Forced Vibrations of Plates with Rigid Bodies of Arbitrary Shape : 1st Report, Basic Equations and Numerical Examples for Axisymmetric Vibrations

Forced vibrations of wave equations with non-monotone nonlinearities

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a mi...

Rigid Body Vibrations of Compressors

Theoretical, numerical, and experimental analyses of free vibrations of glass fiber reinforced polymer plates with central cutouts and free boundaries

This study explored the free vibration problem in relation to glass fiber reinforced polymer (GFRP) plates with central cutouts and free boundaries using theoretical, experimental, and numerical methods. The theoretical formulations were derived from the classical lamination plate theory. The rectangular cutout was mathematically modeled into the stiffness matrix of the plate by multiplying Hea...

Forced vibrations of wave equations with non-monotone nonlinearities Vibrations forcées d’équations des ondes avec des non-linéarités non-monotones

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov– Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a m...

Forced Vibrations for a Nonlinear Wave Equation