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Structural Engineering and Mechanics Volume 83, Number 4, August25 2022 , pages 451-463 DOI: https://doi.org/10.12989/sem.2022.83.4.451 |
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Forced vibrations of an elastic circular plate supported by unilateral edge lateral springs |
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Zekai Celep and Mustafa Gençoğlu
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| Abstract | ||
| The present study deals with forced vibrations of an elastic circular plate supported along its circular edge by unilateral elastic springs. The plate is assumed to be subjected to a uniformly distributed and a concentrated load. Under the combination of these loads, equations of motion are explicitly derived for static and dynamic response analyses by assuming a series of the displacement functions of time and other unknown parameters which are to be determined by employing Lagrangian functional. The approximate solution is sought by applying the Lagrange equations of motions by using the potential energy of the external forces that includes the contributions of the edge forces and the external moments, i.e., those of the effects of the boundary condition to the analysis. For the numerical treatment of the problem in the time domain, the linear acceleration procedure is adopted. The tensionless character of the support is taken into account by using an iterative process and, the coordinate functions for the displacement field are selected to partially fulfill the boundary conditions so that an acceptable approximation can be achieved faster. Numerical results are presented in the figures focusing on the nonlinearity of the problem due to the plate lift-off from the unilateral springs at the edge support. | ||
| Key Words | ||
| elastic circular plate; forced vibrations; static and dynamic response; tensionless support | ||
| Address | ||
| Zekai Celep: Department of Civil Engineering, Faculty of Engineering, Fatih Sultan Mehmet Vakif University, TR-34445 Sütlüce, Istanbul, Turkey Mustafa Gençoğlu: Department of Civil Engineering, Faculty of Civil Engineering, Istanbul Technical University, TR-34469 Maslak, Istanbul, Turkey | ||