Steady-state 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

Steady State Analysis of Nanofuel Droplet ‎Evaporation

The potential for nanofuels as one of the clean sources of energy on account of its enhanced combustion performance coupled with low emissions has been established. Considering the importance of the fuel evaporation phase in the entire combustion process, this work presents an attempt at applying the steady state analysis equations to nanofuel experimental data obtained from the li...

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...

Transient and steady-state amplitudes of forced waves in rectangular basins

A weakly-nonlinear analysis of the transient evolution of two-dimensional, standing waves in a rectangular basin is presented. The waves are resonated by periodic oscillation along an axis aligned with the wavenumber vector. The amplitude of oscillation is assumed to be small with respect to the basin dimensions. The effects of detuning, viscous damping, and cubic nonlinearity are all simultane...