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.

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.

Large Deflection of a Rectangular Plate Resting on a Pasternak-Type Elastic Foundation

1977 ◽  
Vol 44 (3) ◽  
pp. 509-511 ◽  
Author(s):  
P. K. Ghosh
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Lateral Load ◽  
Bending Moments ◽  
Shear Forces ◽  
Simply Supported ◽  
Base Parameters ◽  
Square Plate

The problem of large deflection of a rectangular plate resting on a Pasternak-type foundation and subjected to a uniform lateral load has been investigated by utilizing the linearized equation of plates due to H. M. Berger. The solutions derived and based on the effect of the two base parameters have been carried to practical conclusions by presenting graphs for bending moments and shear forces for a square plate with all edges simply supported.

scholarly journals Three Dimensional Static Solution of Simply Supported Single Layer Piezoelectric Plate

2016 ◽  
Vol 82 (4) ◽  
Author(s):  
Sandeep S. Pendhari ◽  
Sameer S. Sawarkar ◽  
Yogesh M. Desai ◽  
Nilesh Patil
Keyword(s):  
Piezoelectric Plate ◽  
Three Dimensional ◽  
Single Layer ◽  
Static Solution ◽  
Simply Supported

scholarly journals “Extraordinary” modulation instability in optics and hydrodynamics

2021 ◽  
Vol 118 (14) ◽  
pp. e2019348118
Author(s):  
Guillaume Vanderhaegen ◽  
Corentin Naveau ◽  
Pascal Szriftgiser ◽  
Alexandre Kudlinski ◽  
Matteo Conforti ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Nonlinear Theory ◽  
Linear Stability Analysis ◽  
Water Waves ◽  
Modulation Instability ◽  
Nonlinear Effects ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

scholarly journals Precessional instability of a fluid cylinder

2011 ◽  
Vol 666 ◽  
pp. 104-145 ◽  
Author(s):  
ROMAIN LAGRANGE ◽  
PATRICE MEUNIER ◽  
FRANÇOIS NADAL ◽  
CHRISTOPHE ELOY
Keyword(s):  
Reynolds Number ◽  
Nonlinear Effects ◽  
Intermittent Flow ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Aspect Ratios ◽  
Image Velocimetry ◽  
Precessional Motion ◽  
Weakly Nonlinear Model

In this paper, the instability of a fluid inside a precessing cylinder is addressed theoretically and experimentally. The precessional motion forces Kelvin modes in the cylinder, which can become resonant for given precessional frequencies and cylinder aspect ratios. When the Reynolds number is large enough, these forced resonant Kelvin modes eventually become unstable. A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two additional free Kelvin modes is carried out. This analysis allows us to predict the spatial structure of the instability and its threshold. These predictions are compared to the vorticity field measured by particle image velocimetry with an excellent agreement. When the Reynolds number is further increased, nonlinear effects appear. A weakly nonlinear theory is developed semi-empirically by introducing a geostrophic mode, which is triggered by the nonlinear interaction of a free Kelvin mode with itself in the presence of viscosity. Amplitude equations are obtained coupling the forced Kelvin mode, the two free Kelvin modes and the geostrophic mode. They show that the instability saturates to a fixed point just above threshold. Increasing the Reynolds number leads to a transition from a steady saturated regime to an intermittent flow in good agreement with experiments. Surprisingly, this weakly nonlinear model still gives a correct estimate of the mean flow inside the cylinder even far from the threshold when the flow is turbulent.

Dynamic-relaxation solution for the large deflection of plates with specified boundary stresses

1969 ◽  
Vol 4 (2) ◽  
pp. 75-80 ◽  
Author(s):  
K R Rushton
Keyword(s):  
Large Deflection ◽  
Relaxation Method ◽  
Plane Boundary ◽  
Dynamic Relaxation ◽  
Simply Supported ◽  
Von Karman ◽  
Relaxation Solution ◽  
Von Kármán Equations ◽  
Mesh Spacing ◽  
Dynamic Relaxation Method

The von Kármán equations for the large deflection of plates are solved by the dynamic-relaxation method. Detailed results are presented for square plates having simply supported edges with zero in-plane boundary stresses. The results show that high stresses occur towards the corners of the plates. The mesh effect is investigated and recommendations are made for the optimum mesh spacing.

A weakly nonlinear framework to study shock–vorticity interaction

2022 ◽  
Vol 933 ◽  
Author(s):  
Pranav Thakare ◽  
Vineeth Nair ◽  
Krishnendu Sinha
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Significant Contribution ◽  
Interaction Analysis ◽  
Nonlinear Effects ◽  
Normal Shock ◽  
Linear Interaction ◽  
Weakly Nonlinear ◽  
High Incidence ◽  
Vorticity Generation

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

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