Related Experiment Video
Updated: Aug 2, 2025
09:39
Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
Published on: June 28, 2024
998
Dynamics of time-modulated, nonlinear phononic lattices
B L Kim1, C Chong2, S Hajarolasvadi3
1Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Physical Review. E
|April 19, 2023
Summary
This study explores acoustic and elastic wave propagation in time-periodic phononic lattices. Researchers found that controlling nonlinearity and external modulation enables advanced signal processing and telecommunication devices.
Area of Science:
- Physics
- Materials Science
- Engineering
Background:
- Acoustic and elastic wave propagation differs in time-varying media compared to traditional media.
- Phononic lattices offer unique wave control capabilities.
Purpose of the Study:
- Investigate the response of a one-dimensional phononic lattice with time-periodic elastic properties.
- Explore both linear and nonlinear regimes of wave propagation.
- Analyze the potential for advanced signal processing applications.
Main Methods:
- Experimental, numerical, and theoretical approaches were employed.
- A system with repelling magnetic masses and time-periodic stiffness was studied.
- Floquet theory was used to analyze instabilities and parametric amplification.
Main Results:
- Wave-number band gaps emerged in the linear regime, consistent with theory.
- Parametric amplification was observed due to underlying instabilities.
- Nonlinearity stabilized large-amplitude responses, leading to nonlinear time-periodic states.
- Linear theory accurately predicted bifurcations to time-periodic states.
- External drives resulted in bounded, stable, temporally quasiperiodic responses.
Conclusions:
- Controlling wave propagation by balancing nonlinearity and external modulation is a novel approach.
- This control enables advanced signal processing and telecommunication devices.
- Potential applications include time-varying operations, frequency conversion, and enhanced signal-to-noise ratios.
Related Concept Videos
01:28Standing Waves in a Cavity
969
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
969
01:03Modes of Standing Waves - I
3.0K
A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
3.0K
01:07Damped Oscillations
5.8K
In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Although friction and other non-conservative...
5.8K
01:30Oscillations In An LC Circuit
2.4K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
2.4K
01:21Time and frequency -Domain Interpretation of Phase-lag Control
127
Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any...
127
01:20Types of Damping
6.5K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
6.5K