural optimization problem. A first approach for using optimization techniques to explore the potential of the wavelet model is presented and briefly discussed. Results from the analysis of the vibration response are presented to illustrate the dynamic characterization obtained by using this method. Numerical examples reflecting the results of numerical optimizations with respect to a multilayered medium parameters are also presented.
Highlights
Due to the continuous development of train and road transportation the analysis of solids’ dynamic behaviour became crucial for a construction of better and safer structures and vehicles [1−5] as well as for an improvement of environment protection methods
A two-dimensional theoretical model is analyzed, where infinitely long beam rests on a surface of a viscoelastic half-space and it is subjected to a moving load
The model of a beam supported by a multilayered infinite medium [9], presented in this paper, try to reflect a more natural variability of the solid
Summary
Due to the continuous development of train and road transportation the analysis of solids’ dynamic behaviour became crucial for a construction of better and safer structures and vehicles [1−5] as well as for an improvement of environment protection methods. The previously developed wavelet-based method, with an application of coiflets filter, is used in the present paper as an efficient tool replacing numerical integration [11,12]. It allows to omit analytical singularities and alleviates numerical instabilities that are common in complex dynamic systems [6−9]. The most needed features of the developed method are the computational power and time efficiency allowing to execute the optimization procedure This optimization process is very difficult with an application of the numerical integration instead of the wavelet-based approximation for the considered model due to numerical instabilities and increased time of calculations. The performed investigations allowed to formulate basic guidelines for the wavelet-based optimization methodology in the analysis of dynamic systems related to structural dynamics problems
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