Nonlinear dynamics and active/passive control of parametrically excited slender structures

Abstract

This dissertation deals with the nonlinear dynamics and active/passive control of parametrically excited beam-like slender structures using piezoelectric actuators, viscoelastic damping materials and functionally graded materials (FGMs). First, the dynamics of smart slender beams is studied where the main focus is to investigate the usefulness of shear mode and extensional mode piezoelectric actuators in active control of complex nonlinear dynamics of the smart beams in pre- and post-buckled states. The subsequent study is carried out to investigate the usefulness of viscoelastic damping materials in passive control of complex dynamics of parametrically excited beams. However, for the corresponding dynamic analysis, a formulation of the HBM-based full-order FE model (FOM) is derived by introducing three new strategies, namely (a) a special factorization of the nonlinear strain-displacement matrix, (b) exploitation of orthogonality of Fourier basis functions and (c) reduction of various viscoelastic constitutive relations into a generalized mathematical form for the time-periodic stress/strain. Further, to achieve reduced computational time in evaluating nonlinear transient/frequency responses, the nonlinear FOMs are subsequently reduced to reduced-order FE models (ROMs). The formulation of nonlinear ROMs is carried out at the elemental level without involving the full-order system matrices/vectors, where the primary contribution lies in the formulation of the nonlinear memory-load vector. Besides the reduced computational time, the accuracy of the nonlinear ROMs is achieved by proposing a new methodology for computation of appropriate reduced basis vectors (RBVs) using normal vibration modes (NMs), static modal derivatives (MDs) and proper orthogonal decomposition (POD) method. Finally, an FGM is taken as the material of a beam-like slender structure, where the main focus is to investigate the influence of graded material properties of the slender FGM structure on its nonlinear dynamic characteristics under the parametric excitation. This study is performed considering a pinned-pinned vertical/inclined FG pipe conveying hot fluid with the steady/pulsatile flow velocity.