Characterisation of a low-voltage actuated gold microswitch

Attia, Patrick; Tremblay, G.; Laval, R; Hesto, P.

doi:10.1016/s0921-5107(97)00281-x

Cited by 15 publications

(5 citation statements)

References 5 publications

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“…Within the confines of continuum mechanics, there are many applications of micro beams, particularly in the design and developments of micro-electromechanical systems (Attia et al, 1998; Li et al, 2003; Moeenfard and Ahmadian, 2013; Pei et al, 2004). For such applications, classical beam theories are inapplicable because these theories ignore the microstructure dependent size effect.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

Banerjee

Papkov

et al. 2021

Journal of Vibration and Control

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Several models within the framework of continuum mechanics have been proposed over the years to solve the free vibration problem of micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified couple stress theories. Many of these models retain the basic features of the Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one or more material scale length parameters to tackle the problem. The work described in this paper deals with the free vibration problems of micro beams based on the dynamic stiffness method, through the implementation of the modified couple stress theory in conjunction with the Timoshenko–Ehrenfest theory. The main advantage of the modified couple stress theory is that unlike other models, it uses only one material length scale parameter to account for the smallness of the structure. The current research is accomplished first by solving the governing differential equations of motion of a Timoshenko–Ehrenfest micro beam in free vibration in closed analytical form. The dynamic stiffness matrix of the beam is then formulated by relating the amplitudes of the forces to those of the corresponding displacements at the ends of the beam. The theory is applied using the Wittrick–Williams algorithm as solution technique to investigate the free vibration characteristics of Timoshenko–Ehrenfest micro beams. Natural frequencies and mode shapes of several examples are presented, and the effects of the length scale parameter on the free vibration characteristics of Timoshenko–Ehrenfest micro beams are demonstrated.

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Section: Introductionmentioning

confidence: 99%

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

Banerjee

Papkov

et al. 2021

Journal of Vibration and Control

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“…Micro/nano-structural elements such as beams and plates hold substantial promise as building blocks for modern miniaturized systems. Small-scale pressure sensors (Yeung and Ong, 2007; Mannsfeld et al , 2010), biosensors (Filippini et al , 2003), resonators (Ayela and Fournier, 1998) and switches (Attia et al , 1998) are examples of their applications. The mechanical behaviors of these structures have been the subject of several research works based on the continuum mechanics theory.…”

Section: Introductionmentioning

confidence: 99%

Integral and differential nonlocal micromorphic theory

Norouzzadeh

Oskouie

Ansari

et al. 2019

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Purpose This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of micro-rotational/stretch/shear degrees of freedom of material particles and nonlocality simultaneously. Design/methodology/approach To consider nonlocal influences, both integral (original) and differential versions of Eringen’s nonlocal theory are used. Accordingly, integral nonlocal-micromorphic and differential nonlocal-micromorphic beam models are formulated using matrix-vector relations, which are suitable for implementing in numerical approaches. A finite element (FE) formulation is also provided to solve the obtained equilibrium equations in the variational form. Timoshenko micro-/nano-beams with different boundary conditions are selected as the problem under study whose static bending is addressed. Findings It was shown that the paradox related to the clamped-free beam is resolved by the present integral nonlocal-micromorphic model. It was also indicated that the nonlocal effect captured by the integral model is more pronounced than that by its differential counterpart. Moreover, it was revealed that by the present approach, the softening and hardening effects, respectively, originated from the nonlocal and micromorphic theories can be considered simultaneously. Originality/value Developing a hybrid size-dependent Timoshenko beam model including micromorphic and nonlocal effects. Considering the nonlocal effect based on both Eringen’s integral and differential models proposing an FE approach to solve the bending problem, and resolving the paradox related to nanocantilever.

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“…Microbeams are increasingly Being considered in various applications of Micro electromechanical systems (MEMS), Nano electromechanical systems (NEMS), and Atomic force microscopes (AFMS) such as those in actuators [1], microswitches [2], microresonators [3], AFMS [4], and sensors [5] in which thicknesses and lengths of microbeams are typically on the order of microns and sub-microns. Several experimental works reveal that the mechanical behavior of some materials are size-dependent and classical theory cannot predict reliable results because of lack of material scale parameters when the size of structures is at micron or nano scale.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of gradient elastic microbeams with arbitrary boundary conditions

Yaylı

2015

J Mech Sci Technol

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Based on gradient elasticity theory with surface energy, a simple and unified method is presented for the stability analysis of a generally supported microbeam. The proposed method conveniently computes an accurate buckling parameter for microbeams using both classical and non-classical boundary conditions restrained by translational and rotational springs. The Fourier coefficient and fundamental relations of strain gradient beams are obtained first. Stokes' transformation is applied to transform these equations into a set of algebraic equations with buckling parameter. The derived expressions can be useful for theoretical investigation that leads to a determinant calculation of a 4´4 matrix. The critical buckling loads of microbeams for variant scale parameters under different boundary conditions are computed using the proposed method. Comparing results with those in the literature validates the present analysis.

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Characterisation of a low-voltage actuated gold microswitch

Cited by 15 publications

References 5 publications

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications

Integral and differential nonlocal micromorphic theory

Stability analysis of gradient elastic microbeams with arbitrary boundary conditions

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