Response to Concentrated Moving Masses of Elastically Supported Rectangular Plates Resting on Winkler Elastic Foundation

Abstract

The dynamic response to moving concentrated masses of elastically supported rectangular plates resting on Winkler elastic foundation is investigated in this work. This problem, involving non-classical boundary conditions, is solved and illustrated with two common examples often encountered in engineering practice. Analysis of the closed form solutions shows that, for the same natural frequency (i) the response amplitude for the moving mass problem is greater than that one of the moving force problem for fixed Rotatory inertia correction factor R0 and foundation modulus F0, (ii) The critical speed for the moving mass problem is smaller than that for the moving force problem and so resonance is reached earlier in the former. The numerical results in plotted curves show that, for the elastically supported plate, as the value of R0 increases, the response amplitudes of the plate decrease and that, for fixed value of R0, the displacements of the plate decrease as F0 increases. The results also show that for fixed R0 and F0, the transverse deflections of the plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Hence, the moving force solution is not a save approximation to the moving mass problem. Also, as the mass ratio Γ approaches zero, the response amplitude of the moving mass problem approaches that one of the moving force problem of the elastically supported rectangular plate resting on constant Winkler elastic foundation.

Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load

“…The results also indicate that the amplitude of vibrations of the plate under moving mass is greater than that of the moving force for same values of shear modulus and rotary inertia. Results obtained in this study is consistent with results obtained by [6,[14][15][16].…”

“…The researchers, in [1,2,4] worked on the effect of shear deformation and rotary inertia on anisotropic plates with consideration for flexural vibrations, wave amplitude and natural frequencies but not on moving loads. The problem moving loads transversing plates have received little attention unlike the effect of moving loads on isotropic plates and beams have also been studied by authors including [5][6][7] have given solutions using analytic and approximate methods such as he finite difference, Galerkin, Rayleigh-Ritz, transfer matrix and finite element methods. Kocaturk [8] studied rectangular anisotropic (orthotropic) plates on a tensionless elastic foundation and Ozgan [9] modeled laminated orthotropic plate-foundation interaction subjected to moving load using Vlasov model.…”

Response characteristics of a beam‐mass system with general boundary conditions under compressive axial force and accelerating masses

“…When the inertia effect of the mass of the load moving on the elastic solid body is considered, the governing differential equation of motion becomes complex, intractable, and cumbersome as the coefficients become variable and singular Awodola and Omolofe . This scenario is referred to as the moving mass problem.…”