In this paper, the effect of the crack on dynamic behavior of cracked micro-beam in the presence of DC and AC loads are investigated. By applying the residual axial stress and fringing field stress, a nonlinear analytical model of cracked micro-beam is presented and crack is modeled by a massless rotational spring. The governing equation of the system is solved using Galerkin procedure and shooting method. The equilibria curve and dynamic response of cracked cantilever and clamped-clamped micro-beam are extracted below and at the onset of the dynamic pull-in instability. The results show that the behavior of cracked micro-beam is different from ordinary cracked beam due to nonlinear effects. For a fixed relative crack location, increasing the crack depth causes increasing in the resonance amplitude and reduction in the resonance frequency below dynamic pull-in instability. Also, in cracked cantilever micro-beams, by approaching the crack to fixed end, the resonance frequency reduces and the resonance amplitude increases. In cracked clamped-clamped micro-beam, trend of variations of resonance frequency and resonance amplitude against the crack location is not regular. At the onset pull-in instability, the presence of the crack causes cyclic-fold bifurcation points to appear at the lower frequency. Therefore, it causes early pull-in phenomenon or unwanted abrupt change at the micro-beam behavior. The achievement of this study is simulation of the response of the faulty low-voltage switch and MEMS resonators for different severity of crack at the onset of dynamic pull-in phenomenon.

http://jsm.iau-arak.ac.ir/article_539697_20af6913b602e12a32ca272bc4531793.pdf

Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability

MEMS resonant accelerometer measures the acceleration by detecting the resonant frequency variation of the resonator before and after the external acceleration is applied. It has the advantages of small volume, light weight, low power consumption, high measurement accuracy, good stability, quasi-digital output and so on, and has become one of the important development directions of inertial sensors. However, due to its working principle, the measurement accuracy error of MEMS resonant accelerometer caused by the change of ambient temperature is the key factor that restricts the performance improvement and application of the accelerometer sensor. Therefore, how to reduce the thermally induced frequency drift of MEMS resonant accelerometer is one of the key problems to be urgently solved. In this paper, three types of MEMS resonant accelerometer packages with different stress-buffering structures were proposed. By means of finite element simulations, the stress isolation effects of the proposed packages were systematically investigated and compared within the temperature range of 25 to 125 °C. Finally, the optimal package structure was picked out, which can effectively relax the thermal stress transmitted into the resonator, and reduce the frequency drift of MEMS resonant accelerometer.

Optimal design of the stress-buffering structure in MEMS resonant accelerometer package

This paper presents a study on the frequency response of a capacitive micro-beam resonator under various applied stresses. The governing equation whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear electrostatic equation. Due to the nonlinearity and complexity of the derived equation analytical solution are not generally available; therefore, the obtained differential equation has been solved by using a step by step linearization scheme and a Galerkin based reduced order model. The obtained static pull-in voltages have been validated by previous reports and a good agreement has been achieved. The dynamic behavior of the beam under residual, axial and thermal stresses has been investigated. It has been shown that applying the positive residual stress and negative temperature changes shifts right the frequency response and decrease the vibration amplitude and vice versa. Also, it has been shown that applying the bias DC voltage beside the exciting AC voltage decreases the stiffness of the system and so, shifts left the frequency response and increases the vibration amplitude.

http://jsm.iau-arak.ac.ir/article_514495_b334dad44e98795d7bb1e5cfc68a17c5.pdf

Frequency response analysis of a capacitive micro-beam resonator considering residual and axial stresses and temperature changes effects

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Frequency response analysis of a capacitive micro-beam resonator considering residual and axial stresses and temperature changes effects