Free and Forced Vibrations of Elastically Connected Structures

Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

Nonlinear vibrations of thin rectangular plates are considered, using the von Kármán equations in order to take into account the effect of geometric nonlinearities. Solutions are derived through an expansion over the linear eigenmodes of the system for both the transverse displacement and the Airy stress function, resulting in a series of coupled oscillators with cubic nonlinearities, where the...

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.

Free and forced vibrations of a segmented bar by a meshless local Petrov–Galerkin (MLPG) formulation

We use the meshless local Bubnov–Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary condition...

Forced Vibrations for a Nonlinear Wave Equation

Asymmetric non-linear forced vibrations of free-edge circular plates. Part 1: Theory

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