Control of Largely-Deformed Nonlinear Electro/Elastic Beam and Plate Systems: Finite Element Formulation and Analysis

Abstract

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generalized nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems is studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

A Discrete-Time Event-Triggered Consensus Algorithm with Optimized Sampling for Multi-Agent Coordination Control

“…In practice, the measurement of velocity and acceleration is much more difficult than the information of displacement [30] . To solve these problems, this paper designs a second-order consensus protocol based on event-triggered mechanism for second-order nonlinear multi-agent systems based on the current and past sampling time position information [31] .…”