Title:

New Results on Nonlinear Vibrations and Stability of Shells

Speaker:

Prof. Marco Amabili

Affiliation:

McGill University, Montreal, Canada

When:

Thursday, March 17, 2011 at 3:30:00 PM   Add to Calendar

Where:

Guggenheim Building, Room 442

Host:

Glenda Duncan
glenda.duncan@aerospace.gatech.edu

Abstract

Because of the optimal distribution of materials, shells collapse for buckling much before the failure strength of the material is reached. For their thin nature, they can present large displacements, with respect to the shell thickness, associated to small strains before collapse. This is the rationale for using a geometrically nonlinear shell theory for studying shell stability. Shells are often subjected to dynamic loads that cause vibrations; vibration amplitudes of the order of the shell thickness can be easily reached in many applications. In these cases, a nonlinear shell theory should be applied. Large-amplitude (geometrically nonlinear) vibrations of shells with different boundary conditions and subjected to harmonic excitation are discussed. Both numerical and experimental results will be shown and compared. Simple and advanced shell theories are used to calculate the elastic strain energy. In-plane inertia and geometric imperfections are taken into account. The solution is obtained by the Lagrangian approach. Reduced-order models based on the proper orthogonal decomposition method (POD) and asymptotic nonlinear normal modes (NNMs) are discussed and compared. Internal resonances are also studied. The nonlinear shell dynamics is investigated by using the pseudo-arclength continuation method, bifurcation analysis, bifurcation diagrams obtained by direct time integration, and calculation of the Lyapunov exponents. Interesting phenomena such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations, (iv) chaotic behavior, and (v) hyperchaos are observed. Applications are addressed.

Biography

Graduating summa cum laude with a Master's degree in Mechanical Engineering from the University of Ancona, Italy in 1992 and completing his PhD in Mechanical Engineering, with a specialization in Vibrations at the University of Bologna, Italy in 1995, Marco Amabili currently is Full Professor in the Department of Mechanical Engineering at McGill University, Montreal, Canada, where he has held a prestigious Canada Research Chair, Tier 1. Prior to joining McGill, Professor Amabili held positions of Assistant and Associate Professor at the University of Parma, Italy.

Professor Amabili's area of research focuses on nonlinear vibrations and stability of shells and plates and fluid-structure interaction. He serves as Chair of the ASME Technical Committee on Dynamics and Control of Systems and Structures. He is Associate Editor of Journal of Fluids and Structures (Elsevier), Applied Mechanics Reviews (ASME), Mechanics Based Design of Structures and Machines (Taylor & Francis). He is Member of the Editorial Board of Journal of Sound and Vibration (Elsevier) and International Journal of Structural Stability and Dynamics (World Scientific). He has written more than 100 journal papers, 140 conference papers and the book publised by Cambridge University Press - Nonlinear vibrations and stability of shells and plates. His present H-index is 21.