Linear Versus Nonlinear Response of a Cantilevered Beam Under Harmonic Base Excitation: Theory and Experiment

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Michal Raviv Sayag ◽  
Earl H. Dowell
Keyword(s):  
Nonlinear Response ◽  
Opposite Effect ◽  
Displacement Amplitude ◽  
Base Excitation ◽  
Fluid Damping ◽  
Cantilevered Beam ◽  
Inertial Nonlinearities ◽  
Base Displacement ◽  
Tip Mass ◽  
Tip Displacement

A computational and experimental study of a uniform cantilever beam with a tip mass under base excitation was performed. The beam was excited at various levels of base displacement to provoke tip displacements greater than 15% of the beam length. Damping and yield stress of the beam were both considered. It was found that a large tip displacement causes nonlinear inertial (NLI) and structural (NLS) effects to arise. Each of the structural and inertial nonlinearities has an opposite effect on the resulting resonance frequency, which are nearly mutually canceling. The result was that resonant frequency calculated using the full nonlinear (FNL) model was essentially equal to the value calculated by linear (LIN) theory, and the tip displacement amplitude varied only modestly from the LIN value. It was also observed that the damping in this system is likely nonlinear, and depends on tip displacement amplitude. A theoretical model for fluid damping is suggested. Initial investigation shows encouraging agreement between the theoretical fluid damping and the measured values.

Non-Linear Piezoelectric Vibration Energy Harvesting From a Vertical Cantilever Beam With Tip Mass

2013 ◽  
Author(s):  
Onur Bilgen ◽  
S. Faruque Ali ◽  
Michael I. Friswell ◽  
Grzegorz Litak ◽  
Marc de Angelis
Keyword(s):  
Energy Harvester ◽  
Harmonic Component ◽  
Vibration Energy ◽  
Base Excitation ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Potential Wells ◽  
Non Linear ◽  
Cantilevered Beam ◽  
Tip Mass

An inverted cantilevered beam vibration energy harvester with a tip mass is evaluated for its electromechanical efficiency and power output capacity in the presence of pure harmonic, pure random and various combinations of harmonic and random base excitation cases. The energy harvester employs a composite piezoelectric material device that is bonded near the root of the beam. The tip mass is used to introduce non-linearity to the system by inducing buckling in some configurations and avoiding it in others. The system dynamics include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. This configuration exploits the non-linear properties of the system using base excitation in conjunction with the tip mass at the end of the beam. Such nonlinear device has the potential to work well when the input excitation does not have a dominant harmonic component at a fixed frequency. The paper presents an extensive experimental analysis, results and interesting conclusions derived directly from the experiments supported by numerical simulations.

Broadband Vibration Energy Harvesting from a Vertical Cantilever Piezocomposite Beam with Tip Mass

2015 ◽  
Vol 15 (02) ◽  
pp. 1450038 ◽  
Author(s):  
Onur Bilgen ◽  
Michael I. Friswell ◽  
Shaikh Faruque Ali ◽  
Grzegorz Litak
Keyword(s):  
Energy Harvester ◽  
Harmonic Component ◽  
Vibration Energy ◽  
Base Excitation ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Potential Wells ◽  
Nonlinear Properties ◽  
Cantilevered Beam ◽  
Tip Mass

An inverted cantilevered beam vibration energy harvester with a tip mass is evaluated for its electromechanical efficiency and power output capacity in the presence of pure harmonic, pure random, and various combinations of harmonic and random base excitation cases. The energy harvester employs a composite piezoelectric material device that is bonded near the root of the beam. The tip mass is used to introduce nonlinearity to the system by inducing buckling in some configurations and avoiding it in others. The system dynamics include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. This configuration exploits the nonlinear properties of the system using base excitation in conjunction with the tip mass at the end of the beam. Such a nonlinear device has the potential to work well when the input excitation does not have a dominant harmonic component at a fixed frequency. The paper presents an extensive experimental analysis, results and interesting conclusions derived directly from the experiments supported by numerical simulations.

A Multi-Point Loaded Piezocomposite Beam: Experiments on Sensing and Vibration Energy Harvesting

2018 ◽  
Author(s):  
Patrick S. Heaney ◽  
Onur Bilgen
Keyword(s):  
Unit Length ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Beam Curvature ◽  
Cantilevered Beam ◽  
Potential Applications ◽  
Tip Mass ◽  
Patch Length ◽  
Piezoelectric Vibration

A common configuration for a piezoelectric vibration energy harvester is the cantilevered beam with the piezoelectric device located near the beam root to maximize energy transduction. The beam curvature in this configuration is monotonically decreasing from root to tip, so the transduction per unit length of piezoelectric material decreases with increasing patch length. As an alternative to such conventional configuration, this paper proposes a so-called inertial four-point loading for beam-like structures. The effects of support location and tip mass on the beam curvature shapes are analyzed for four-point loaded cases to demonstrate the effect of these configurations on the total strain induced on the piezoelectric patch. These configurations are tested experimentally using several different support locations and compared with results from a baseline cantilevered beam. Performance comparisons of their power ratios are made, which indicate improvement in the transduction per unit strain of the four-point loading cases over the cantilevered configuration. The paper concludes with a discussion of potential applications of the inertial four-point loaded configuration.

EFFECT OF ADDED TIP MASS ON THE NONLINEAR FLAPWISE AND CHORDWISE VIBRATION OF CANTILEVER COMPOSITE BEAM UNDER BASE EXCITATION

2012 ◽  
Vol 12 (02) ◽  
pp. 285-310 ◽  
Author(s):  
M. EFTEKHARI ◽  
M. MAHZOON ◽  
S. ZIAEI-RAD
Keyword(s):  
Cantilever Beam ◽  
Multiple Scales ◽  
Equilibrium Points ◽  
Laminated Composite ◽  
Base Excitation ◽  
System A ◽  
Autoparametric Resonance ◽  
The Stability ◽  
Tip Mass ◽  
Made In

In this paper, a comparative study is performed for a symmetrically laminated composite cantilever beam with and without a tip mass under harmonic base excitation. The base is subjected to both flapwise and chordwise excitations tuned to the primary resonances of the two directions and conditions of 2:1 autoparametric resonance. In the literature, the governing nonlinear equations of the same problem without tip mass have been derived using the extended Hamilton's principle. Extension is made in this study to include the effect of a tip mass on the response of the beam. The natural frequencies are obtained numerically using the diversity guided evolutionary algorithm (DGEA). Next, the multiple scales method is applied to determine the nonlinear response and stability of the system. A set of four first-order differential equations describing the modulation of the amplitudes and phases of interacting modes are derived for the perturbation analysis. For verification, the above equations are reduced to the special case of the cantilever beam without tip mass for comparison with existing results. Finally, the effect of the tip mass on the stability of the fixed points and on the amplitude of oscillation about the equilibrium points in both the frequency and force modulation responses is examined.

scholarly journals Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-21
Author(s):  
Luis Fernando Paullo Muñoz ◽  
Paulo B. Gonçalves ◽  
Ricardo A. M. Silveira ◽  
Andréa Silva
Keyword(s):  
Frequency Domain ◽  
Nonlinear Response ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Nonlinear Resonance ◽  
Direct Calculation ◽  
Computational Effort ◽  
System Of Nonlinear Equations ◽  
Base Excitation ◽  
Resonance Curves

The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.

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