Abstract
In previous papers, the problem of double-beam system resting on viscoelastic foundation was solved with the assumption of nonlinear foundation stiffness. This multilayer model finds application in railway modelling, where rails are represented by the infinite Euler-Bernoulli beams and sleepers are modelled as a rigid body. In this paper, another assumption is made. The layer connecting two Euler-Bernoulli beams has nonlinear stiffness. This assumption is related to laboratory tests of fastening systems. These tests show that the stiffness of fasteners and rail pads is nonlinear and this factor should be taken into account in detailed analysis of dynamic features. Therefore inclusion of nonlinearity in double-beam system is justified. The physical model presented in this paper consists of two infinitely long beams connected by viscoelastic layer with nonlinear stiffness and resting on viscoelastic foundation. The mathematical model is described by two coupled fourth order partial differential equations of motion with homogeneous boundary conditions. The system is solved by using the Fourier transform and Adomian’s decomposition, combined with the wavelet based approximation of the response using Coiflet filters. The error index for Adomian series is proposed and the approximate solution for vertical vibrations is shown along with computational examples for some systems of parameters.
Highlights
The problem of double-beam dynamics is very important for engineering
The system presented in this paper consists of two infinitely long Euler-Bernoulli beams connected by the viscoelastic layer with included nonlinearity of stiffness in its classical cubic form
This structure rests on viscoelastic foundation and it is subjected to moving set of forces harmonically varying in time
Summary
The problem of double-beam dynamics is very important for engineering. One of the most crucial fields using the idea of such a system is modelling of beam-foundation structures subjected to moving loads. The analytically solved and parametrically analysed system was directly implemented in the analysis of multilayer rail track model, where the rail was represented by the Euler-Bernoulli beam (upper beam) and the sleepers were described as a rigid body (lower beam with zero damping) [4, 5]. The system presented in this paper consists of two infinitely long Euler-Bernoulli beams connected by the viscoelastic layer with included nonlinearity of stiffness in its classical cubic form. This structure rests on viscoelastic foundation and it is subjected to moving set of forces harmonically varying in time
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