Nonlinear vibrations of shells and plates in traditional, soft and advanced materials

At Cnam, Paris, April 30th 2015, 11 a.m.

Marco Amabili
Professor, Department of Mechanical Engineering, McGill University, Montréal, Canada

The seminar will cover nonlinear vibrations and shell theories to model traditional and advanced materials, and soft tissues. While thin shells can be modeled with classical shell theories, structures in laminated and sandwich composite materials usually requires shell theories with shear deformation and rotary inertia. Biological soft tissues are usually subjected to significant static and dynamic loadings, potentially yielding large deflections and deformations that requires the introduction of hyperelastic models. For soft tissues the thickness deformation may also be very significant, and this requires the introduction of advanced shell theories that retain thickness deformation.

Static deflection as well as free and forced nonlinear vibrations of thin plates made of hyperelastic soft biological (or rubber) materials will be discussed. The material nonlinearities are described through Neo-Hookean, Mooney-Rivlin and Ogden hyperelastic laws. Dynamic local models are first built in the vicinity of a static configuration of interest that has been previously calculated. Numerical results are compared and validated in the static case via a commercial FE software package: they are found to be accurate for deflections reaching 100 times the thickness of the plate. The natural frequency shift during large-amplitude vibrations weakens with an increased initial deflection. An advanced nonlinear plate and shell theory is also presented in the seminar. The effect of retaining nonlinearities in rotations and thickness deformation will be discussed.

Finally, a comparison of numerical simulations and experiments for large amplitude (geometrically nonlinear) vibrations of sandwich plates and other shell structures will be presented.