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| Analysis on natural vibration characteristics of Timoshenko beam and its modified theory with arbitrary boundary conditions |
| Received:October 01, 2022 Revised:November 21, 2022 |
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| DOI：10.7511/jslx20221001002 |
| KeyWord:boundary conditions modified Timoshenko beam natural vibration characteristics Rayleigh-Ritz method IFSM method App design |
| Author | Institution |
| 吴宗欢 |
长安大学 建筑工程学院, 西安 |
| 马乾瑛 |
长安大学 建筑工程学院, 西安 |
| 王亚波 |
长安大学 建筑工程学院, 西安 |
| 李冰冰 |
长安大学 建筑工程学院, 西安 |
| 孙正 |
长安大学 建筑工程学院, 西安 |
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| Abstract: |
| A new method for determining the natural frequencies and mode shapes of a classical Timoshenko beam and modified Timoshenko beam with arbitrary boundary conditions is presented.The improved Fourier series is used to eliminate the boundary non-convergence problem of the traditional Fourier series,and then the Lagrange functionals of the Timoshenko beams are derived by the Rayleigh-Ritz method.According to the Hamilton principle,the original problem is transformed into a generalized matrix eigenvalue problem.Compared with the analytical solution,the method used in this paper has better convergence and higher calculation accuracy.The numerical results show that the natural frequency of the classical Timoshenko beam is slightly higher than that of the modified Timoshenko beam.With the increase of the vibration mode order,the calculation results of the classical Timoshenko beam gradually deviate from the solution from the published literature and the finite element results,while the modified Timoshenko beam can maintain good consistency.The calculation results of the modified Timoshenko beam under different boundary conditions are in good agreement with the finite element results.Finally,the MATLAB software is used to produce an App program.Using this App,for different beams,only the parameters need to be modified,which can provide an efficient and convenient calculation scheme and reliable theoretical basis for practical engineering. |
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