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    题名: Vibrations in an elastic beam with nonlinear supports at both ends
    作者: Yi-Ren Wang;Zhi-Wei Fang
    关键词: vibration;nonlinear boundary conditions;elastic beam
    日期: 2015-06-16
    上传时间: 2016-01-06 11:00:30 (UTC+8)
    摘要: This study analyzed vibrations in an elastic beam supported by nonlinear supports at both ends under the influence of harmonic forces. We hypothesized that the elastic Bernoullis-Euler beam was supported by cubic springs to simulate nonlinear boundary conditions. We described the dynamic behavior of the beam using Fourier expansion and simulated mode shapes using the Bessel function. We then applied the Hankel transform to obtain particular (non-homogeneous) solutions. This study succeeded in describing the jump phenomenon of nonlinear frequency response, from which we derived the resonance frequency and the frequency region(s) of system instability. Models based on linear boundary conditions are unable to capture this phenomenon. A larger modulus of elasticity in nonlinear supports increases the frequency of unstable vibration in the 1st mode and also widens the frequency region of system instability. This influence is less prominent in the 2nd mode, in which the largest amplitude was smaller than those observed in the 1st mode. The model and the analytical approach presented in this study are widely applicable to construction problems, such as shock absorber systems in motorcycles, suspension bridges, high speed railways, and a variety of mechanical devices. According to our results, system stability is influenced by the frequency regions of system instability as well as the nonlinear modulus of elastic supports.
    關聯: Journal of Applied Mechanics and Technical Physics 56(2), pp.337-346
    DOI: 10.1134/S0021894415020200
    显示于类别:[航空太空工程學系暨研究所] 期刊論文


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