Stochastic response of fractionally damped beams |
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| Affiliation: | 1. School of Science, Yanshan University, Qinhuangdao 066004, China;2. College of Science, North China University of Science and Technology, Tangshan 063000, China;1. Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, P.O. Box-71555-313, Iran;2. Departments of Mathematics, Shiraz University of Technology, Shiraz, P.O. Box-71555-313, Iran |
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| Abstract: | This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system.Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional derivative order. Finally, the fractional derivative term introduces in the system dynamics both effective damping and effective stiffness frequency dependent terms. |
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| Keywords: | Euler–Bernoulli beam Fractional constitutive law Power spectral density |
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