Wave Propagation Methods for Conservation Laws with Source Terms

1999 ◽  
pp. 609-618 ◽  
Author(s):  
Randall J. LeVeque ◽  
Derek S. Bale
Keyword(s):  
Wave Propagation ◽  
Conservation Laws ◽  
Source Terms ◽  
Propagation Methods

A novel wave propagation method for measuring viscoelastic properties of pre-strained materials

2021 ◽  
pp. 1-19
Author(s):  
Pierre Lemerle
Keyword(s):  
Wave Propagation ◽  
Viscoelastic Properties ◽  
Time History ◽  
Main Concept ◽  
Frequency Dependent ◽  
Damping Characteristics ◽  
History Of ◽  
Propagation Methods ◽  
The Time Domain ◽  
Waveform Pattern

Abstract Viscoelastic materials are widely used for vibroacoustic solutions due to their ability to mitigate vibration and sound. Wave propagation methods are based on the measurement of the waveform pattern of a transitory pulse in one-dimensional structures. The time evolution of the pattern can be used to deduce the material elasticity and damping characteristics. The most popular propagation methods, namely Hopkinson bar methods, assume no dispersion, i.e. the complex elasticity modulus is not frequency-dependent. This is not significant for resilient materials such as elastomers. More recent approaches have been developed to measure frequency-dependent properties from a pulse propagating in a slender bar. We showed in previous works how to adapt these techniques for shorter samples of materials, representing a real advance, as extrusion is a cumbersome process for many materials. The main concept was to reconstruct the time history of the wave propagating in a composite structure composed of a long incident bar made of a known material and extended by a shorter sample bar. Then the viscoelastic properties of the sample material were determined in the frequency domain within an inverse method held in the time domain. In industry, most isolation solutions using mounts or bushings must support structural weights. This is why it is particularly interesting to know the viscoelastic properties of the material in stressed state. Here, we show how to overcome this challenging issue. The theoretical framework of the computational approach is detailed and the method is experimentally verified.

Configurational balance laws for incompatibility in stress space

2007 ◽  
Vol 463 (2081) ◽  
pp. 1379-1392 ◽  
Author(s):  
Xanthippi Markenscoff ◽  
Anurag Gupta
Keyword(s):  
Conservation Laws ◽  
Thermal Stresses ◽  
Stress Gradient ◽  
Positive Definite ◽  
Balance Laws ◽  
Source Terms ◽  
Stress Space ◽  
Lagrange Equations ◽  
Compatibility Conditions ◽  
Surface Data

Conservation laws have been recently obtained by requiring that a positive definite functional of the stress gradient (the Euler–Lagrange equations of which are the Beltrami–Michell compatibility conditions) be invariant under certain transformations. Here these laws are extended to include body forces, thermal stresses and Kröner's incompatibility tensor as source terms in the configurational balance laws, which allows for the incompatibility in the volume to be measured from surface data. An example is presented.

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