Forced Vibrations

Forced Vibrations of a Nonhomogeneous String

We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov–Schmidt reduction and a Nash–Moser iteration scheme.

Forced Vibrations for a Nonlinear Wave Equation

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...

Determination of the Viscoelastic Shear Modulus Using Forced Torsional Vibrations

Many methods exist for the experimental determination of the viscoelastic properties of materials. Some of these methods have been summarized [1,2]' and those that have been used more recently appear in a collection of abstracts [3]. The method described herein, which uses forced torsional vibrations, is an updated version of previous works [4,5]. It was selected because it most easily met the ...

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...