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Wave energy conversion by floating and submerged piezoelectric bimorph plates

Zachary J. Wegert, Ben Wilks, Ngamta Thamwattana, Vivien J. Challis, Santanu Koley, Michael H. Meylan

Abstract

Gaining insight into the interaction between flexible piezoelectric structures and ocean waves can inform the development of compact, high-efficiency wave-energy converters that harvest renewable energy from the marine environment. In this paper, the problem of wave energy absorption by floating and submerged piezoelectric plates is investigated. The equations of motion for a plate consisting of two piezoelectric layers separated by an elastic substrate are derived in dimensional form from the full piezoelectric constitutive laws. A novel solution method based on conversion of hypersingular equations to a matrix operator is presented, which is general and can solve the equations of motion for submerged rigid, flexible elastic or flexible piezoelectric plates. Extensive numerical results are given for a range of parameters, including different piezoelectric materials: polyvinylidene fluoride (PVDF) and lead zirconate titanate (PZT-5H). Importantly, greater energy absorption is obtained for submerged plates when compared to plates floating on the surface. Furthermore, clamped boundary conditions give slightly larger energy absorption compared to the simply supported case. Our open-source code is provided at https://github.com/zjwegert/SemiAnalyticWECs.jl.

Wave energy conversion by floating and submerged piezoelectric bimorph plates

Abstract

Gaining insight into the interaction between flexible piezoelectric structures and ocean waves can inform the development of compact, high-efficiency wave-energy converters that harvest renewable energy from the marine environment. In this paper, the problem of wave energy absorption by floating and submerged piezoelectric plates is investigated. The equations of motion for a plate consisting of two piezoelectric layers separated by an elastic substrate are derived in dimensional form from the full piezoelectric constitutive laws. A novel solution method based on conversion of hypersingular equations to a matrix operator is presented, which is general and can solve the equations of motion for submerged rigid, flexible elastic or flexible piezoelectric plates. Extensive numerical results are given for a range of parameters, including different piezoelectric materials: polyvinylidene fluoride (PVDF) and lead zirconate titanate (PZT-5H). Importantly, greater energy absorption is obtained for submerged plates when compared to plates floating on the surface. Furthermore, clamped boundary conditions give slightly larger energy absorption compared to the simply supported case. Our open-source code is provided at https://github.com/zjwegert/SemiAnalyticWECs.jl.

Paper Structure

This paper contains 14 sections, 65 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Mathematical theory
  3. Equations of motion for a piezoelectric bimorph
  4. Constitutive laws
  5. Circuiting
  6. Bending
  7. Charge
  8. Time harmonic formulation
  9. Equations of motion for the fluid
  10. The coupled system
  11. Solution methods
  12. Surface problem
  13. Submerged problem
  14. Diffraction problem

Figures (2)

  • Figure 1: Visualisation of a piezoelectric bimorph circuited in series comprising two oppositely poled piezoelectric layers with arbitrary poling direction $\theta$, resistance $R$, and thicknesses $d_p$ and $d_0$ for the piezoelectric layers (pink) and elastic substrate (blue), respectively. The black dashed lines represent the electrodes on the top and bottom of each piezoelectric plate.
  • Figure 2: Visualisation of the problem setup. For the plate on the surface ($h=0$), the complex-valued surface load is given by $\mathrm{p} = \mathrm{i}\omega\rho_w\phi-\mathrm{w} \rho_w g$. When the plate is submerged ($-H<h<0$), the surface load is instead $\mathrm{p}=-\mathrm{i}\omega\rho_w\llbracket\phi\rrbracket$.