Abstract
Deviation of the actual system from the ideal supporting conditions caused by micromachining errors and manufacturing defects or the requirement of innovative design and optimization of microelectromechanical systems (MEMS) make the nonideal boundary in the micro-/nanoresonator system receive wide attention. In this paper, we consider the neutral plane tension, fringing field, and nonideal boundary factors to establish a continuum model of electrostatically driven microbeam resonators. The convergent static solution with nine-order Galerkin decomposition is calculated. Then, based on the static solution, a 1-DOF dynamic equation of up to the fifth-order of the dynamic displacement using a Taylor expansion is derived. The method of multiple scales is used to study the effect of spring stiffness coefficients on the primary frequency response characteristics and hardening-softening conversion phenomena in four cases. The various law of the system’s static and dynamic performances with the spring stiffness coefficients is obtained. The conditions for judging the hardening-softening transition are derived. So, adjusting the support stiffness values can be a measure of optimizing the resonator performance.
Highlights
Electrostatic microbeam resonators have the advantages of small size and light weight and are widely used in many fields, for instance, microelectromechanical systems (MEMS) resonant sensor [1] and actuator [2]. eir small size allows sensitive systems to consume minimal energy and have low fabrication costs
The above-mentioned works of literature only considered the ideal boundary conditions. Both macro- and microstructures have errors and manufacturing defects, such as structure with elastically restrained, structure with nonuniform [20, 21], overcutting near anchor points [22], and initial deformation [23,24,25,26] of microstructures caused by residual stress. ese cause the boundary conditions of the actual system to deviate from the ideal support conditions such that the displacement and rotation angle of the two fixed ends are not equal to zero
With the growth of support stiffness before pull-in phenomenon occurs, the static deflection corresponding to the same voltage goes down, the static pull-in voltage goes up, and eventually reaches a stable value
Summary
Electrostatic microbeam resonators have the advantages of small size and light weight and are widely used in many fields, for instance, MEMS resonant sensor [1] and actuator [2]. eir small size allows sensitive systems to consume minimal energy and have low fabrication costs. Bashma et al [36] used the finite element method based on wavelet transform to obtain the influence of nonideal support and edge effect on static attraction voltage and first-order natural frequency of the microcantilever beam. Tadi Beni et al [40] introduced the modified couple stress theory, in conjunction with the MAD solving method, to investigate the effect of the Casimir attraction, Elastic boundary conditions, and size dependency on nonlinear pull-in behavior of the supported beam. Shojaeian et al [41] studied the electromechanical instabilities of micro-/nanobeams with an initial curved shape and subjected to the electrostatic field and Casimir intermolecular force using a modified couple stress theory They seldom analyze their effects on dynamic response. E paper is organized as follows: an introduction including the literature review and motivation of the research, equation of motion and methods, results and discussion, and lastly, conclusions
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