An Efficient Layerwise Finite Element Model for Active Vibration Control of Piezolaminated Composite Shells considering Strong Electric Field Nonlinearity

Prof. Santosh Kapuria, Indian Institute of Technology Delhi

18 Jul 2013, 17:00–18:30; Location: S4|10-1

In this work, we present a computationally efficient finite element (FE) model for statics, dynamics and vibration control of smart composite and sandwich shallow shells integrated with piezoelectric sensors and actuators, considering their nonlinear characteristics under strong electric field. The nonlinearity is modeled using the rotationally invariant nonlinear constitutive equations of Tiersten (1993), with the assumption of large electric field and small strains. The FE is based on the fully coupled zigzag theory, which has accuracy similar to the layerwise theories, and but retains the economy of the equivalent single-layer theories, with only five displacement unknowns. The nonlinear equations are derived using the extended Hamilton’s principle of virtual work. For static analysis, these equations are solved using the direct iteration method. For active vibration control, the FE model is transformed to the reduced order modal space considering first few modes and expressed in the state space form. The resulting nonlinear control problem with LQG controller is solved using the feedback linearization approach. The results predicted by the nonlinear model compare very well with the experimental data available in the literature for static response. The effect of the piezoelectric nonlinearity on the static response and active vibration control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, composite and sandwich substrates. The linear model significantly overestimates the peak control voltage required to achieve a given settling time. While in the linear model, the control voltage for a given settling time is almost independent of the actuator thickness, its nonlinear prediction reduces significantly with the decrease in the actuator thickness.

Category: CE Seminar


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