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| A semi-analytical method for vibration characteristic of variable cross-section beam |
| CUI Can, JIANG Han, LI YING-hui |
| School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China |
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Abstract Abstract: A semi-analytical approach for bending vibration of variable cross-section beam is developed in this research. The variable cross-section beam model allowed parameters, such as bending stiffness and mass per unit, to vary in a manner of continuous and non-continuous which are related to axial coordinate. Based on Euler-Bernoulli beam theory, the transverse oscillation equation of variable cross-section beam is derived. Then, the beam is modeled a number of segments connected by continuity condition, and each segment of the continuous beam is assumed to obey characteristic of uniform cross section. The relation of modal functions of contiguous segments is derived by using the conditions for continuity of displacement, slope of deflection curve, moment, and shear force at the connecting point between contiguous segments. Furthermore, the modal functions are determined for simply supported boundary conditions, and the natural frequencies can be obtained using Newton-Raphson method. To verify the effect of this method, the first five natural frequencies and modal shape of beam are presented. Results show that the natural frequencies of variable cross-section beam approximately encouraging agreement those numerically obtained by the finite-element method.
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Received: 09 June 2011
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2012, Vol. 31 
