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| Analytical study of free vibration for cracked rectangular plate |
| Received:October 29, 2018 Revised:December 11, 2018 |
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| DOI：10.7511/jslx20181029001 |
| KeyWord:cracked rectangular plate double sine Fourier series equilibrium condition free vibration analytical study |
| Author | Institution |
| 王春玲 |
西安建筑科技大学 理学院, 西安 |
| 赵鲁珂 |
西安建筑科技大学 理学院, 西安 |
| 王涵 |
西安建筑科技大学 理学院, 西安 |
| 李东波 |
西安建筑科技大学 理学院, 西安 |
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| Abstract: |
| A double sine Fourier series with supplementary functions is adopted to investigate a cracked rectangular plate.It is decomposed into several sub-domains and a simplified function for each sub-domain is derived.For each specific function,the boundary conditions and the physical meanings for constants in the mode functions are considered.The equation system,which contains the governing equations,the remaining boundary conditions,compatibility conditions for shared boundaries and the proposed equilibrium condition for shared free corners in this paper,is converted to a generalized eigenvalue problem to compute the non-dimensional frequencies.An example is calculated and the results in this paper are close to published data,which verifies the correctness of derivaition.Moreover,the validity of the proposed equilibrium condition for shared free corners is proved.The adopted function,whose canstant contain certain physical meanings,could conveniently investigates layered rectangular plates with aribitrary boundary conditions.Therefore,the method in this paper could unify the solution and simplify the approach for the study of rectangular plates. |
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