Dynamic Analysis under Uniformly Distributed Moving Masses of Rectangular Plate with General Boundary Conditions

Emem Ayankop Andi,Sunday Tunbosun Oni

doi:10.1155/2014/140407

Abstract

The problem of the flexural vibrations of a rectangular plate having arbitrary supports at both ends is investigated. The solution technique which is suitable for all variants of classical boundary conditions involves using the generalized two-dimensional integral transform to reduce the fourth order partial differential equation governing the vibration of the plate to a second order ordinary differential equation which is then treated with the modified asymptotic method of Struble. The closed form solutions are obtained and numerical analyses in plotted curves are presented. It is also deduced that for the same natural frequency, the critical speed for the system traversed by uniformly distributed moving forces at constant speed is greater than that of the uniformly distributed moving mass problem for both clamped-clamped and simple-clamped end conditions. Hence resonance is reached earlier in the uniformly distributed moving mass system. Furthermore, for both structural parameters considered, the response amplitude of the moving distributed mass system is higher than that of the moving distributed force system. Thus, it is established that the moving distributed force solution is not an upper bound for an accurate solution of the moving distributed mass problem.

Highlights

The problem of assessing the dynamic behaviour of structures carrying moving loads has been almost exclusively reserved in the literature to that of one-dimensional structural members such as the response of railroad rails to moving trains, the response of bridges and elevated roadways to moving vehicles, the response of belt drives to conveyor belts, and the response of computer tape drives to floppy disks [1,2,3,4,5,6,7,8].Where two-dimensional structures such as plates have been considered, the load acting on the structure has been simplified as lumped mass, point load, or concentrated load
This technique was later used by Oni [10] to solve the problem of the dynamic response of an elastic rectangular plate under the actions of several moving concentrated masses
The analysis of the dynamic response to a uniformly distributed moving mass of isotropic rectangular plates resting on a Winkler foundation and subjected to arbitrary boundary conditions is carried out

Summary

Introduction

Where two-dimensional structures such as plates have been considered, the load acting on the structure has been simplified as lumped mass, point load, or concentrated load Among researchers in this subject are Gbadeyan and Oni [9] who developed an analytical technique which is based on the generalized two-dimensional integral transform, the expression of the Dirac delta function as a Fourier Cosine series, and the use of the modified Struble’s asymptotic method to solve the problem of rectangular plates under moving loads. This technique was later used by Oni [10] to solve the problem of the dynamic response of an elastic rectangular plate under the actions of several moving concentrated masses. The above completed works on concentrated loads are impressive, they do not represent the Journal of Computational Engineering

Results

Discussion

Conclusion