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Novel current actuated piezoelectric composite model with fully dynamic electromagnetic field

Matthijs C. de Jong, Jacquelien M. A. Scherpen

Abstract

In this paper we propose a novel current actuated fully dynamic piezoelectric composite model. This new model complements the existing modeling framework of deriving piezoelectric models. We show that the novel composite model is well-posed. Furthermore, we consider two approximation methods, FEM and MFEM and investigate the stabilizability properties. Finally, we include the closed-loop behaviour in the numerical results.

Novel current actuated piezoelectric composite model with fully dynamic electromagnetic field

Abstract

In this paper we propose a novel current actuated fully dynamic piezoelectric composite model. This new model complements the existing modeling framework of deriving piezoelectric models. We show that the novel composite model is well-posed. Furthermore, we consider two approximation methods, FEM and MFEM and investigate the stabilizability properties. Finally, we include the closed-loop behaviour in the numerical results.

Paper Structure

This paper contains 10 sections, 7 theorems, 65 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Derivation physical model
  3. Well-posedness
  4. Approximations of piezoelectric composites
  5. FEM approximation
  6. MFEM approximation
  7. Verification of approximation
  8. Stabilizability of piezoelectric composite approximations
  9. Numerical results
  10. Conclusion

Key Result

Theorem 1

(Lumer-Phillips theorem) The closed and densely defined operator $A$ generates a strongly continuous semigroup of contractions $T(t)$ on $X$, if and only if both $A$ and its adjoint $A^*$ are dissipative, i.e.

Figures (5)

  • Figure 1: Piezoelectric composite with longitudinal deflection $v$ and transverse deflection $w$.
  • Figure 2: Converging transverse and longitudinal displacement for increasing approximation order $N=12162024$.
  • Figure 3: Closed-loop stabilizing trajectories. The longitudinal and traverse deflection of the fully dynamic piezoelectric composite using FEM approximations
  • Figure 4: Closed-loop stabilizing trajectories. The longitudinal and traverse deflection of the fully dynamic piezoelectric composite using MFEM approximations.
  • Figure 5: Eigenvalues of the closed-loop systems.

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Remark 3
  • Theorem 3: Brockett condition
  • ...and 6 more