Nonlinear oscillations of viscoelastic microcantilever beam based on modi ed strain gradient theory

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Taheran F.; AHMADIAN M.T.; FIROOZBAKHSH K.

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Journal Paper

Paper Information

Journal: Scientia Iranica Year:2021 | Volume:28 | Issue:2 (Transactions B: Mechanical Engineering) Page(s): 785-794

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Title

Nonlinear oscillations of viscoelastic microcantilever beam based on modi ed strain gradient theory

Author(s)

Taheran F. | AHMADIAN M.T. | FIROOZBAKHSH K. | Issue Writer Certificate

Keywords

Microcantilever beam

Multiple time scale method

Nonlinear free vibration

Strain gradient theory

Viscoelastic material

Abstract

A viscoelastic Microcantilever beam is analytically analyzed based on the modi ed Strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening e ect theory and discretized by Galerkin method. Inner damping, nonlinear curvature e ect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and sti ness, as well as modeling the size e ect using modi ed coupled stress or modi ed strain gradient theories. First-mode nonlinear frequency and time response of the viscoelastic Microcantilever beam are analytically evaluated using Multiple time scale method and then, validated through numerical ndings. The obtained results indicate that nonlinear terms have an appreciable e ect on natural frequency and time response of a viscoelastic microcantilever. Moreover, further investigations suggest that due to the size e ects, natural frequency would drastically increase, especially when the thickness of the beam and the length scale parameter are comparable. The ndings elaborate the signi cance of size e ects in analyzing the mechanical behavior of small-scale structures.

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APA: Copy

Taheran, F., AHMADIAN, M.T., & FIROOZBAKHSH, K.. (2021). Nonlinear oscillations of viscoelastic microcantilever beam based on modi ed strain gradient theory. SCIENTIA IRANICA, 28(2 (Transactions B: Mechanical Engineering)), 785-794. SID. https://sid.ir/paper/988185/en

Vancouver: Copy

Taheran F., AHMADIAN M.T., FIROOZBAKHSH K.. Nonlinear oscillations of viscoelastic microcantilever beam based on modi ed strain gradient theory. SCIENTIA IRANICA[Internet]. 2021;28(2 (Transactions B: Mechanical Engineering)):785-794. Available from: https://sid.ir/paper/988185/en

IEEE: Copy

F. Taheran, M.T. AHMADIAN, and K. FIROOZBAKHSH, “Nonlinear oscillations of viscoelastic microcantilever beam based on modi ed strain gradient theory,” SCIENTIA IRANICA, vol. 28, no. 2 (Transactions B: Mechanical Engineering), pp. 785–794, 2021, [Online]. Available: https://sid.ir/paper/988185/en

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