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| Nonlinear dynamic modelling and free vibration for a tapered cantilever beam based on hyper-geometric function and Meijer-G function |
| BO Zhe,GE Gen |
| School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300387, China |
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Abstract Here, a tapered cantilever beam’s nonlinear vibration was studied theoretically.The beam’s modal function was based on the hyper-geometric function and Meijer-G one without needing perturbation and approximation.Kane’s equation was used to establish the beam’s vibration equation with geometric and inertial nonlinearities.The calculation results for various coefficients of this equation were the same as those obtained with other modeling methods in literature and their expressions were more concise.The beam’s fundamental natural frequency gained with the proposed method was compared with that obtained with the FE one, Rayleigh-Ritz one and other ones, and it has a very good accuracy.Under strong nonlinear vibration cases, the system’s amplitude-frequency response relation was obtained with the variational method and the energy balance one, the results calculated using this relation are more accurate than those gained with the multi-scale method under the condition of large amplitude.Furthermore, the energy balance method was improved, and the results obtained with the improved one are closer to numerical solution.Finally, the effective nonlinearity coefficients were calculated to judge the system characteristics becoming hard or soft.
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Received: 14 May 2018
Published: 28 November 2019
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