Related Experiment Video
Updated: Feb 27, 2026
15:06
Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
13.5K
Scattering of harmonic waves from a nonlinear elastic inclusion
1U.S. Army Research Laboratory, Weapons and Materials Research Directorate, Building 4600, Aberdeen Proving Ground, Maryland 21005-5069, USA.
The Journal of the Acoustical Society of America
|July 7, 2017
Summary
This study models harmonic scattering from nonlinear elastic inclusions. The findings offer a new experimental method to probe material nonlinear elastic properties.
Area of Science:
- Solid Mechanics
- Acoustics
- Materials Science
Background:
- Understanding wave propagation in heterogeneous media is crucial.
- Nonlinear elastic properties significantly influence wave behavior.
- Characterizing material nonlinearities is essential for advanced applications.
Purpose of the Study:
- To develop a theoretical framework for harmonic scattering from nonlinear elastic inclusions.
- To provide a method for quantifying acoustic nonlinearity parameters.
- To explore potential experimental techniques for material characterization.
Main Methods:
- Derivation of elastodynamic equations for anisotropic materials with cubic nonlinearity.
- Application of the method of successive approximations to decouple equations.
- Utilizing Green's functions to calculate scattering amplitudes for arbitrary shapes.
Main Results:
- General forms of scattering amplitudes derived as functions of quadratic and cubic nonlinearity parameters.
- Closed-form solutions obtained for specific geometries, including spherical inclusions.
- Analysis of the influence of elastic stiffnesses, wave modes, and scattering angles.
Conclusions:
- The developed scattering model accurately describes harmonic generation in nonlinear elastic composites.
- The study presents a viable approach for experimental determination of nonlinear elastic properties.
- This work contributes to the field of nonlinear acoustics and materials characterization.
Related Concept Videos
01:03Modes of Standing Waves - I
4.2K
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...
4.2K
02:18Interference and Diffraction
52.9K
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
52.9K
01:28Standing Waves in a Cavity
1.5K
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:
1.5K
01:07Interference and Superposition of Waves
7.2K
When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
7.2K
01:17Standing Waves
5.6K
Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
5.6K
01:07Damped Oscillations
7.4K
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...
7.4K