Abstract
Microbeams are key elements in most of the micro‐electromechanical systems (MEMS). Electromechanical instability of microbeams in turn plays an important role in their applications. The shape and mechanical properties of microbeams dictate their functional characteristics. Focusing on their instability‐based working mechanism, one can appreciate that viscoelasticity of MEMS materials cannot be neglected. Consequently, the analysis of instability in viscoelastic curved microbeams is an essential demand. In this research, assuming a clamped‐clamped initially curved microbeam, the effects of viscoelastic behavior on the snap‐through and pull‐in instabilities are investigated. The standard inelastic linear solid model is used for the simulation of viscoelastic behavior. Integrodifferential governing equation of the curved viscoelastic microbeam is obtained by assuming modified couple stress theory and using Hamilton’s principle. By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. Through a quasi‐static analysis, the voltage and location of snap‐through and pull‐in instabilities are identified. The effects of different viscoelastic parameters including the creep moduli and relaxation coefficient upon the snap‐through and pull‐in instabilities are investigated. The effects of different short‐ and long‐term creeping characteristics of viscoelastic microbeam are studied and discussed in detail.
Highlights
Micro-electromechanical systems (MEMS) are widely used in modern daily life and more sophisticated technical devices such as the cellphones or car-making industries
All previous researches about curved microbeams are based on the assumption of pure elasticity [8, 12, 13], some recent experimental results have shown that viscoelastic behavior widely exists in many materials used in the construction of micro-electromechanical systems (MEMS) devices such as silicon [14, 15], polysilicon [16,17,18], and metals [19, 20]. erefore, the consideration of viscous dissipative force in microbeams seems to be necessary
The effective range of the parameters is selected according to the results provided in other studies on viscoelastic noncurved microbeams such as Zhang and Fu [5], Fu and Zhang [21], and Lee et al [24]
Summary
Micro-electromechanical systems (MEMS) are widely used in modern daily life and more sophisticated technical devices such as the cellphones or car-making industries. E dynamic pull-in instability and snap-through buckling of initially curved microbeams due to a suddenly applied voltage have been investigated by Zand [12] He considered the effects of midplane stretching load and employed a finite element model and Newmark time discretization to solve the equations. All previous researches about curved microbeams are based on the assumption of pure elasticity [8, 12, 13], some recent experimental results have shown that viscoelastic behavior widely exists in many materials used in the construction of MEMS devices such as silicon [14, 15], polysilicon [16,17,18], and metals [19, 20]. The main novelties sought in this paper would be the extraction and solution of integrodifferential equations of curved viscoelastic microbeam as well as the introduction of snap-through and pull-in phenomena in instantaneous and durable states under the effect of creep modulus and relaxation coefficient of element
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