Free transverse vibration analysis of tapered Bernoulli&ndash;Euler beams based on spline finite point method

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (11) : 66-73.

Free transverse vibration analysis of tapered Bernoulli–Euler beams based on spline finite point method

LIU Peng1, LIU Hong-jun1, LIN Kun1, Qin Rong2

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Abstract

Based on the Bernoulli–Euler beam theory（EBT）, a new model was presented in the paper to study the free transverse vibration problems of tapered Euler beam by using Spline Finite Point method (SFPM)with consideration the effects of breadth and height double linearly tapered along the longitudinal direction. In proposed method, the beam was discretized by a set of uniformly scattered spline nodes along the beam axis direction instead of meshes, and the cubic B spline interpolation functions were utilized to approximate the displacement filed of the beam. The free vibration equation was derived base on the Hamilton Principle, and the global stiffness and mass matrices for tapered beams with varied cross-section were deduced in detail. Results shows that the solutions of natural frequencies of tapered beams based on the proposed method are in agreement with those reported literatures very well with higher accuracy, lower computational cost and easier way of boundary treatment. Solutions with higher accuracy can be achieved by selecting the spline nodes number to be no less than 15. The presented model is suitable for the transverse free vibration of tapered beams with various cross-sections type, tapered ratios and boundary conditions..

Key words

Bernoulli–Euler beam theory / Tapered beam / free transverse vibration / spline finite point method;

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LIU Peng1, LIU Hong-jun1, LIN Kun1, Qin Rong2. Free transverse vibration analysis of tapered Bernoulli–Euler beams based on spline finite point method[J]. Journal of Vibration and Shock, 2016, 35(11): 66-73

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