MODEL DEVELOPMENT FOR DYNAMIC ENERGY CONVERSION IN POST- BUCKLED MULTI-STABLE SLENDER COLUMNS

Broadband piezoelectric energy harvesting solutions from ambient loading have been extensively studied with the purpose of increasing the efficiency of vibration-based harvesters. Most of the previously developed methods focus on the transducer’s properties and configurations, and require vibration input excitations. In contrast, we have previously experimentally shown a mechanical energy concentrator system that exploits the quasi-static input deformations (strains) generated within the structure and induces an amplified amplitude and frequency up-converted response. The tested energy converting devices transform low-amplitude and low-rate service strains into an amplified vibration input to the piezoelectric transducer. The snap-through behavior of bilaterally constrained columns was used as the mechanism for energy concentration. This paper presents a theoretical model, based on energy method, for the post-buckling behavior of a bilaterally constrained slender column under quasi-static axial loadings. The total potential energy of the buckled elastic element is the sum of the potential energies due to bending, compression and external applied force. The transverse deflection is limited by the lateral constraints. Therefore a constrained minimization problem of the total potential energy is solved to determine the equilibrium configurations. Equilibrium transitions are correlated to the changes in the magnitude of the weight coefficients that define the contribution of buckling modes to the deflected shape. Transition states are defined in terms of the axial displacements, axial forces, column shape, and energies stored in the system.Copyright © 2014 by ASME

[1]  David A W Barton,et al.  Energy harvesting from vibrations with a nonlinear oscillator , 2010 .

[2]  Jiashi Yang,et al.  Connected Vibrating Piezoelectric Bimorph Beams as a Wide-band Piezoelectric Power Harvester , 2009 .

[3]  Peter Wriggers,et al.  Stability of rods with unilateral constraints, a finite element solution , 1984 .

[4]  Philip Holmes,et al.  Constrained euler buckling , 1997 .

[5]  F. Essenburg,et al.  On the Significance of the Inclusion of the Effect of Transverse Normal Strain in Problems Involving Beams With Surface Constraints , 1975 .

[6]  Di Chen,et al.  A MEMS-based piezoelectric power generator array for vibration energy harvesting , 2008, Microelectron. J..

[7]  Xavier Chateau,et al.  Buckling of elastic structures in unilateral contact with or without friction , 1991 .

[8]  S. Jung,et al.  Energy-harvesting device with mechanical frequency-up conversion mechanism for increased power efficiency and wideband operation , 2010 .

[9]  Yaowen Yang,et al.  Toward Broadband Vibration-based Energy Harvesting , 2010 .

[10]  Mohammed F. Daqaq,et al.  Response of uni-modal duffing-type harvesters to random forced excitations , 2010 .

[11]  Daniel J. Inman,et al.  Modeling of Piezoelectric Energy Harvesting from an L-shaped Beam-mass Structure with an Application to UAVs , 2009 .

[12]  Nizar Lajnef,et al.  A concept for energy harvesting from quasi-static structural deformations through axially loaded bilaterally constrained columns with multiple bifurcation points , 2014 .

[13]  M. B. Rubin,et al.  On the significance of normal cross-sectional extension in beam theory with application to contact problems , 1989 .

[14]  Benoit Roman,et al.  Postbuckling of bilaterally constrained rectangular thin plates , 2002 .

[15]  Nizar Lajnef,et al.  Characterization of Mechanically-Equivalent Amplifiers and Frequency Modulating Concepts for Energy Harvesting Devices , 2012 .

[16]  Herzl Chai,et al.  The post-buckling response of a bi-laterally constrained column , 1998 .

[17]  Neil D. Sims,et al.  Energy harvesting from human motion and bridge vibrations: An evaluation of current nonlinear energy harvesting solutions , 2013 .

[18]  Neil D. Sims,et al.  Energy harvesting from the nonlinear oscillations of magnetic levitation , 2009 .