|
Abstract
|
In this paper a nonlinear approach to studying the vibration characteristic of laminated composite
plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange
type of strain–displacements relations, by incorporating higher-order terms arising from
nonlinear relations of kinematics into mathematical formulations. The equations of motion are
obtained through the energy method, based on Lagrange equations and by using higher-order
shear deformation theories with von Karman–type nonlinearities, so that transverse shear strains
vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is
provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch.
Different boundary conditions are investigated. Optimal locations of piezoelectric patches are
found using a genetic algorithm to maximize spatial controllability/observability and
considering the effect of residual modes to reduce spillover effect. Active attenuation of
vibration of laminated composite plate is achieved through an optimal control law with
inequality constraint, which is related to the maximum and minimum values of allowable voltage
in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the
Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of
control inputs. The results are compared with similar ones, proving the accuracy of the model
especially for the structures undergoing large deformations. The convergence is studied and
nonlinear frequencies are obtained for different thickness ratios. The structural coupling between
plate and piezoelectric actuators is analyzed. Some examples with new features are presented,
indicating that the piezo-patches significantly improve the damping characteristics of the plate
for suppressing the geometrically nonlinear transient vibrations
|