Abstract
The nonlinear vibration analysis of a directly excited cantilever beam modeled as an inextensible viscoelastic Euler–Bernoulli beam has been studied by the authors and is reported in the literature. The viscoelastic damping was modeled as Kelvin–Voigt damping, and the nonlinearities arisen from the inextensibility assumption. This paper extends our theoretical developments presented in the previous papers and utilizes the method of multiple scales in order to arrive at the modulation equations and the closed-form frequency response function. The analytically derived frequency response is experimentally verified through harmonic force excitation of samples of carbon nanotube-reinforced beams. The beam used in experiment consists of two elastic layers of high-carbon steel sandwiched together through a viscoelastic layer of carbon nanotube–epoxy mixture. The results demonstrate that increasing the excitation amplitude or decreasing damping ratio can cause a minor decrease in the nonlinear resonance frequency despite the significant increase in the amplitude of vibration due to reduced damping.
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