Quality factor control of mechanical resonators using variable phononic bandgap on periodic microstructures

The quality factor (Q-factor) is an important parameter for mechanical resonant sensors, and the optimal values depend on its application. Therefore, Q-factor control is essential for microelectromechanical systems (MEMS). Conventional methods have some restrictions, such as additional and complicated equipment or nanoscale dimensions; thus, structural methods are one of the reasonable solutions for simplifying the system. In this study, we demonstrate Q-factor control using a variable phononic bandgap by changing the length of the periodic microstructure. For this, silicon microstructure is used because it has both periodicity and a spring structure. The bandgap change is experimentally confirmed by measuring the Q-factors of mechanical resonators with different resonant frequencies. The bandgap range varies depending on the extended structure length, followed by a change in the Q-factor value. In addition, the effects of the periodic structure on the Q-factor enhancement and the influence of stress on the structural length were evaluated. Although microstructures can improve the Q-factors irrespective of periodicity; the result of the periodic microstructure is found to be efficient. The proposed method is feasible as the novel Q-factor control technique has good compatibility with conventional MEMS.

Homogenization of the wave equation with non-uniformly oscillating coefficients

The focus of our work is a dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g., functionally graded) media endowed with periodic microstructure. For this class of quasi-periodic medium variations, we pursue homogenization of the scalar wave equation in [Formula: see text], [Formula: see text], within the framework of multiple scales expansion. When either [Formula: see text] or [Formula: see text], this model problem bears direct relevance to the description of (anti-plane) shear waves in elastic solids. By adopting the lengthscale of microscopic medium fluctuations as the perturbation parameter, we synthesize the germane low-frequency behavior via a fourth-order differential equation (with smoothly varying coefficients) governing the mean wave motion in the medium, where the effect of microscopic heterogeneities is upscaled by way of the so-called cell functions. In an effort to demonstrate the relevance of our analysis toward solving boundary value problems (deemed to be the ultimate goal of most homogenization studies), we also develop effective boundary conditions, up to the second order of asymptotic approximation, applicable to one-dimensional (1D) shear wave motion in a macroscopically heterogeneous solid with periodic microstructure. We illustrate the analysis numerically in one dimension by considering (i) low-frequency wave dispersion, (ii) mean-field homogenized description of the shear waves propagating in a finite domain, and (iii) full-field homogenized description thereof. In contrast to (i) where the overall wave dispersion appears to be fairly well described by the leading-order model, the results in (ii) and (iii) demonstrate the critical role that higher-order corrections may have in approximating the actual waveforms in quasi-periodic media.

Functionally Graded Non-Periodic Cellular Structure Design and Optimization

Topological tailoring of materials at a micro-scale can achieve a diverse range of exotic physical and mechanical properties that are not usually found in nature. Modification of material properties through customizing the structural pattern paves an avenue for novel functional products design. This paper explores a non-periodic microstructure design framework for functional parts design with high-strength and lightweight. To address the geometric frustration problem commonly found in non-periodic microstructure designing, we employ a smooth transition layer to connect distinct structural patterns and thus achieve functional gradation among adjacent microstructures. The concept of spatial control points is introduced for the interpolation of this transition layer. To achieve a high-strength macro-structural performance for designing functional parts, we formulate the control points as the design variables and encapsulate them into a macro-structural design optimization problem. Given that our objective function involves expensive finite element (FE) simulations, a Bayesian optimization scheme is exploited to address the computational challenge brought by the FE simulation. Experimental results demonstrate that the proposed design framework can yield both functionally graded lightweight structures and high-strength macro-mechanical performance for the designing parts. The compatibility issue of non-periodic microstructure design is well-addressed. Comparative studies reveal that the proposed framework is robust and can achieve superior mechanical performance to design functional parts with spatially varying properties.

Functionally Graded Non-Periodic Cellular Structure Design Using a Surrogate Model-Based Optimization Scheme

Topological tailoring of materials at a micro-scale can achieve a diverse range of extreme physical and mechanical properties. Modification of material properties through customizing the structural pattern paves an avenue for novel functional product design. In this paper, a non-periodic microstructure design framework is explored for functional parts design with high-strength and functional property gradation. To address the common problem of geometric frustration in non-periodic microstructure design, we employ a smooth transition layer to connect distinct structural patterns and thus achieve functional gradation between adjacent microstructures. The concept of spatial control points is introduced for implementing the transition layer. To pursue a superior macro-structural performance for designing objects, we formulate the control point as design variables and encapsulate it into macro-structural design optimization problems. Given that our objective function involves finite element (FE) simulations, a surrogate model-based optimization scheme is utilized to cope with the computational challenge brought by the FE simulation. Experimental results demonstrate that the proposed design framework can yield both functionally graded light-weight structures and high-strength macro-mechanical performance. The compatibility issues in traditional non-periodic microstructure design are addressed. Comparative studies reveal that the proposed framework is robust and can potentially generate desired functional products with spatially varying properties.