In this paper, we develop closed expressions for the equivalent bending and shear stiffness of beams with regular square perforations, and apply them to the problem of determining the resonance frequencies of slender, regularly perforated clamped–clamped beams, which are of interest in the development of MEMS resonant devices. We prove that, depending on the perforation size, the Euler–Bernoulli equation or the more complex shear equation needs to be used to obtain accurate values for these frequencies. Extensive finite element method simulations are used to validate the proposed model over the full practical range of possible hole sizes. An experimental verification of the model is also presented.
We present a simple and computationally inexpensive method to design 1-D MEMS flexural phononic crystals (PnCs) with assigned width and central frequency of the acoustic bandgap based on the analysis of the characteristic polynomial of the acoustic transmission matrix of the crystal elementary cell. Our analysis shows that a high acoustic contrast does not necessarily lead to wide bandgaps, unless the modulation of the mechanical properties is properly chosen. We also demonstrate that the acoustic attenuation inside the bandgap, which is an important design target, is essentially predetermined once that the bandgap width and center have been chosen. The method can be valuable for fast design of PnC devices with applications spanning from sensors to filters and resonators
In this work, a piezoelectrically actuated MEMS flexural phononic crystal (PC) mass sensor aimed at biosensing applications, and based on a single crystal silicon beam with periodic perforations, is presented. We introduce a transmission matrix approach based on the Timoshenko beam theory suited for the fast design of such devices. The calculated transmission spectra are in excellent agreement with FEM simulations. A preliminary estimate of the device sensitivity, assuming the prostate specific antigen (PSA) as the target analyte, is reported
Simplified one-dimensional models for composite beams with piezoelectric layers, which are intrinsically three-dimensional structures, are important for many applications, including piezoelectric energy harvesters. To reduce the dimensionality of the system, assumptions on the stress/strain state in the transverse direction are typically made. The most common are those of null transverse stress, used for narrow beams, null transverse deformation, used for wide beams, and continuous interface strain, suited for thin piezoelectric layers (we call this assumption thin film continuous). We show that the models based on these assumptions are often used uncritically for beam geometries for which large errors may result. In particular, null transverse stress fails even for narrow beams if the thickness is much smaller than the beam width. We give clear geometric criteria that, for any geometry, allow the selection of the most accurate model among the three. We also develop a single, unified beam equation encompassing the three models and compare the analytical results from this equation with finite element simulations over a wide range of beam lengths, widths, and layer thicknesses. The selection criteria and the unified beam equation form a valuable tool for fast and accurate design of composite piezoelectric beams.
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