Thin Microbeam Research Articles

Design of capacitive acoustic sensors using highly compliant microbeam arrays

We have previously shown that the viscous forces acting on a periodic array of infinitesimally thin micro-beams due to air-borne sound are frequency-independent and directional [Mahdi Farahikia and Ronald Miles, “Viscous flow sensing using micro-beam arrays,” J. Acoust. Soc. Am. 146(4), 2837–2837 (2019)]. Utilizing this phenomenon in the design of acoustic sensors requires a means of converting their structural motion into electronic signals. Capacitive sensing, as a method for this purpose, requires the combination of both fixed and moving electrodes while eliminating the instability associated with high bias voltages [Ronald N. Miles, “A compliant capacitive sensor for acoustics: Avoiding electrostatic forces at high bias voltages,” IEEE Sens. J. 18(14), 5691–5698 (2018)]. In this study, the motion of moving micro-beams adjacent to fixed micro-breams in periodic arrays due to air-borne sound is examined through the finite element method. It is concluded that thinner, narrower micro-beams lead to a desired flat frequency response. The optimum gap between the micro-beams is found to be between 0.5 and 1 times the micro-beam width. The results from this study are fundamental in implementing a capacitive sensing mechanism to fabricate miniature acoustic sensors using micro-beam arrays.

Static, free and forced vibration analysis of a delaminated microbeam-based MEMS subjected to the electrostatic force

In this paper, the delamination effect on the static and natural frequency response of a microbeam subjected to the nonlinear electrostatic force is studied using a semi-analytical approach for the first time. The Euler–Bernoulli beam assumption along with the non-classical modified couple stress theory is used to obtain the governing differential equation of motion and then a reduced-order model based on Galerkin’s decomposition method is obtained. At first the microbeam with very small delamination like an intact microbeam is solved and then the solution is compared with those reported in the literature and the solution obtained using 3D-coupled electromechanical software. After validation, the effects of delamination length and its locations in thickness and length directions on the microbeam behavior are investigated in details. It is shown that the delamination has remarkable effects on the characteristics of the microbeam, especially near the pull-in voltage. Also, the delaminated microbeam with various thicknesses is studied using both the classical and the non-classical theories. It is found that the difference between the two models is significant for the thin microbeam with a thickness near of below than its material length scale parameter. This investigation is helpful for the nondestructive detection of the delamination in the beams.

Viscous flow sensing using micro-beam arrays

Thin, compliant fibers have been shown to provide a remarkably accurate means of detecting sound [Zhou et al., “Sensing fluctuating airflow with spider silk,” Proc. Natil. Acad. Sci., 201710559 (2017) ]. The present study extends these results by examining the forces due to air-borne sound on a periodic array of infinitely long and thin micro-beams having rectangular cross section. Results obtained using both the Finite Element Method and analytical solutions to Stokes’ equations are shown to be in excellent agreement. It is found that viscous forces are dominant when the width of the beams is less than 10 μm. Unlike typical MEMS resonators, which perform best in the absence of air, the dominance of viscous damping forces is desirable in directional acoustic flow sensors using these micro-beams. Furthermore, the frequency independent characteristic of these forces promises a flat response across a wide range of frequencies. It is predicted that smaller beams with wider gaps provide better sensitivity. For beams that are sufficiently thin, their thickness is found to have minimal influence on their performance.

Size-Dependent Strain Gradient-Based Thermoelastic Damping in Micro-Beams Utilizing a Generalized Thermoelasticity Theory

The small-scale effects on the thermoelastic damping (TED) in Euler–Bernoulli micro-beams is investigated in this study. To this purpose, by utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model, the coupled equations of motion and heat conduction are derived. By solving these equations simultaneously and using the Galerkin method, the real and imaginary parts of the frequency and the amount of TED in thin micro-beams are obtained. The results predicted by SGT are compared with those given by the modified couple stress theory (MCST) and the classical continuum theory. In addition, TED is calculated on the basis of energy dissipation approach which shows that the difference between the obtained results and those evaluated based on the frequency approach is negligible. Some numerical results are also presented in order to study the effects of different parameters of the micro-beams as well as the type of the boundary conditions on TED and the critical thickness; these parameters include the micro-beam height, its aspect ratio and type of the material.

A new deformation beam theory for static and dynamic analysis of microbeams

In this paper, a new deformation beam theory is proposed for static and dynamic analysis of microbeams. This theory including two unknown functions takes into account shear deformation and satisfies both of shear and couple-free conditions on the upper and lower surfaces of the beam. Based on this deformation beam theory and the modified couple stress model, the governing equations and the related boundary conditions are derived using the principal of the minimum total potential energy. These equations are used to investigate the effect of shear deformation on the static bending, buckling and vibration responses of a simply supported microbeam. In order to evaluate the accuracy and ability of this beam theory in capturing shear deformation effects, the obtained responses for both thick and thin microbeams are compared to the other existing beam deformation theories such as the Euler–Bernoulli, Timoshenko and higher order beam theories. The obtained results for the thick beam reveal that the deflection, natural frequency and the critical buckling load predicted by the proposed beam theory is comparable to those obtained using higher order theories which have more number of unknown functions. With increasing the beam length (thin beams), the difference between the results diminishes as expected.

Analytical modeling of mechanical behavior of structures: Comparative analysis, experimental validation and numerical correction with FEM of material defects generated by anisotropic etching

This paper presented semi-analytical approach in order to investigate the influence of manufacturing process defects on the elasticity of thin microbeam. The Rayleigh Beam Model (RBM) will be analyzed and corrected using 3D FEM scripts including the effects of the cross-section shape and the under-etching. This model was tested on measurements of thin chromium microbeam of dimensions (80 × 2 × 0.95 μm3). The results show that the influence of defects is very significant for the extracted value of Young's modulus where it is very close to the measured value and it is about 279.1 GPa.

Microbeam radiation therapy: Tissue dose penetration and BANG-gel dosimetry of thick-beams’ array interlacing

The tissue-sparing effect of parallel, thin (narrower than 100 μm) synchrotron-generated X-ray planar beams (microbeams) in healthy tissues including the central nervous system (CNS) is known since early 1990s. This, together with a remarkable preferential tumoricidal effect of such beam arrays observed at high doses, has been the basis for labeling the method microbeam radiation therapy (MRT). Recent studies showed that beams as thick as 0.68 mm (“thick microbeams”) retain part of their sparing effect in the rat's CNS, and that two such orthogonal microbeams arrays can be interlaced to produce an unsegmented field at the target, thus producing focal targeting. We measured the half-value layer (HVL) of our 120-keV median-energy beam in water phantoms, and we irradiated stereotactically bis acrylamide nitrogen gelatin (BANG)-gel-filled phantoms, including one containing a human skull, with interlaced microbeams and imaged them with MRI. A 43-mm water HVL resulted, together with an adequately large peak-to-valley ratio of the microbeams’ three-dimensional dose distribution in the vicinity of the 20 mm × 20 mm × 20 mm target deep into the skull. Furthermore, the 80–20% dose falloff was a fraction of a millimeter as predicted by Monte Carlo simulations. We conclude that clinical MRT will benefit from the use of higher beam energies than those used here, although the current energy could serve certain neurosurgical applications. Furthermore, thick microbeams particularly when interlaced present some advantages over thin microbeams in that they allow the use of higher beam energies and they could conceivably be implemented with high power orthovoltage X-ray tubes.

Interlaced x-ray microplanar beams: A radiosurgery approach with clinical potential

Studies have shown that x-rays delivered as arrays of parallel microplanar beams (microbeams), 25- to 90-microm thick and spaced 100-300 microm on-center, respectively, spare normal tissues including the central nervous system (CNS) and preferentially damage tumors. However, such thin microbeams can only be produced by synchrotron sources and have other practical limitations to clinical implementation. To approach this problem, we first studied CNS tolerance to much thicker beams. Three of four rats whose spinal cords were exposed transaxially to four 400-Gy, 0.68-mm microbeams, spaced 4 mm, and all four rats irradiated to their brains with large, 170-Gy arrays of such beams spaced 1.36 mm, all observed for 7 months, showed no paralysis or behavioral changes. We then used an interlacing geometry in which two such arrays at a 90-degree angle produced the equivalent of a contiguous beam in the target volume only. By using this approach, we produced 90-, 120-, and 150-Gy 3.4 x 3.4 x 3.4 mm(3) exposures in the rat brain. MRIs performed 6 months later revealed focal damage within the target volume at the 120- and 150-Gy doses but no apparent damage elsewhere at 120 Gy. Monte Carlo calculations indicated a 30-microm dose falloff (80-20%) at the edge of the target, which is much less than the 2- to 5-mm value for conventional radiotherapy and radiosurgery. These findings strongly suggest potential application of interlaced microbeams to treat tumors or to ablate nontumorous abnormalities with minimal damage to surrounding normal tissue.