Stefanie Gutschmidt

An experimentally validated double-mass piezoelectric cantilever model for broadband vibration–based energy harvesting

Narrow bandwidth is the major challenge to today’s vibration-based energy harvesters. Compared with other broadband approaches that involve moving parts and control electronics, a double-mass piezoelectric cantilever beam provides a simple and reliable solution to widen the effective bandwidth as a vibration energy harvester. In this article, a continuum model of a double-mass lead zirconate titanate cantilever subject to sinusoidal base excitation is presented. First, the undamped equation of motion along with boundary and transition conditions is derived from Hamilton’s principle, followed by modal analysis that determines the eigenfunctions and natural frequencies. Next, the coupled electromechanical equations for sinusoidal base excitation are obtained. The output voltage and relative displacement are solved analytically. The frequency response function and mode shapes predicted by the model are validated against experiments.

A two-mass cantilever beam model for vibration energy harvesting applications

While vibration energy harvesting has become a viable means to power wireless sensors, narrow bandwidth is still a hurdle to the practical use of the technology. For conventional piezoelectric or electromagnetic harvesters, having multiple proof masses mounted on a beam is one way to widen the effective bandwidth. This is because the addition of proof masses increases the number of resonant modes within the same frequency range. Based on the assumptions of the Euler-Bernoulli beam theory, this paper presents a continuum-based model for a two-mass cantilever beam. First, the equation of motion is derived from Hamiltons principle. Next, the modal analysis is presented and a steady state solution for harmonic base excitation is derived. The two-mass beam is considered as two serially connected beam segments. In the derivation, emphasis is given to the transition conditions, which would otherwise not appear in the traditional single mass beam model. Experimental validation on a stainless steel beam confirms that the model can accurately predict both natural frequencies and the frequency response of an arbitrary point along the beam. The derivation procedure presented in this paper is applicable to a beam with any number of proof masses. Lastly, it is demonstrated how the model can be applied to a piezoelectric energy harvester

The Influence of Higher-Order Mode Shapes for Reduced-Order Models of Electrostatically Actuated Microbeams

Reduced-order models for micro-electromechanical structures possess several attractive features when compared with computational approaches using, e.g., finite-element packages. However, also within the business of reduced-order modeling, there are different approaches that yield different results. The efficiency of such approaches has to be judged according to, first, the purposes and aims of the model and, second, according to computational expenses and modeling efforts. This paper deals specifically with the frequently asked question of how many modes have to be considered in the discretization procedure to ensure an efficient reduced-order model. A consistent nonlinear continuum model is employed to describe a doubly clamped microbeam subject to two cases of electromechanical actuation. The analysis, confined to the static behavior, concentrates on two discretization techniques and addresses the differences between the final reduced-order models, accordingly. The results show significant differences with respect to the number of implemented linear-undamped mode shape functions, which are used as basis functions in the approximation procedure. This is demonstrated for the two mentioned distinct excitation schemes of the doubly clamped microbeam. The purposes of this paper are twofold. First, it draws attention to the differences between reduced-order models, which have been discretized one way or the other according to investigation goals and purposes. Second, it serves as a guideline for future micro- and nano-electromechanical system modeling by elaborating the advantages and disadvantages of both techniques.

INTERNAL RESONANCES AND BIFURCATIONS OF AN ARRAY BELOW THE FIRST PULL-IN INSTABILITY

A nonlinear continuum model is used to investigate the dynamic behavior of an array of N nonlinearly coupled microbeams. Investigations concentrate on the region below the arrays first pull-in instability, which is shown to be governed by several internal three-to-one and combination resonances. The nonlinear equations of motion for a two-element system are solved using the asymptotic multiple-scales method for the weak nonlinear system. The analytically obtained periodic response of two coupled microbeams is numerically evaluated by a continuation technique and complemented by a numerical analysis of a three-element array which exhibits quasi-periodic responses and lengthy chaotic transients. This study of small-size microbeam arrays serves for design purposes and the understanding of nonlinear nearest-neighbor interactions of medium- and large-size arrays.

Tip Motion—Sensor Signal Relation for a Composite SPM/SPL Cantilever

An array of microbeams is a promising approach to increase the throughput of scanning probe microscopes and lithography. This concept requires integrated sensors and actuators which enable individual measurement and control. Thus, existing models for single beams need to be reassessed in view of its applicability for arrays, which involve additional physical interactions and a varying geometry along the beams length. This paper considers a single composite microbeam, which is excited by a thermal actuator and its displacement is measured by a piezoresistive sensor. We derive a model that incorporates the beams composite structure, varying geometry along its length, its thermal coupling for actuation, and thermoelastic damping. Subsequently, the influence of the beams geometry on its eigenmodes and frequencies is analyzed in far and close proximity operation to a surface. We observe parametric excitation phenomena of multiple integers of the fundamental excitation frequency, which originates from the geometrical composition of the beam. Furthermore, we observe that the so far constant assumed factor to convert the sensor signal to the beams displacement depends on the dissipated power within the actuator, as well as on the dynamic behavior of the system, and thus is not constant.

The Kinematics and Dynamics of Undulatory Motion of a Tuna-mimetic Robot

This paper presents the steps for the mathematical modelling of a fish robot with four degrees of freedom (DOF) called UC-Ika 1. The swimming motion of the robot, which is inspired by tuna fish, needs to generate an undulatory motion by its tail peduncle and caudal fin. Hence, the robot has the benefit of a tail mechanism that plays a determining role in the dynamic behaviour of the robot. Analysing this tail mechanism and the hydrodynamic forces acting upon the fish robot, the governing equations of motion of the robot are derived. Solving these dynamic equations reveals that the robot has a cruising speed of 0.29 m/s, a slight oscillation in the Y direction, and a small swing around its centre of mass. These results are validated by the experimental results of UC-Ika 1.

Sensor guided biped felling machine for steep terrain harvesting

This paper outlines the design of a novel teleoperated robotic system that is proposed for the felling process of Pinus Radiata on steep terrain. The system uses arboreal locomotion similar to that used by monkeys for the method of traversal between trees which has not been used in this manner previously. Machine vision for tree recognition and optimal path planning are used to maximize the efficiency in felling operations. Other research works have explored autonomous systems for pruning by enclosing the tree and scaling vertically, however these systems neither perform felling operations nor do they have the ability to traverse from tree to tree which our proposed solution is capable of. Existing mechanized approaches to felling are generally limited to flat terrain and are manually operated but due to the unique motion of this machine, it can traverse over many terrains impractical for traditional ground based felling systems.

Christchurch Women's Hospital: Analysis of Measured Earthquake Data during the 2011–2012 Christchurch Earthquakes

A network of acceleration and displacement sensors installed in the Christchurch Womens Hospital (CWH) in July 2011 captured an extensive range of earthquake signals, allowing for a unique opportunity to analyze the performance of the New Zealand South Islands only base-isolated structure. Key characteristics of a range of earthquake signals, including frequency spectra and response patterns, are identified, with particular focus on the swarm of earthquakes on 23 December 2011, including four earthquake events greater than magnitude 5.0 on the Richter scale. The findings indicate that the response of the isolators and the superstructure was essentially elastic for the events analyzed during this period. Accelerations measured above and below the isolators were similar, indicating that the behavior of the devices resembled that of rigid blocks. No significant rocking or torsional motion of the building was observed.

Christchurch Women’s Hospital: Performance Analysis of the Base-Isolation System during the Series of Canterbury Earthquakes 2011–2012

AbstractLive monitoring data and simple dynamic reduced-order models of the Christchurch Women’s Hospital (CWH) help explain the performance of the base-isolation (BI) system of the hospital during the series of Canterbury earthquakes in 2011–2012. A Park-Wen-Ang hysteresis model is employed to simulate the performance of the BI system and results are compared to measured data recorded above the isolation layer and on the sixth story. Simplified single, two, and three degree-of-freedom models (SDOF, 2DOF, and 3DOF) show that the CWH structure did not behave as an isolated but as a fixed-base structure. Comparisons of accelerations and deflections between simulated and monitored data show a good match for isolation stiffness values of approximately two times of the value documented in the design specification and test protocol. Furthermore, an analysis of purely measured data revealed very little to no relative motion across the isolators for large events of moment magnitude scale (Mw) 5.8 and 6.0 that occ...

Design, Fabrication, and Swimming Performance of a Free-Swimming Tuna-Mimetic Robot

High efficiency in cruising is a determining factor in developing tuna-mimetic robots. So far, a number of tuna-like robots have been made. Nevertheless, the University of Canterbury has developed its own tuna-like robot called UC-Ika 1 to investigate and to accordingly improve the swimming performance of the biomimetic swimming robots. In order to do so, the propulsion system of a tuna with respect to its thrust and resistive forces is studied. Following that, the fish robot is designed and fabricated considering the tuna propulsion system. The robot is then tested several times to investigate its swimming performance. Comparison of the speed and efficiency of UC-Ika 1 with those of other tuna-like robots shows a promising improvement of cruising performance of UC-Ika 1.