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Modified Couple Stress Theory for Micro-Machined Beam Resonators with Linearly Varying Thickness and Various Boundary Conditions

Zenkour A. M.

Archive of Mechanical Engineering

2018

Vol. LXV, nr 1

43--64

This article employs the classical Euler–Bernoulli beam theory in connection with Green–Naghdi’s generalized thermoelasticity theory without energy dissipation to investigate the vibrating microbeam. The microbeam is considered with linearly varying thickness and subjected to various boundary conditions. The heat and motion equations are obtained using the modified couple stress analysis in terms of deflection with only one material length-scale parameter to capture the size-dependent behavior. Various combinations of free, simply-supported, and clamped boundary conditions are presented. The effect of length-to-thickness ratio, as well as the influence of both couple stress parameter and thermoelastic coupling, are all discussed. Furthermore, the effect of reference temperature on the eigenfrequency is also investigated. The vibration frequencies indicate that the tapered microbeam modeled by modified couple stress analysis causes more responses than that modeled by classical continuum beam theory, even the thermoelastic coupled is taken into account.