Session: 07-02-02: Nonlinear Dynamics, Control, and Stochastic Mechanics

Paper Number: 145041

145041 - Theoretical Investigation of Nonlinear Dynamics in Electrostatic Energy Harvesters for Iot Applications 

The rise of IOT (Internet of Things) devices has increased the need for power sources at the microscale. One of the many possible ways to achieve these power needs is the conversion of ambient vibration (kinetic) to electrical energy. Among existing kinetic energy converters, electrostatic vibrational energy harvesters (E-VEHS) remain of high interest due to their compatibility with CMOS microfabrication techniques and on-chip integration potential. They consist of a variable silicon-based capacitor, which acts as the transducer for kinetic energy conversion. One of the drawbacks of such devices is the limited bandwidth and power output. Although many research efforts focus on enhancing the power output of these devices via various techniques such as novel spring design, impact-based frequency up-conversion or multi-device array, the fundamentals of nonlinear dynamics are oftentimes overlooked, which may hinder performance enhancements.  

            In this context, this research presents a comprehensive theoretical investigation into the basic building blocks of e-VEHs: a mechanical oscillator coupled with an electrical circuit. The variable capacitors under investigation here feature a central shuttle mass supported within an anchored frame by suspension springs. Such devices operate by translating vibrational stimuli into the oscillation of interdigitated electrodes of a capacitor formed between mobile electrodes attached to the mass and fixed electrodes attached to the anchor, which, in turn, produces an increase in the electrostatic energy stored on the capacitor. This study focuses on the nonlinear phenomena inherent in these systems, exploring aspects such as frequency-up conversion due to bifurcation phenomena at low frequencies. Frequency up-conversion refers to a higher frequency response which typically occurs when electrode plates collide and produce individual electrode oscillations higher than the excitation frequency. In this work, conditions for period-doubling non-collision frequency-up conversion are investigated, developing an understanding of distinct dynamical zones and their unique features.

            The theoretical analysis solves Newton’s second law and Kirchhoff’s circuit law for the variable capacitor in series with a resistive load and DC bias voltage source - the electrical elements commonly used for rapid testing of device performance. This variable capacitor is modeled using lumped capacitance and is nonlinear due to the air damping forces and electrostatic forces acting between electrodes, governing their interaction. A parametric study varying excitation frequency and acceleration amplitudes, and DC bias voltages is undertaken to understand the relative displacement between the electrodes, and resulting voltage drop across the resistive load. Through this analysis, several dynamical zones of oscillation are discovered. These regions indicate shifts in the magnitudes of the various forces. The primary zone exhibits continuous harmonic oscillation near equilibrium as the excitation force is weak. An increase in energy input to the system transitions to dynamic pull-in, where the oscillating mass is pulled away from equilibrium. Most notably, the dynamic pull-in region gives rise to a cycle-adding phenomena, which may increase the power output as this is proportional with cycle frequency. When the mass approaches the fixed plates, the electrostatic force becomes dominant, with high voltage peaks that lead to destructive motion and inevitable electrode pull-in. This characterizes the final dynamical zone. This study suggests that appropriately choosing operating parameters can result in impact-less frequency up-conversion that is beneficial to power output.

Presenting Author: Matthew Galarza Rensselaer Polytechnic Institute

Presenting Author Biography: Matthew Galarza is a PhD candidate studying Mechanical Engineering at Rensselaer Polytechnic Institute focusing on nonlinear dynamics and controls of MEMs for power harvesting.

Authors:

Matthew Galarza Rensselaer Polytechnic Institute
Diana-Andra Borca-Tasciuc Rensselaer Polytechnic Institute