Two-coupled Oscillator System Research Articles

Scaling properties of resonant cavities driven by piezo-electric actuators

Acoustic-structural properties of piezo-electric driven resonant cavities usually employed to generate the so-called synthetic jets are theoretically and numerically investigated in order to characterize the performances of such devices. It is shown that the actuator behaves as a two-coupled oscillators system and the dimensionless form of the governing equations allows one to identify various operating conditions, in particular those leading to their decoupling. The theoretical predictions are validated through analytical, numerical and experimental findings for devices having different mechanical and geometrical characteristics, designed to achieve an increasing coupling effect. Considerations about the strength of jet formation at the Helmholtz frequency are made as well.

Modeling and Experimental Validation of the Frequency Response of Synthetic Jet Actuators

A lumped-element mathematical model of the operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillator system, and simple relationships are given to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

Fluid-structure coupling effects in synthetic jet devices

The operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated by means of a lumped element mathematical model, in order to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillators system and simple relationships are given in order to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

Application of new entangled state representation to a two-coupled oscillator system

We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation |γ composed of the common eigenvectors of operators (x1+p2) and (p1+x2) is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in |γ representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can be used to derive the normally ordered product expression of eigenvector in Fock space. In particular, we find that the ground state of the Hamiltonian is a kind of generalized two-mode squeezed state.

Stochastic resonance in delayed two-coupled oscillators with input signals different in frequency

Stochastic resonance (SR) is investigated in a two-coupled oscillator system with time delay and a pinning force. Each oscillator is driven by a periodic signal and Gaussian white noise. Periodic signals at their inputs have equal amplitude but different frequencies. We find that each oscillator's SR behavior, which is described by the change of the signal-to-noise ratio (SNR) at the frequency of the signal into itself against the noise intensity, is in good agreement with that of the corresponding uncoupled single oscillator. In addition, the output SNR of one oscillator at the frequency of the signal into the other oscillator also demonstrates SR-like behavior with the increment of noise intensity. The results indicate the coexistence of decoupling and coupling effects and have implications in the area of information transmission in coupled-element neural network.

Stochastic resonance in delayed two-coupled oscillators without common perturbations.

Stochastic resonance (SR) in a two-coupled oscillator system with time delay is investigated. The system shows multistability of a desynchronized state and two synchronized states with different collective frequencies, which may be interpreted as multistable perception of ambiguous or reversible figures. To model the situations where the two oscillators exist in different environments, periodic signals and noises at their inputs are not uniformly given. SR in an individual oscillator, characterized by the output signal-to-noise ratio, is examined based on numerical simulations. We find that phase shift between the signals at inputs of different oscillators weakens SR, the oscillator with only an input signal does not show SR, and the oscillator with input noise shows SR irrespective of it having an input signal or not. The results have implications in the area of information transmission in biological systems.