The transverse vibration of Mindlin rectangular plates with internal elastic supports and arbitrary boundary supports. (English) Zbl 1517.74044
In this paper, the transverse vibrations of rectangular plates with internal rectangular supports and general elastically restrained boundary conditions are solved using the Rayleigh-Ritz technique using trigonometric functions as admissible functions. Four terms of sinusoidal auxiliary functions have been found to be adequate to get accurate numerical results. The authors states that accuracy of the current method is verified by comparing with the finite element calculation results and numerical solutions provided in previous studies, and a good agreement has been observed in these comparisons and the result converges faster when the number of auxiliary functions is four. For the trial function with four auxiliary functions, when the total truncation number is 12, the error of the first eight free vibration frequencies between the result of the program and FEM is within one percent. The total truncation number is selected as 16 to ensure higher accuracy in the subsequent calculation of each case. Extensive numerical results are presented for various combination of simply supported, clamped, elastic constraints and free boundary conditions along the edges. The data presented may be useful to civil engineers in design.
Reviewer: Girish Kumar Ramaiah (Bangalore)
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K20 | Plates |
| 74S99 | Numerical and other methods in solid mechanics |
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