Two Methods to Broaden the Bandwidth of a Nonlinear Piezoelectric Bimorph Power Harvester

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Hongping Hu ◽  
Longxiang Dai ◽  
Hao Chen ◽  
Shan Jiang ◽  
Hairen Wang ◽  
...  
Keyword(s):  
Large Deformations ◽  
Initial Conditions ◽  
Flexural Vibration ◽  
Nonlinear Effects ◽  
Voltage Source ◽  
Energy Scavenging ◽  
Piezoelectric Bimorph ◽  
Near Resonance ◽  
Jump Phenomena ◽  
Power Harvester

We propose two methods to broaden the operation bandwidth of a nonlinear pinned–pinned piezoelectric bimorph power harvester. The energy-scavenging structure consists of a properly poled and electroded flexible bimorph with a metallic layer in the middle, and is subjected to flexural vibration. Nonlinear effects at large deformations near resonance are considered by taking the in-plane extension of the bimorph into account. The resulting output powers are multivalued and exhibit jump phenomena. Two methods to broaden the operation bandwidth are proposed: The first method is to extend the operation frequency to the left single-valued region through optimal design. The second method is to excite optimal initial conditions with a voltage source. Larger output powers in the multivalued region of the nonlinear harvester are obtained. Hence, the operation bandwidth is broadened from the left single-valued region to the whole multivalued region.

Weakly Nonlinear Characteristics of a Three-Layer Circular Piezoelectric Plate-Like Power Harvester Near Resonance

2013 ◽  
Vol 30 (1) ◽  
pp. 97-102 ◽  
Author(s):  
H. R. Wang ◽  
X. Xie ◽  
Y. T. Hu ◽  
J. Wang
Keyword(s):  
Large Deflection ◽  
Piezoelectric Plate ◽  
Nonlinear Effects ◽  
Energy Scavenging ◽  
Nonlinear Characteristics ◽  
Weakly Nonlinear ◽  
Simply Supported ◽  
Near Resonance ◽  
Jump Phenomena ◽  
Power Harvester

ABSTRACTThe nonlinear characteristics of a simply-supported three-layer circular piezoelectric plate-like power harvester near resonance are examined in the paper, where the energy-scavenging structure consists of two properly poled piezoceramic layers separated by a central metallic layer. The structure is subjected to a uniform harmonic pressure on the upper surface. Nonlinear effects of large deflection near resonance to induce the incidental in-plane extension are considered. Results on output powers are presented, which exhibit multi-valuedness and jump phenomena.

scholarly journals Connected Vibrating Piezoelectric Bimorph Beams as a Wide-band Piezoelectric Power Harvester

2008 ◽  
Vol 20 (5) ◽  
pp. 569-574 ◽  
Author(s):  
Zengtao Yang ◽  
Jiashi Yang
Keyword(s):  
Exact Analytical Solution ◽  
Mechanical Vibration ◽  
Flexural Vibration ◽  
Wide Band ◽  
Electrical Energy ◽  
Vibration Energy ◽  
Piezoelectric Bimorph ◽  
Near Resonance ◽  
Beam Equations ◽  
Power Harvester

We analyze coupled flexural vibration of two elastically and electrically connected piezoelectric beams near resonance for converting mechanical vibration energy to electrical energy. Each beam is a so-called piezoelectric bimorph with two layers of piezoelectrics. The 1D equations for bending of piezoelectric beams are used for a theoretical analysis. An exact analytical solution to the beam equations is obtained. Numerical results based on the solution show that the two resonances of individual beams can be tuned as close as desired by design when they are connected to yield a wide-band electrical output. Therefore, the structure can be used as a wide-band piezoelectric power harvester.

Evolution of solitary waves in a two-pycnocline system

2009 ◽  
Vol 642 ◽  
pp. 235-277 ◽  
Author(s):  
M. NITSCHE ◽  
P. D. WEIDMAN ◽  
R. GRIMSHAW ◽  
M. GHRIST ◽  
B. FORNBERG
Keyword(s):  
Solitary Waves ◽  
Initial Conditions ◽  
Oscillation Period ◽  
Resonance Phenomenon ◽  
Numerical Code ◽  
Asymptotic Model ◽  
Narrow Region ◽  
Near Resonance ◽  
Long Time ◽  
The Waves

Over two decades ago, some numerical studies and laboratory experiments identified the phenomenon of leapfrogging internal solitary waves located on separated pycnoclines. We revisit this problem to explore the behaviour of the near resonance phenomenon. We have developed a numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on two separated pycnoclines in a three-layer stratified fluid bounded by rigid horizontal top and bottom walls. We study the dependence of the solution on input system parameters, namely the three fluid densities and the two interface thicknesses, for fixed initial conditions describing isolated mode-two disturbances on each pycnocline. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. However, in a narrow region of parameter space, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is only quasi-periodic, as each wave loses energy into its respective dispersive tail, which causes the spatial oscillation magnitude and period to increase until the waves eventually separate. We record the separation time, oscillation period and magnitude, and the final amplitudes and celerity of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

Plastic Instability of Thin Shells Deformed by Rigid Punches and by Hydraulic Pressure

1973 ◽  
Vol 95 (1) ◽  
pp. 36-40 ◽  
Author(s):  
Bilgin Kaftanog˘lu
Keyword(s):  
Large Deformations ◽  
Initial Conditions ◽  
Plastic Anisotropy ◽  
Plastic Instability ◽  
Strain History ◽  
Thin Shells ◽  
Hydraulic Pressure ◽  
Varying Thickness ◽  
New Criterion ◽  
Hydraulic Bulging

A theory has been developed to provide a solution for axisymmetrical shells in the plastic range for large deformations up to fracture. It includes the effects of strain history, nonlinear strain-hardening characteristics of materials, plastic anisotropy in the thickness direction, prestrain, through-thickness stress, and boundary tractions. It is also possible to use nonuniform initial conditions such as varying thickness and varying prestrain. A numerical solution has been developed especially suitable for stretch forming by a rigid punch and for hydraulic bulging of shells or diaphragms. It can easily be modified for the deep-drawing problem. Different instability criteria have been studied. It was found that the conventional criteria would not yield satisfactory results. A new criterion called the “strain propagation” criterion gave satisfactory results in the prediction of the onset of fracture. It could expalin the fracture taking place at increasing or decreasing pressures in the hydraulic bulging problem.

Mathematical models of resonance and antiresonance processes

2021 ◽  
pp. 17-27
Author(s):  
V. D. Pavlov ◽  
Keyword(s):  
Current Source ◽  
Voltage Source ◽  
Complex Method ◽  
Connecting Rod ◽  
Parallel Connection ◽  
Near Resonance ◽  
Serial Connection ◽  
Mechanical Analogue ◽  
In Series ◽  
Pneumatic Cylinders

The use of the symbolic (complex) method has significantly simplified the study of resonance and near-resonance phenomena, in particular, it has made it possible to deeply unify and formalize the consideration of various mechanical systems. The cumbersome and time-consuming operations associated with composing and solving differential equations have been replaced by simple algebraic transformations. The method is based on the mechanical analogue of Ohm’s law in a complex representation and the concept of mechanical reactance, resistance, impedance, susseptance, conductance and admittance. Resonances and antiresonances of forces and velocities are determined. Resonances occur when the elements are connected in parallel with a force source, or when the elements are connected in series with a velocity source. Antiresonances occur when a parallel connection and a speed source are combined, or a serial connection and a force source are combined. These concepts are a generalization to mechanics of the concepts of «voltage source» and «current source» from theoretical electrical engineering. The closest to the source of speed in its properties is a crank-rocker (connecting rod) mechanism with a massive flywheel. The source of force corresponds more to the rod of the significantly smaller of the two connected pneumatic cylinders.

scholarly journals Nonlinear gas oscillations in pipes. Part 1. Theory

1973 ◽  
Vol 59 (1) ◽  
pp. 23-46 ◽  
Author(s):  
J. Jimenez
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Wave Form ◽  
Cube Root ◽  
Acoustic Oscillations ◽  
Open Mouth ◽  
Near Resonance ◽  
Reflexion Coefficient ◽  
Two Parameters

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance.The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there.In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

scholarly journals Bifurcation and global dynamical behavior of the f(T) theory

2014 ◽  
Vol 29 (07) ◽  
pp. 1450033 ◽  
Author(s):  
Chao-Jun Feng ◽  
Xin-Zhou Li ◽  
Li-Yan Liu
Keyword(s):  
Dynamical System ◽  
Critical Points ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Nonlinear Effects ◽  
Local Analysis ◽  
Local Method ◽  
Initial Values ◽  
Bifurcation Phenomenon

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

Transients in Certain Autonomous Multiple-Degree-of-Freedom Nonlinear Vibrating Systems

1963 ◽  
Vol 30 (1) ◽  
pp. 44-50 ◽  
Author(s):  
P. R. Sethna
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Nonlinear Effects ◽  
Degree Of Freedom ◽  
Method Of Averaging ◽  
Dissipative Forces ◽  
Weakly Nonlinear ◽  
Vibrating Systems

Oscillations of weakly nonlinear autonomous multiple-degree-of-freedom dynamical systems are studied. The analysis includes nonlinear effects arising from the potential as well as the kinetic energies of the systems and the systems include elements that produce nonlinear dissipative forces. The method of averaging is applied to a suitably transformed set of equations. In several important cases nonperiodic solutions for arbitrary initial conditions are obtained by quadratures.

Nonlinear Adaptive Vibration Absorber for the Control of Plate Vibrations

2001 ◽  
Author(s):  
Osama N. Ashour ◽  
Ali H. Nayfeh
Keyword(s):  
Control Strategy ◽  
Flexible Structures ◽  
Digital Signal ◽  
Nonlinear Effects ◽  
Frequency Measurement ◽  
Control Technique ◽  
Vibration Absorber ◽  
Plate Vibrations ◽  
Near Resonance ◽  
Modeling Software

Abstract A nonlinear adaptive vibration absorber to control the vibrations of flexible structures is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems possessing quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the structure’s response through a sensor and an actuator. Energy is exchanged between the structure and the controller and, near resonance, the structure’s response saturates to a small value. Experimental results are presented for the control of a rectangular plate and a cantilever beam using piezoelectric ceramics and magnetostrictive alloys as actuators. The control technique is implemented using a digital signal processing board and a modeling software. The control strategy is made adaptive by incorporating an efficient frequency-measurement technique. This is validated by successfully testing the control strategy for a non-conventional problem, where nonlinear effects hinder the application of the nonadaptive controller.

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