Laminated composite beams containing magnetostrictive layers are modeled as distributed parameter systems and the magnetostrictive layers are used to control the vibration suppression. Velocity feedback with constant gain distributed controller is chosen to achieve vibration suppression. A general formulation of the problem based on classical and shear deformation (the first-order as well as the third-order) theories is presented, and analytical solutions of the equations are developed for simply supported boundary conditions. The effect of material properties, lamination scheme, and placement of the magnetostrictive layers on vibration suppression is investigated.

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The corotational method for frame-invariant elements is generalized to obtain a consistent large-strain shell element incorporating thickness extensibility. The resulting element allows arbitrary in-plane deformations and is distinct from the traditional corotational methods (either quadrature-based or element-based) in the sense that the corotational frame is exact. The polar decomposition operation is performed in two parts, greatly simplifying the linearization calculations. Expressions for the strain-degreesof-freedom matrices are given for the first time. The symbolic calculations are performed with a well-known algebraic system with a code generation package. Classical linear benchmarks are shown with excellent results. Applications with hyperelasticity and finite strain plasticity are presented, with asymptotically quadratic convergence and very good benchmark results. An example of finite strain plasticity with fracture is solved successfully, showing remarkable robustness without the need of enrichment techniques.