In this manuscript, we investigate the use topology optimization to design planar resonators with modal fre- quencies that occur at 1 : n ratios for kinetic energy scavenging of ambient vibrations that exhibit at least two frequency components. Furthermore, we are interested in excitations with a fundamental component containing large amounts of energy and secondary component with smaller energy content. This phenomenon is often seen in rotary machines; their frequency spectrum exhibits peaks on multiple harmonics, where the energy is primarily contained in the rotation frequency of the device.
Several theoretical resonators are known to exhibit modal frequencies that at integer multiples 1:2 or 1:3. However, designing manufacturable resonators for other geometries is still a daunting task. With this goal in mind, we utilize topology optimization to determine the layout of the resonator. We formulate the problem in its non-dimensional form, eliminating the constraint on the allowable frequency. The frequency can be obtained a posteriori by means of linear scaling. Conversely, to previous research, which use the clamped beam as initial guess, we synthesize the final shape starting from a ground structure (or structural universe) and remove of the unnecessary beams from the initial guess by means of a graph-based filtering scheme. The algorithm determines the simplest structure that gives the desired frequency’s ratio. Within the optimization, the structural design is accomplished by a linear FE analysis. The optimization reveals several trends, the most notable being that having members connected orthogonally as in the L-shaped resonator is not the preferred topology of this devices.
In order to fully explore the angle of orientation of connected members on the modal characteristics of the device; we derive a reduced-order model that allows a bifurcation analysis on the effect of member orientation on modal frequency. Furthermore, the reduced order approximation is used solve the coupled electro-mechanical equation of a vibration based energy harvester (VEH). Finally, we present the performance of the VEH under various base excitations. These results show an infinite number of topologies that can have integer ratio modal frequencies, and in some cases harvest more power than a nominal L shaped harvester, operating in the linear regime.
This manuscript is motivated by research that shows the shear, d15, mode energy harvesters offer significant improvement in power generation over the traditional normal, d31, mode based harvesters. The premise behind this study is to examine the effect of expanding the design domain of PZT based energy harvesters by considering an arbitrary poling angle. In the first part of the manuscript, we derive the equation of motions of a harvester based on Timoshenko beam theory in an unimorph configuration. The resulting equations are solved using a Rayleigh Ritz analysis. The electric displacement depends on both the normal and shear strain. Thus the proposed device operates using a combination of shear and normal modes to extract power. The extent to which each mode is used depends on the polarization orientation. We examine the effect of poling on the fundamental short and open circuit frequencies. Next, the poling angle is examined over a range to determine the effect on the power harvested at the fundamental modal frequencies of the system. The study demonstrates that an arbitrary poled piezoelectric increases the power that the harvester produces over traditionally poled devices; however, the performance is highly dependent on the geometry.
Actuators based on smart materials generally exhibit a tradeoff between force and stroke. Researchers have surrounded piezoelectric materials (PZT's) with compliant structures to magnify either their geometric or mechanical advantage. Most of these designs are literally built around a particular piezoelectric device, so the design space consists of only the compliant mechanism. Materials scientists researchers have demonstrated the ability to pole a PZT in an arbitrary direction, and some engineers have taken advantage of this to build "shear mode" actuators.
The goal of this work is to determine if the performance of compliant mechanisms improves by the inclusion of the piezoelectric polarization as a design variable. The polarization vector is varied via transformation matrixes, and the compliant actuator is modeled using the SIMP (Solid Isotropic Material with Penalization) or "power-law method." The concept of mutual potential energy is used to form an objective function to measure the piezoelectric actuator's performance. The optimal topology of the compliant mechanism and orientation of the polarization method are determined using a sequential linear programming algorithm. This paper presents a demonstration problem that shows small changes in the polarization vector have a marginal effect on the optimum topology of the mechanism, but improves actuation.