Related Experiment Video
Updated: May 12, 2026
10:52
Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
Published on: April 13, 2016
Effect of multiple time-delay on vibrational resonance
C Jeevarathinam1, S Rajasekar, M A F Sanjuán
1School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India. c.jeeva1987@gmail.com
Chaos (Woodbury, N.Y.)
|April 6, 2013
Summary
Multiple time-delays impact vibrational resonance in Duffing oscillators. Analytical expressions reveal parameter regions for enhanced resonance and signal propagation in coupled systems.
Area of Science:
- Nonlinear Dynamics
- Vibrational Systems
- Chaos Theory
Background:
- Duffing oscillators are fundamental models for nonlinear systems.
- Vibrational resonance is a key phenomenon in understanding system dynamics.
- Time-delay effects can significantly alter system behavior.
Purpose of the Study:
- To investigate the influence of multiple time-delays on vibrational resonance.
- To analyze resonance in single and coupled Duffing oscillator systems.
- To derive analytical expressions for resonance parameters and signal propagation.
Main Methods:
- Analytical derivation of response amplitude and resonance conditions.
- Examination of parameter space for resonance enhancement.
- Analysis of coupled Duffing oscillators with single and multi time-delay couplings.
Main Results:
- For a single oscillator, time-delay introduces a band-like structure in resonance regions.
- In multi-delayed coupled systems, undamped signal propagation occurs above a critical coupling strength.
- Response amplitude in n-coupled oscillators becomes independent of time-delay for single time-delay coupling.
Conclusions:
- Time-delay plays a crucial role in modulating vibrational resonance in Duffing oscillators.
- Analytical insights into resonance and signal propagation are provided for coupled systems.
- The study offers a deeper understanding of complex dynamics in delayed nonlinear systems.
Related Concept Videos
01:19Concept 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...
01:12Double Resonance Techniques: Overview
Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
Spin decoupling is usually achieved by...
01:14Sound Waves: Resonance
Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
01:08IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
01:16IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
According to Hooke's law, the vibrational frequency is directly proportional to the...
01:20Types of Damping
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...