Nonlinear acoustic response of two bubble oscillators

First Integrals for Two Linearly Coupled Nonlinear Duffing Oscillators

We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled nonlinear Duffing oscillators. Then, the first integrals with respect to Noether and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration. Mor...

Simulation of bubble motion in acoustic cavitation

The many particle problem of moving cavitation bubbles in a liquid exposed to ultrasound need certain ingredients: Besides N bubbles and their positions ~xi and velocities ~ui, one has to specify the bubble sizes and shapes. Mechanisms for nucleation and annihilation or coalescence of bubbles have to be introduced, and a sound field distribution has to be given. Additionally, a liquid motion ca...

Synchronization of driven nonlinear oscillators

Mathematical models of nonlinear oscillators are used to describe a wide variety of physical and biological phenomena that exhibit self-sustained oscillatory behavior. When these oscillators are strongly driven by forces that are periodic in time, they often exhibit a remarkable ‘‘mode-locking’’ that synchronizes the nonlinear oscillations to the driving force. The purpose of this paper is to d...

A Perturbation Procedure for Nonlinear Oscillations ( the Dynamics of Two Oscillators with Weak Nonlinear Coupling

Synchronization Analysis of Nonlinear Oscillators

The possibilities of studying nonlinear physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. The feedback resonance and synchronization phenomena are studied for 2-DOF system consisting of two coupled pendulums. Computer simulation results are presented.