Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

Abstract

In this paper the dynamic response of a simply-supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation acted upon by a moving concentrated force is studied. The Galerkin method is utilized in order to solve the governing equations of motion. Results are compared with the finite element solution for the linear foundation model in order to validate the accuracy of the solution technique. A good agreement between the two solution techniques is observed. The effect of the nonlinearity of foundation stiffness on beam displacement is analyzed for different damping ratios and different speeds of the moving load. The results for the time response of the midpoint of the beam are presented graphically.

Analytical Solution for the Sound Radiation Field of a Viscoelastically Supported Beam Traversed by a Moving Load

“…The maximum deflection will occur at the location of the load. Furthermore, excellent agreement of the present result and [19] for load velocity V = 50m/s is obtained. Figure 3 displays the comparison between the results of the analytical and Rayleigh-Ritz methods for selected load velocity V = 55m/s and for a beam extended 15 m in longitudinal direction.…”

“…Steele [15] and Chen and Huang [16,17] investigated the response of Timoshenko beam on Winkler foundation for a variety of beam, foundation, and loading conditions. Yang and Ge [18] and Senalp et al [19] investigated the dynamic behavior of Euler-Bernoulli beam resting on viscoelastic foundation subjected to moving load by using the mode decomposition method together with the precise time integration method (MDPIM). Vlasov and Leont' ev [20] showed that the mechanical behavior of an elastic continuum can be quite accurately simulated using springs with shear interactions between them.…”

Dynamic analysis of beams on fractional viscoelastic foundation subject to a variable speed moving load

“…2 shows the comparison between results of Ref [7] and the present work for a linear foundation for time response of beam. The results show a perfect agreement with those in Ref [7], and this verifies the accuracy of presented method. Another point is that for = 1, the transverse displacement of the beam is close to be symmetrical but as the fractional order derivative used, the symmetry of the displacement is destroyed.…”

“…Fig. 2 shows the comparison between results of Ref [7] and the present work for a linear foundation for time response of beam. The results show a perfect agreement with those in Ref [7], and this verifies the accuracy of presented method.…”

Nonlinear Dynamic Identification of Beams Resting on Nonlinear Viscoelastic Foundations Based on the Time-Delayed Transfer Entropy and Improved Surrogate Data Algorithm

“…Kargarnovin et al [2] used a perturbation method in conjunction with a complex Fourier transformation to study the response of infinite beams supported by nonlinear viscoelastic foundations subjected to harmonic moving loads. A. D. Senalp et al [3] investigated the dynamic response of a simply supported, finite length Euler-Bernoulli beam with uniform cross-section resting on a linear and nonlinear viscoelastic foundation subjected to a moving concentrated load and utilized the Galerkin method to solve the governing equations of motion. Ansari et al [4] used the Galerkin method and the Multiple Scales Method (MSM) to 2 Mathematical Problems in Engineering study the transverse vibration of a finite Euler-Bernoulli beam supported by nonlinear viscoelastic foundations.…”