Abstract

The response of simply supported rectangular plates carrying moving masses and resting on variable Winkler elastic foundations is investigated in this work. The governing equation of the problem is a fourth order partial differential equation. In order to solve this problem, a technique based on separation of variables is used to reduce the governing fourth order partial differential equations with variable and singular coefficients to a sequence of second order ordinary differential equations. For the solutions of these equations, a modification of the Struble's technique and method of integral transformations are employed. Numerical results in plotted curves are then presented. The results show that response amplitudes of the plate decrease as the value of the rotatory inertia correction factor R0 increases. Furthermore, for fixed value of R0, the displacements of the simply supported rectangular plates resting on variable elastic foundations decrease as the foundation modulus F0 increases. The results further show that, for fixed R0 and F0, the transverse deflections of the rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Therefore, the moving force solution is not a safe approximation to the moving mass problem. Hence, safety is not guaranteed for a design based on the moving force solution. Also, the analyses show that the response amplitudes of both moving force and moving mass problems decrease both with increasing Foundation modulus and with increasing rotatory inertia correction factor. The results again show that the critical speed for the moving mass problem is reached prior to that of the moving force for the simply supported rectangular plates on variable Winkler elastic foundation.

Highlights

  • The analyses of elastic structures, resting on a subgrade, such as railway tracks, highway pavements, navigation locks and structural foundations, constitute an important part of the Civil Engineering and applied Mathematics literatures

  • 6 CONCLUSION The problem of the dynamic behaviour under moving concentrated masses of rectangular plates resting on variable elastic foundation is considered in this work

  • The objective of the work has been to study the problem of the dynamic response to moving concentrated masses of rectangular plates on variable Winkler elastic foundations

Read more

Summary

INTRODUCTION

The analyses of elastic structures (beams, plates and shells), resting on a subgrade, such as railway tracks, highway pavements, navigation locks and structural foundations, constitute an important part of the Civil Engineering and applied Mathematics literatures. Such analyses are mathematically complex due to the difficulty in modeling the mechanical response of the subgrade which is governed by many factors. Oni and Awodola [16] considered the dynamic response under a moving load of an elastically supported non-prismatic Bernoulli-Euler beam on variable elastic foundation. This study concerns the response to moving concentrated masses of supported rectangular plate resting on Winkler elastic foundation with stiffness variation

GOVERNING EQUATION
ANALYTICAL APPROXIMATE SOLUTION
DISCUSSION
NUMERICAL CALCULATIONS AND DISCUSSION OF RESULTS
CONCLUSION
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.