New Insight Into Energy Harvesting via Axially-Loaded Beams

2009 ◽  
Author(s):  
Mohammed F. Daqaq
Keyword(s):  
Steady State ◽  
Energy Harvesting ◽  
Axial Load ◽  
Excitation Frequency ◽  
Axial Loading ◽  
Response Amplitude ◽  
Resistive Load ◽  
Steady State Response ◽  
State Response ◽  
Axially Loaded

Driven by the study of Leland and Wright [1], this manuscript delves into the qualitative understanding of energy harvesting using axially-loaded beams. Using a simple nonlinear electromechanical model and the method of multiple scales, we study the general nonlinear physics of energy harvesting from a piezoelectric beam subjected to static axial loading and traversal dynamic excitation. We obtain analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. We utilize these expression to study the effect of the axial loading on the overall nonlinear behavior of the harvester. It is demonstrated that, in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in i) increasing the electric damping in the system thereby enhancing the energy transfer from the beam to the electric load, ii) amplifying the effect of the external excitation on the structure, and hence, increases the steady-state response amplitude and output voltage, and iii) increasing the bandwidth of the harvester by enhancing the effective nonlinearity of the system.

Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Ravindra Masana ◽  
Mohammed F. Daqaq
Keyword(s):  
Steady State ◽  
Output Power ◽  
Axial Load ◽  
Excitation Frequency ◽  
Response Amplitude ◽  
Steady State Response ◽  
Smart Mater ◽  
Energy Harvesters ◽  
State Response ◽  
Piezoelectric Vibration

To maximize the electromechanical transduction of vibratory energy harvesters, the resonance frequency of the harvesting device is usually tuned to the excitation frequency. To achieve this goal, some concepts call for utilizing an axial static preload to soften or stiffen the structure (Leland and Wright, 2006, “Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload,” Smart Mater. Struct., 15, pp. 1413–1420; Morris et al., 2008, “A Resonant Frequency Tunable, Extensional Mode Piezoelectric Vibration Harvesting Mechanism,” Smart Mater. Struct., 17, p. 065021). For the most part, however, models used to describe the effect of the axial preload on the harvester’s response are linear lumped-parameter models that can hide some of the essential features of the dynamics and, sometimes, oppose the experimental trends. To resolve this issue, this study aims to develop a comprehensive understanding of energy harvesting using axially loaded beams. Specifically, using nonlinear Euler–Bernoulli beam theory, an electromechanical model of a clamped-clamped energy harvester subjected to transversal excitations and static axial loading is developed and discretized using a Galerkin expansion. Using the method of multiple scales, the general nonlinear physics of the system is investigated by obtaining analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. These theoretical expressions are then validated against experimental data. It is demonstrated that in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in (i) increasing the electric damping in the system, thereby enhancing the energy transfer from the beam to the electric load, (ii) amplifying the effect of the external excitation on the structure, and (iii) enhancing the effective nonlinearity of the device. These factors combined can increase the steady-state response amplitude, output power, and bandwidth of the harvester.

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

Air-Conduction Auditory Steady-State Response: Comparison of Interchannel Recording Using Two Modulation Frequencies

2008 ◽  
Vol 19 (09) ◽  
pp. 696-707 ◽  
Author(s):  
Wafaa A. Kaf ◽  
Ali A. Danesh
Keyword(s):  
Steady State ◽  
Carrier Frequency ◽  
Young Female ◽  
Response Amplitude ◽  
Normal Female ◽  
Steady State Response ◽  
State Response ◽  
Auditory Steady State Response ◽  
The Mean ◽  
Contralateral Response

Background: Two-channel auditory steady-state response (ASSR) recording at high and low MF (modulation frequency) most likely provides an insight about the response amplitude and latency from different directions at the brainstem level and at the thalamus or cortical level. Little is known about the combined relationship between MF (39 and 79 Hz) and electrode montages (ipsilateral and contralateral) to single AM (amplitude modulation) tones on the ASSR amplitude and latency. Purpose: To determine if ipsilateral versus contralateral response asymmetries are present at the brainstem level (79 Hz ASSR) and at the thalamus or cortical levels (39 Hz ASSR). Research Design: Descriptive and inferential statistics for interchannel ipsilateral and contralateral ASSR amplitude and latency to 79 and 39 Hz. Study Sample: Twenty-five normal-hearing, right-handed young female adults participated in the study. All participants were right-handed, and their age ranged between 18 to 28 years (mean 24.5 ± 1.6 years). Data Collection and Analysis: Ipsilateral and contralateral ASSR to 39 and 79 Hz MF and 100% AM stimuli were recorded at 500, 2000, and 4000 Hz carrier frequencies at 65 dB SPL. The ASSR amplitudes and phases were determined for each MF across Fc (carrier frequency) for the two channels to the test (right) ear. ASSR amplitude and latency between recording montages for each MF and across carrier frequency were compared by computing two-way repeated measures ANOVA. Results: The mean ipsilateral ASSR amplitudes to 39 Hz across frequency were slightly larger (228.6 ± 61.6 µV) than the contralateral response amplitude (223.2 ± 78 µV) while the mean ipsilateral 79 Hz amplitudes were smaller (127.3 ± 114.8) compared to contralateral 79 Hz amplitude (154.6 ± 112.7 µV). For latency response, the mean ipsilateral/contralateral latency difference, on average, was 1 msec or less for both MFs. Results, in normal female adults, indicated no significant interchannel ASSR asymmetries for amplitude and latency (p > 0.05) at the brainstem (79 Hz ASSR) and at the thalamus or cortical levels (39 Hz ASSR). Conclusions: Interchannel ipsilateral and contralateral ASSR amplitude and latency to 79 and 39 Hz are not significantly different in normal, young female adults. Two-channel recording of ASSR to different MFs may be of clinical value in otoneurologic assessment.

Steady-State Response and Stability of Rotating Composite Blades With Frictional Damping

1998 ◽  
Vol 120 (1) ◽  
pp. 131-139 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady state response and stability analysis of rotating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

Effect of Axial Load on the Response of Beams on Nonlinear Viscoelastic Unilateral Foundations

2014 ◽  
Author(s):  
Udbhau Bhattiprolu ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Steady State ◽  
Axial Load ◽  
Galerkin Approximation ◽  
Computation Time ◽  
Polyurethane Foams ◽  
Steady State Response ◽  
Approximation Solution ◽  
Solution Approach ◽  
State Response ◽  
Nonlinear Viscoelastic

Flexible polyurethane foams used for cushioning in the furniture and automotive industries serve as foundations and exhibit complex nonlinear viscoelastic behavior. To design systems that incorporate these materials, it is important to model their mechanical behavior and then to predict the dynamic response of such systems. The example of a pinned-pinned beam interacting with a nonlinear viscoelastic foundation is the focus of the present study. The foundation can either react in compression as well as tension (bilateral), or react only in compression (unilateral). In the latter case, the contact regions between the beam and the foundation are not known a priori, and thus the coefficients of the modal equations obtained in a Galerkin approximation solution approach, are functions of the solution as well. It is therefore computationally expensive to predict the dynamic and steady-state response of these structures to static and harmonic loads. For polynomial-type nonlinearities, it is possible to speed up the computation time by using a convolution method to evaluate integral terms in the model. Also, if only the steady-state response is of interest, direct-time integration can be replaced by incremental harmonic balance to make the frequency response predictions more efficient. The effect of axial load and the influence of various parameters e.g., loading configuration, excitation amplitude, linear and nonlinear stiffness, on the response of the beam on unilateral and bilateral foundations are studied.

Steady-state response of normal subjects to inspiratory resistive load

1986 ◽  
Vol 60 (5) ◽  
pp. 1471-1481 ◽  
Author(s):  
V. Im Hof ◽  
P. West ◽  
M. Younes
Keyword(s):  
Steady State ◽  
Normal Subjects ◽  
Driving Pressure ◽  
Resistive Load ◽  
Steady State Response ◽  
Occlusion Pressure ◽  
State Response ◽  
Inspiratory Resistance ◽  
Residual Capacity ◽  
Loaded Breathing

Tidal volume (VT) is usually preserved when conscious humans are made to breathe against an inspiratory resistance. To identify the neural changes responsible for VT compensation we calculated the respiratory driving pressure waveform during steady-state unloaded and loaded breathing (delta R = 8.5 cmH2O X 1(-1) X s) in eight conscious normal subjects. Driving pressure (DP) was calculated according to the method of Younes et al. (J. Appl. Physiol. 51: 963–989, 1981), which provides the equivalent of occlusion pressure at functional residual capacity throughout the breath. VT during resistance breathing was 108% of unloaded VT, as opposed to a predicted value of 82% of control in the absence of neural compensation. Compensation was accomplished through three changes in the DP waveform: 1) peak amplitude increased (+/- 23%), 2) the duration of the rising phase increased (+42%); and 3) the rising phase became more concave to the time axis. There were no changes in the relative decay rate of inspiratory pressure during expiration, in the shape of the declining phase of DP, or in end-expiratory lung volume.

Steady State Response and Stability of Rotating Composite Blades With Frictional Damping

1996 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady stale response and stability analysis of ratating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

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