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摘要
An analytic solution for bending vibration of stepped beam was developed. Based on Euler-Bernoulli beam theory, the transverse oscillation equation of stepped beam was derived firstly. For studying stepped beam, the relation of modal functions of contiguous steps was derived by using the conditions for continuity of displacement, slope of deflection curve, moment, and shear force at the connecting point between contiguous steps. Furthermore, the modal functions were determined for boundary conditions of simply supported, and the natural frequency can be obtained using Newton-Raphson method, and the modal shape can be obtained using natural frequency. To verify the effect of this method, the first four natural frequencies and modal shape of a model beam were presented. Results showed that the natural frequencies of stepped beam approximately agree with the results obtained by the finite-element method.
- 出版日期2011
- 单位西南交通大学
