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Active vibration control of smart composite laminates with partial debonding of actuator

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Abstract

The effect of actuator debonding on the performance of active vibration control is analytically investigated through an optimal control strategy. An improved layerwise theory with Heaviside step functions, which addresses discontinuous displacement fields, is used for modeling the actuator debonding. General finite element procedures are developed to derive the governing equation taking into consideration the electro-mechanical coupling effect. A reduced-order model based on the state-space model is adopted for the design of the active controller. Generally, debonding in actuators reduces their load carrying capability, dynamic properties and vibration control characteristics. The effect of debonding on the vibration control is investigated by the proposed analytical modeling. Numerical results using a 16-layer cross-ply laminate with healthy actuator and partially debonded actuator are given for the investigation of the vibration suppression efficiency and control effort. It is observed that the control authority of the composite laminates with partially debonded piezoelectric actuator is dramatically reduced by increasing the size of the actuator debonding. Since debonding failure may occur during the service life of smart composite laminates, the results showed that actuator debonding must be considered as an uncertainty parameter in the design of active controllers.

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Abbreviations

Al k, Bl k, Cl k, Dl k, El k and Fl k :

layerwise coefficients

α, β:

proportional damping ratios

[b]:

permittivity matrix

{D}:

dielectric displacement vector

{E}:

electric field vector

Ez j :

mid-plane electric field

{ε}:

mechanical strain vector

{η}:

modal coordinate

F ϕ :

electrical field vector

F u :

mechanical force vector

{ϕ}:

eigenvector

ϕ 1, ϕ 2 :

rotations of the normal to the reference plane

ϕ j :

electric potential function

ϕ 0 j :

mid-plane electric potential

\(\bar \varphi ^j\) :

potential difference between the top and bottom electrodes of the jth piezoelectric layer

H m , H xm , H ym :

Hermite interpolation functions

h j :

thickness of jth piezoelectric layer

ξ :

material damping constant

ξ i :

ith modal damping

K ϕϕ , K uϕ , K ϕu :

dielectric stiffness matrix, coupling stiffness matrices, respectively

k :

kth layer of laminate

M uu , C uu , K uu :

mass, damping and stiffness matrices, respectively

N :

number of layers

N m :

Lagrange interpolation function

n :

number of node in one element

{Q}:

elastic stiffness matrix

q e :

applied surface charge density

ρ :

mass density

{σ}:

mechanical stress vector

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Authors and Affiliations

  1. Department of Mechanical, Robotics and Energy Engineering, Dongguk University-Seoul, 30, Pildong-ro 1-gil, Jung-gu, Seoul, 100-715, South Korea

    Bin Huang & Heung Soo Kim

  2. Department of Mechanical and Aerospace Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-742, South Korea

    Byeng Dong Youn

Authors
  1. Bin Huang
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  2. Heung Soo Kim
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Correspondence to Heung Soo Kim.

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Huang, B., Kim, H.S. & Youn, B.D. Active vibration control of smart composite laminates with partial debonding of actuator. Int. J. Precis. Eng. Manuf. 16, 831–840 (2015). https://doi.org/10.1007/s12541-015-0109-y

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  • DOI: https://doi.org/10.1007/s12541-015-0109-y

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