An analytical solution is presented for the static deformation and steady-state vibration of simply supported hybrid cylindrical shells consisting of fiber-reinforced layers with embedded piezoelectric shear sensors and actuators. The piezoelectric shear actuator, which is poled in the circumferential direction, will induce transverse shear deformation of the hybrid shell when it is subjected to an electric field in the radial direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the governing equations of static deformation and steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations in the radial coordinate, which are solved by employing the Frobenius method. Natural frequencies, mode shapes, displacements, electric potential, and stresses are presented for four-layer hybrid laminates consisting of a piezoelectric shear sensor and actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using a positive position feedback controller. Frequency response curves for different controller frequencies, controller damping ratio, and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is demonstrated that vibration suppression of thickness modes is also feasible using the piezoelectric shear actuator.
Analysis of Static Deformation, Vibration and Active Damping of Cylindrical Composite Shells with Piezoelectric Shear Actuators
Vel, S. S., and Baillargeon, B. P. (August 5, 2004). "Analysis of Static Deformation, Vibration and Active Damping of Cylindrical Composite Shells with Piezoelectric Shear Actuators." ASME. J. Vib. Acoust. August 2005; 127(4): 395–407. https://doi.org/10.1115/1.1898337
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