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Related Concept Videos

Parallel Resonance01:23

Parallel Resonance

The parallel RLC circuit is an arrangement where the resistor (R), inductor (L), and capacitor (C) are all connected to the same nodes and, as a result, share the same voltage across them. The parallel RLC circuit is analyzed in terms of admittance (Y), which reflects the ease with which current can flow. The admittance is given by:
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
Concept of Resonance and its Characteristics01:19

Concept of Resonance and its Characteristics

If a driven oscillator needs to resonate at a specific frequency, then very light damping is required. An example of light damping includes playing piano strings and many other musical instruments. Conversely, to achieve small-amplitude oscillations as in a car's suspension system, heavy damping is required. Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies. Speed bumps and gravel roads prove that even a car's suspension system is not immune...
Characteristics of Series Resonant Circuit01:24

Characteristics of Series Resonant Circuit

Series resonance occurs in a circuit containing inductive (L), capacitive (C), and resistive (R) elements connected sequentially. At the resonance frequency, the inductive and capacitive reactances are equal in magnitude but opposite in sign, effectively canceling each other. This causes the circuit's impedance is minimal, primarily determined by the resistance R. The resonant frequency of an RLC circuit is defined as:
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Series Resonance01:17

Series Resonance

The RLC circuit impedance is defined as the ratio of the supply voltage to the circuit current. Resonance in such a circuit occurs when the imaginary part of this impedance equals zero. This specific condition means that the inductive reactance is exactly equal to the capacitive reactance. The frequency at which this happens is known as the resonant frequency. Mathematically, the resonant frequency is inversely proportional to the square root of the product of the inductance (L) and capacitance...

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Pattern selection in parametrically driven arrays of nonlinear resonators.

Eyal Kenig1, Ron Lifshitz, M C Cross

  • 1Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

This study investigates pattern selection in nonlinear resonators, revealing hysteretic effects during transitions between standing-wave patterns. These findings are crucial for microelectromechanical and nanoelectromechanical systems.

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Area of Science:

  • Nonlinear Dynamics
  • Condensed Matter Physics
  • Applied Physics

Background:

  • Parametrically driven nonlinear resonators are key components in microelectromechanical and nanoelectromechanical systems.
  • Understanding pattern selection is essential for controlling the behavior of these systems.

Purpose of the Study:

  • To investigate pattern selection in arrays of parametrically driven nonlinear resonators.
  • To analyze transitions between standing-wave patterns with varying wave numbers.
  • To explore hysteretic effects in these transitions.

Main Methods:

  • Utilizing an amplitude equation derived by Bromberg, Cross, and Lifshitz (Phys. Rev. E 73, 016214 (2006)).
  • Describing pattern transitions under quasistatic, abrupt, and linear ramp variations of drive amplitude.
  • Confirming analytical findings through numerical integration of the original equations of motion.

Main Results:

  • Identified transitions between standing-wave patterns with different wave numbers.
  • Observed significant hysteretic effects as drive amplitude is modulated.
  • Numerical simulations validated the predicted hysteretic phenomena.

Conclusions:

  • The study provides a comprehensive analysis of pattern selection dynamics in nonlinear resonator arrays.
  • Hysteretic effects are a critical feature influencing pattern transitions.
  • The findings have direct implications for the design and application of micro- and nanoelectromechanical systems.