Journal of Theoretical
and Applied Mechanics
52, 3, pp. 687-697, Warsaw 2014
and Applied Mechanics
52, 3, pp. 687-697, Warsaw 2014
Wavelet approximation of Adomian's decomposition applied to the nonlinear problem of a double-beam response subject to a series of moving loads
The dynamic response of a double-beam resting on a nonlinear viscoelastic foundation and subjected to a finite series of moving loads is analysed. The beams are connected by a viscoelastic layer and the load moving along the upper beam represents motion of a train on the rail track. The mathematical model is described by a coupled system of fourth order partial differential equations with homogeneous boundary conditions. The nonlinearity is included in the foundation stiffness of medium supporting a lower beam. The coiflet based approximation combined with Adomian's decomposition is adopted for the displacements derivation. The developed approach allows one to overcome difficulties related to direct calculation of Fourier integrals as well as the small parameter method. The conditions for correctness of the approximate solution are defined. The influence of some factors on the system sensitivity is discussed, with special focus on the distance between the separated loads. Numerical examples are presented for a certain system of physical parameters.
Keywords: infinite double-beam; nonlinear problem; Adomian's decomposition; coiflet approximation; moving load