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Static, free and forced vibration analysis of a delaminated microbeam-based MEMS subjected to the electrostatic force

Razeghi-Harikandeei A., Azizollah Ganji B., Jafari-Talookolaei R.-A., Abdipour A.

Archives of Mechanics

2020

Vol. 72, nr 2

169--188

In this paper, the delamination effect on the static and natural frequency response of a microbeam subjected to the nonlinear electrostatic force is studied using a semi-analytical approach for the first time. The Euler–Bernoulli beam assumption along with the non-classical modified couple stress theory is used to obtain the governing differential equation of motion and then a reduced-order model based on Galerkin’s decomposition method is obtained. At first the microbeam with very small delamination like an intact microbeam is solved and then the solution is compared with those reported in the literature and the solution obtained using 3D-coupled electromechanical software. After validation, the effects of delamination length and its locations in thickness and length directions on the microbeam behavior are investigated in details. It is shown that the delamination has remarkable effects on the characteristics of the microbeam, especially near the pull-in voltage. Also, the delaminated microbeam with various thicknesses is studied using both the classical and the non-classical theories. It is found that the difference between the two models is significant for the thin microbeam with a thickness near of below than its material length scale parameter. This investigation is helpful for the nondestructive detection of the delamination in the beams.

A study of critical point instability of micro and nano beams under a distributed variable-pressure force in the framework of the inhomogeneous non-linear nonlocal theory

Rahimi Z., Rezazadeh G., Sumelka W., Yang X.-J.

Archives of Mechanics

2017

Vol. 69, nr 6

413--433

Fractional derivative models (FDMs) result from introduction of fractional derivatives (FDs) into the governing equations of the differential operator type of linear solid materials. FDMs are more general than those of integer derivative models (IDMs) so they are more fixable to describe physical phenomena. In this paper the inhomogeneous nonlocal theory has been introduced based on conformable fractional derivatives (CFD) to study the critical point instability of micro/nano beams under a distributed variable-pressure force. The phase of distributed variable-pressure force is used for electrostatic force, electromagnetic force and so on. This model has two free parameters: i) parameter to control the order of inhomogeneity in constitutive relations that gives a general form to the model, and ii) a nonlocal parameter to consider size dependence effects in micron and sub-micron scales. As a case study the theory has been used to model micro cantilever (C-F) and doubly-clamped (C-C) silicon beams under a distributed uniform electrostatic force in the presence of von-Karman nonlinearity and their static critical point (static pull-in instability), moreover, effects of different inhomogeneity have been shown on the pull-in instability.