Author : K.Meera Saheb and M.Shasikanth

Large amplitude vibration phenomenon of structural members like short (Timoshenko) beams requires the values of the Young’s modulus and shear (rigidity) modulus. Though the shear modulus can be obtained from the Young’s modulus, it is necessary to know the values of the Poisson ratio for the isotropic beams. The value of the Poisson ratio lies in a band for the isotropic materials. The generally used Poisson ratio for isotropic materials is in between 0.25 to 0.33 and most often is arbitrarily used in the analysis. The main aim of this paper is to study the effect of the variation of Poisson ratio with reference to the large amplitude free vibrations of beams, which is the simplest structural element. The coupled displacement field method is used in the analysis because of its inherent simplicity; where in the number of undetermined coefficients are reduced by a factor two in the admissible functions assumed for the lateral deflection and the total rotation. The present paper, though aimed at demonstrating the effect of Poisson ratio, on the large amplitude vibrations of Timoshenko beams, where in the effect of the transverse shear has to be considered, and a brief on method of analysis (coupled displacement formulation) is provided for the sake of completeness. For isotropic materials, the effect of transverse shear is linearly dependent on the shear modulus, which in turn is related to the Young’s modulus through the Poisson ratio. The effect of taking a specific value of the Poisson ratio in the analysis is discussed in detail. The numerical results are obtained for several values of the Poisson ratio varying from 0 to 0.5 in steps of 0.1. the numerical results show that the values of the Poisson ratio taken affects the ratios of the nonlinear to linear radian frequencies, for several amplitude ratios considered; the effect is seen to be considerable for higher amplitude and slenderness ratios.

Key words: Large amplitude vibrations, Poisson’s ratio, coupled displacement field method.

Article published in International Conference on Advances in Mechanical Sciences 2014, Special Issue-2 (Feb 2014)