Free vibration of a cantilever beam with a crack at clamped end based on elasticity theory

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (15) : 196-201.

JIANG Jie, ZHOU Ding, HU Chaobin

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Abstract

Here, based on the 2-D linear elasticity theory, free vibration characteristics of a cantilever beam with a crack at clamped end were analyzed using Chebyshev-Ritz method.Firstly, at crack tip along the beam length direction, the cracked beam was divided into two sub-beam layers with different boundary conditions.The 1st kind Chebyshev polynomials multiplied by boundary characteristic functions satisfying geometric boundary conditions were chosen as each sub-beam layer’s displacement trial functions.Ritz method was used to acquire vibration equations of two sub-beam layers, respectively.Then, utilizing the displacement continuity condition at the interface between two sub-beam layers, the whole beam’s vibration equation was derived.The numerical results were compared with those using the finite element method and available ones in literature, and it was shown that all of them agree well with each other.Finally, effects of height to span ratio and crack depth on non-dimensional natural frequencies and modal shapes were analyzed in detail.

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two-dimensional elasticity theory / cracked cantilever beam / free vibration / Chebyshev-Ritz method

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JIANG Jie, ZHOU Ding, HU Chaobin. Free vibration of a cantilever beam with a crack at clamped end based on elasticity theory[J]. Journal of Vibration and Shock, 2019, 38(15): 196-201

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