Active control of large amplitude vibrations of smart magneto–electro–elastic doubly curved shells

Abstract

This paper deals with the analysis of active constrained layer damping (ACLD) of large amplitude vibrations of smart magneto–electro–elastic (MEE) doubly curved shells. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composite (PZC). The constrained viscoelastic layer of the ACLD treatment is modeled by using the Golla–Hughes–McTavish method in the time domain. A three-dimensional finite element model of the overall smart MEE doubly curved shells has been developed taking into account the effects of electro–elastic and magneto–elastic couplings, while the von Karman type nonlinear strain displacement relations are used for incorporating the geometric nonlinearity. Influence of the curvature ratio, the curvature aspect ratio, the thickness aspect ratio on the nonlinear frequency ratios of the MEE doubly curved shells has been investigated. Effects of the location of the ACLD patches and the edge boundary conditions on the control of geometrically nonlinear vibrations of paraboloid and hyperboloid MEE shells have been studied. Particular attention has been paid to investigate the performance of the ACLD treatment due to the variation of the piezoelectric fiber orientation angle in the 1–3 PZC constraining layer of the ACLD treatment.