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.

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.

Signal Processing Techniques for Nonlinear Structural Dynamical Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S214-S218 ◽  
Author(s):  
C. Pezeshki ◽  
W. H. Miles ◽  
S. Elgar
Keyword(s):  
Signal Processing ◽  
Steady State ◽  
Wavelet Transforms ◽  
Galerkin Approximation ◽  
Higher Order ◽  
Steady State Response ◽  
State Response ◽  
Higher Order Spectra ◽  
Processing Techniques ◽  
Signal Processing Techniques

Various signal processing techniques are introduced into the structural dynamics literature, notably higher-order spectra for steady-state response and wavelet transforms for transient response of systems. The structural behavior of the buckled beam, modeled by the one-mode Galerkin approximation is examined to demonstrate the utility of the techniques. Higher-order spectra illuminate nonlinear energy coupling mechanisms in the frequency domain for the steady state response. Wavelet transforms show the development of the frequency spectrum in the transient portion of the response.

The Auditory Steady-State Response: Full-Term and Premature Neonates

2002 ◽  
Vol 13 (05) ◽  
pp. 260-269 ◽  
Author(s):  
Barbara Cone-Wesson ◽  
John Parker ◽  
Nina Swiderski ◽  
Field Rickards
Keyword(s):  
Steady State ◽  
Premature Infants ◽  
Modulation Frequency ◽  
Otoacoustic Emission ◽  
Full Term ◽  
Steady State Response ◽  
Pass Rates ◽  
Term Infants ◽  
State Response ◽  
Auditory Steady State Response

Two studies were aimed at developing the auditory steady-state response (ASSR) for universal newborn hearing screening. First, neonates who had passed auditory brainstem response, transient evoked otoacoustic emission, and distortion-product otoacoustic emission tests were also tested with ASSRs using modulated tones that varied in frequency and level. Pass rates were highest (> 90%) for amplitude-modulated tones presented at levels ≥ 69 dB SPL. The effect of modulation frequency on ASSR for 500- and 2000-Hz tones was evaluated in full-term and premature infants in the second study. Full-term infants had higher pass rates for 2000-Hz tones amplitude modulated at 74 to 106 Hz compared with pass rates for a 500-Hz tone modulated at 58 to 90 Hz. Premature infants had lower pass rates than full-term infants for both carrier frequencies. Systematic investigation of ASSR threshold and the effect of modulation frequency in neonates is needed to adapt the technique for screening.

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