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.