DSC regularized Dirac-delta method for dynamic analysis of FG graphene platelet-reinforced porous beams on elastic foundation under a moving load

This research presents a numerical approach to address the moving load problem of functionally graded (FG) beams with rotational elastic edge constraints, in which the regularized Dirac-delta function is used to describe a time-dependent moving load source. The governing partial differential equations of the system, derived in accordance with the classical Euler–Bernoulli beam theory, are approximated by the discrete singular convolution (DSC) method. The resulting set of algebraic equations can then be solved by the Newmark-β integration scheme. Such a singular Dirac-delta formulation is also employed as the kernel function of the DSC method. In this work, the material properties of FG beams are assumed to be changed in the thickness direction. A convergence study is performed to validate the accuracy and reliability of the numerical results. In addition, the effects of moving load velocity and material distribution on the dynamic behavior of elastically restrained FG beams are also studied to serve as new benchmark solutions. By comparing with the available results in the existing literature, the present results show good agreement. More importantly, the major finding of this work indicates that the DSC regularized Dirac-delta approach is a good candidate for moving load problems, since the equally spaced grid system adopted in the DSC scheme can achieve a preferable representation of moving load sources.

Download Full-text

Seismic Analysis of Simply Supported Damped Rayleigh Beams on Elastic Foundation

Asian Research Journal of Mathematics ◽

10.9734/arjom/2020/v16i1130240 ◽

2020 ◽

pp. 31-47

Author(s):

Ogunbamike Oluwatoyin Kehinde

Keyword(s):

Dynamical System ◽

Elastic Foundation ◽

Seismic Analysis ◽

Integral Transformation ◽

Structural Parameters ◽

Moving Load ◽

Transverse Displacement ◽

Simply Supported ◽

Rayleigh Beam ◽

Beams On Elastic Foundation

In this paper, the flexural analysis of a simply supported damped Rayleigh beam subjected to distributed loads and with damping due to resistance to the transverse displacement resting on elastic foundation is obtained. The characteristics of the beam are assumed uniform over the beam length while the foundation is considered of Winkler type. In order to evaluate the vibration characteristics of the dynamical system, the Fourier sine integral transformation in conjunction with the asymptotic method of Struble is used to solve the governing equations for the transversal vibrations in the beam structure induced by moving load. The effect of prestress and other structural parameters were considered. Numerical results show that the structural parameters have significant influence on the behaviour of the dynamical system.

Download Full-text

A New Approach on the Response of Non-Uniform Prestressed Timoshenko Beams on Elastic Foundation Subjected to Harmonic Loads

African Journal of Mathematics and Statistics Studies ◽

10.52589/ajmss-nzxsum3i ◽

2021 ◽

Vol 4 (2) ◽

pp. 66-87

Author(s):

O.K. Ogunbamike

Keyword(s):

Elastic Foundation ◽

Moving Load ◽

Closed Form Solution ◽

Complete Information ◽

Form Solution ◽

Mode Shapes ◽

Accurate Information ◽

Timoshenko Beams ◽

Beams On Elastic Foundation ◽

Vibration Responses

The dynamic response of the Timoshenko beam resting on an elastic foundation subjected to harmonic moving load using modal analysis (MA) was investigated. The method of MA was employed to obtain a closed form solution to this class of dynamical systems. In order to use MA, accurate information is needed on the natural frequencies, mode shapes and orthogonality of the mode shapes. A thorough literature survey reveals that the method has not been reported in existing literature to solve non-prestressed Timoshenko beams. Thus, we present complete information on how to use MA to derive the forced vibration responses of a simply thick beam subjected to harmonic moving loads. The effects of axial force and foundation parameters on the dynamic characteristics of the beams are studied and described in detail. In order to validate the accuracy of this method, we compare the frequency parameter with the existing literature which appears to compare favorably.

Download Full-text