Forced Response Vibration of Simply Supported Beams With an Elastic Pasternak Foundation Under a Distributed Moving Load

Abstract

<jats:p>In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.</jats:p>

The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

“…Those comparisons are shown in Tables 1 and 2. An excellent identification between the present work and the results of the references [2,3] can be observed. The change of the natural frequencies with the difference in the stiffness values of the connected layer between the two beams can be noted in Figure 2 and Table 3.…”

“…The displacement components were stated as Fourier cosine series with auxiliary polynomial functions. Hammed et al [3] examined the dynamical responses of a double Euler-Bernoulli beam system under the influence of a moving distributed force, which is elastically coupled by a two -parameter Pasternak constructional work. The fourth order partial differential equations describing the beam motion were transformed into second order ordinary differential equations using the Finite Fourier sine transformation.…”