Z. Hryniewicz

Dynamic Response of a Beam Resting on a Nonlinear Foundation to a Moving Load: Coiflet-Based Solution

This paper presents a new semi-analytical solution for the Timoshenko beam subjected to a moving load in case of a nonlinear medium underneath. The finite series of distributed moving loads harmonically varying in time is considered as a representation of a moving train. The solution for vibrations is obtained by using the Adomians decomposition combined with the Fourier transform and a wavelet-based procedure for its computation. The adapted approximating method uses wavelet filters of Coiflet type that appeared a very effective tool for vibration analysis in a few earlier papers. The developed approach provides solutions for both transverse displacement and angular rotation of the beam, which allows parametric analysis of the investigated dynamic system to be conducted in an efficient manner. The aim of this article is to present an effective method of approximation for the analysis of complex dynamic nonlinear models related to the moving load problems.

On the range of applicability of Bourret approximation

Abstract In the analysis of many dynamic soil-foundation interaction problems we have to deal with the unbounded dynamic systems for which the material parameters of the semi-infinite elastic medium are random functions of space variables. This paper, related to the above-mentioned problem deals with the range of validity of the approximate average solution for the simplified equation of motion. The solution is obtained by means of two different methods: Adomians decomposition and Bourrets approximation. The formula for the error evaluation is derived and mean square convergence of the solution series is proved. Parametric study shows that Bourrets approximation may lead to quite reasonable results.

Dynamic response of coupled foundations on layered random medium for out-of-plane motion

Abstract The case of two basemats excited by incident SH-waves is considered. The dynamic-stiffness coefficients of surface foundations on a randomly inhomogeneous layered medium, based on the stiffness matrix approach, are calculated. The solution for the harmonic response of the coupled system of basemats on a layered viscoelastic half-space is obtained.

Wavelet analysis of beam-soil structure response for fast moving train

This paper presents a wavelet based approach for the vibratory analysis of beam-soil structure related to a point load moving along a beam resting on the surface. The model is represented by the Euler-Bernoulli equation for the beam, elastodynamic equation of motion for the soil and appropriate boundary conditions. Two cases are analysed: the model with a half space under the beam and the model where the supporting medium has a finite thickness. Analytical solutions for the displacements are obtained and discussed in relation to the used boundary conditions and the type of considered loads: harmonic and constant. The analysis in time-frequency and velocity-frequency domains is carried out for realistic systems of parameters describing physical properties of the model. The approximate displacement values are determined by applying a wavelet method for a derivation of the inverse Fourier transform. A special form of the coiflet filter used in numerical calculations allows to carry out analysis without loss of accuracy related to singularities appearing in wavelet approximation formulas, when dealing with standard filters and complex dynamic systems.

Dynamic-stiffness matrix for in-plane motion in a layered depth dependent randomly inhomogeneous semi-infinite medium

SummaryThe analytical solution for the average displacements and stresses, in the case of in-plane harmonic motion for a randomly inhomogeneous layered half-space, is derived. The method used is based on the fundamental matrix and neglect of third and higher order correlations. The resulting system of integrodifferential equations is solved by Laplace transform. The results are used to calculate the dynamic-stiffness matrix. The closed form solution for the case of exponential correlation function is obtained.

Dynamic response of a bar embedded in semi-infinite medium: stochastic approach

SummaryThe idealized problem of the dynamic response of a bar with random modulus of elasticity, embedded in a randomly inhomogeneous semi-infinite medium, is analysed. The analytical approximate average solution is obtained on the basis of two different methods. Adomians decomposition method leads to the solution for the average displacement, dynamic-stiffness coefficient and variance function which are represented by the series of multiple integrals. On the other hand closed form analytical solution is obtained on the basis of Bourrets approximation using Laplace transform and residue theorem. The numerical example is presented. The wider parametric study can be easily carried out employing Maple V and Mathematica system.

Coupled vibration of a rigid rectangular block bonded to an elastic half-space

Abstract The characteristics of the coupled vertical, horizontal and rocking vibration of the rigid rectangular block bonded to the elastic half-space medium were explored and examined. An approximate analytical solution has been compared with the exact half-space model solution. Depending on the combination of certain parameters (weight, height of the block and force location) the vibrating block may exhibit resonance at three frequencies. In practical cases the response is dominated by the first resonant peak amplitudes.

Dynamic-stiffness matrix for SH-waves in a layered depth dependent randomly inhomogeneous half-space

SummaryThis paper is concerned with the derivation of the dynamic-stiffness matrix for a multilayered viscoelastic half-space, with material parameters which are depth dependent random functions. The mean displacements and stresses are obtained for the out-of-plane motion resulting from inclined SH-waves. An explicit solution for the case of exponential correlation function is obtained.

Numerical Generation Methods of Homogeneous and Nonhomogeneous Two-Dimensional Gaussian Random Fields

A simple model is presented for generating random fields defined on a two-dimensional rectangular array. The field is Gaussian and Markovian and easy to generate with a computer. As a special case of the nonhomogeneous fields, we have one which is stationary and homogeneous with respect to both the horizontal and vertical directions. A numerical example is presented.