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Sandwich beams with piezoelectric layers

Sandwich beams with piezoelectric layers. sensor. Elastic. Elastic core. Elastic. actuator. W e present, an analytical analysis in the case of a simply supported beam and a finite element analysis using Abaqus code. z. sensor. elastic. G. viscoelastic. x.

imani-patel
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Sandwich beams with piezoelectric layers

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  1. Sandwich beams with piezoelectric layers

  2. sensor Elastic Elastic core Elastic actuator • We present, an analytical analysis in the case of a simply supported beam and a finite element analysis using Abaqus code.

  3. z sensor elastic G viscoelastic x The electric field of piezoelectric layers: Ez = as used in many studies(Gopinathan et al. 2000) elastic actuator *Hypothesis:  Electric displacement depends on x. Thin piezoelectric layers with extension mechanism.  Classical laminate theory is used. No slips occurs at the interfaces between layers. Materials are linear, homogeneous and isotropic. The core is conductive with an uniform potential fixed to zero.

  4. *Kinematics: W = 0  T = Alembert principle H + T + W = 0  He =  Hp =  Hv = Elastic layers (e) Piezoelectric layers (p) Euler Bernoulli beam Viscoelastic layer (v) Timoshenko beam + Continuity conditions of displacement at the interfaces The core variables will be used: u, w,  *Variational Formulation:

  5. s depends on kinematics variables a = Gc s Direct proportional feedback control H + T = 0 u, w,  and Gc *Control law - Sensor : D3s = 0 - Actuator : Control *Validation We’ve computed different value of Gc under Maple Software and have compared the frequency and damping obtained with a 2D F.E.A. supported by Abaqus.

  6. *FEM with Abaqus support • Sandwiches with different, thickness layer, viscoelastic modulus and proportional feedback (Gc) were studied. Tab1:Frequency and damping ratios for different value of proportionnal feedback

  7. Our analytical results are in good agreement with the F.E.A. under Abaqus. • Indeed the difference on frequency obtain analytically and with the FEM is under 0.1 % and the damping give good result too ( unless when damping is to weak ). • Limitation: • Under Abaqus the frequency and the damping were obtained using a direct frequency method. • Analytical analysis is possible only under simple boundary conditions. Shell piezoelectric element is needed

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