Measurement of Residual Stress and Young’s Modulus on Micromachined Monocrystalline 3C-SiC Layers Grown on and Silicon

3C-SiC is an emerging material for MEMS systems thanks to its outstanding mechanical properties (high Young’s modulus and low density) that allow the device to be operated for a given geometry at higher frequency. The mechanical properties of this material depend strongly on the material quality, the defect density, and the stress. For this reason, the use of SiC in Si-based microelectromechanical system (MEMS) fabrication techniques has been very limited. In this work, the complete characterization of Young’s modulus and residual stress of monocrystalline 3C-SiC layers with different doping types grown on <100> and <111> oriented silicon substrates is reported, using a combination of resonance frequency of double clamped beams and strain gauge. In this way, both the residual stress and the residual strain can be measured independently, and Young’s modulus can be obtained by Hooke’s law. From these measurements, it has been observed that Young’s modulus depends on the thickness of the layer, the orientation, the doping, and the stress. Very good values of Young’s modulus were obtained in this work, even for very thin layers (thinner than 1 mm), and this can give the opportunity to realize very sensitive strain sensors.

Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.

Dynamic Large Deflection Response of RC Beams under Low-Speed Impact Loading

The dynamic large deflection response of RC beams under low-speed impact loading at their midspan is investigated in this paper. Two simple methods such as extended Hamilton’s principle and equivalent static hypothesis are used to establish the theoretical models for both simply supported and fully clamped RC beams; analytical formulas for the maximum midspan deflection-input impact energy are obtained. The “equal area” method based on the deflection history of beams is only used during these derivations to determine the plastic bending moment and the stress distribution of the structure. Then, finite element simulations are carried out to verify the validity of the proposed predictions. It is shown that the maximum deflections for both simply supported and fully clamped beams are almost proportional with respect to the input impact energy, which agrees well with both simulations and other experimental results. Also, the boundary condition has more effect on the deflection response of the RC beams which is relatively longer.

Free Vibration of Bistable Clamped-Clamped Beams: A Preliminary Study

We present a preliminary study on bistable clamped-clamped beams both analytically and experimentally relating the linear post-buckling vibrations to the generated sound. In the analytical study, closed-form natural frequencies and mode shapes around the first buckled configuration are derived from an eigenvalue problem. It is found that as the static deflection of the buckled beam increases, the natural frequencies of the anti-symmetric vibrational modes stay constant, while those of the symmetric vibrational modes increase asymptotically. In the experimental study, a bistable clamped-clamped buckled beam made of steel is switched quasi-statically by hand between the two stable configurations. The generated sound is measured by a microphone and analyzed in both temporal and frequency domains, which agrees well with the analytical results. This work lays the foundation for using bistable beams in a variety of applications such as actuators, resonators, energy harvesters, and vibration reduction.

Output of MEMS Piezoelectric Energy Harvester of Double-Clamped Beams with Different Width Shapes

For a microelectromechanical system (MEMS) piezoelectric energy harvester consisting of double-clamped beams, the effects of both beam shape and electrode arrangement on the voltage outputs are analyzed. For two kinds of harvester structures including millimeter-scale and micro-scale, and different shapes including rectangular, segmentally trapezoidal and concave parabolic are taken into account. Corresponding electric outputs are calculated and tested. Their results are in good agreement with each other. The experimental results validate the theoretical analysis.

Bending of piezoelectric beams with the flexoelectric effect under applied load at any position

Flexoelectricity describes the coupling between polarization and strain gradients and presents a strong size dependence at nanoscale. In the current work, based on the extended linear piezoelectricity theory with flexoelectricity, we study bending of piezoelectric beams with consideration of flexoelectric effect. When a concentrated force at any position and electric voltage is exerted, the expression for bending deflection of simply-supported and clamped beams is derived. The obtained results show that flexoelectric effect can cause a softer elastic behavior of simply-supported and clamped beams. Sensitivity analysis of the transverse deflection and bending moment is made for two typical boundary conditions. Flexoelectric effect has a more significant effect on the bending response of a piezoelectric beam with smaller thickness.