Effect of initial stresses and deformations on the natural frequencies of beams

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (2) : 46-51.

ZHANG Jiawei,SUN Lin,ZHANG Xiangyan,ZHANG Chenyu

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Abstract

Based on the Hamilton principle,the governing differential equations were established for beams,considering the effects of both axial and flexural deformations induced by initial load and the analytical expression for the natural frequencies of a simply-supported beam under these effects was derived by the Galerkin method.A discussion on the analytical expression demonstrates the susceptivity of the two types of effects to the magnitude of initial load,beam stiffness and restraint conditions.Under the same amount of deformation energy produced,the effects of the two types of initial deformations on the natural frequencies of beams with various boundary conditions were compared quantitatively.

Key words

initial stress / axial deformation / flexural deformation / natural frequency / Hamilton principle / Galerkin method

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ZHANG Jiawei,SUN Lin,ZHANG Xiangyan,ZHANG Chenyu. Effect of initial stresses and deformations on the natural frequencies of beams[J]. Journal of Vibration and Shock, 2019, 38(2): 46-51

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