Linear Elastic Waves

Abstract Elastic waves in fluid-saturated granular media depend on the grain rheology, which can be complicated by the presence of gas bubbles. We investigated the effect of the bubble dynamics and their role in rheological scheme, on the linear Frenkel-Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum and bubbles surrounded by the fluid. We derived the Nikolaevskiy-type equation describing the velocity of the solid matrix in the moving reference system. The equation is linearized to yield the decay rate λ as a function of the wave number k. We compared the λ (k) -dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For both the cases, the λ(k) curve lies entirely below zero, which implies a global decay of the wave. We found that the increase of the radius of the bubbles leads to a faster decay, while the increase in the number of the bubbles leads to slower decay of the wave.

Download Full-text

Linear elastic waves

Choice Reviews Online ◽

10.5860/choice.39-4631 ◽

2002 ◽

Vol 39 (08) ◽

pp. 39-4631-39-4631

Keyword(s):

Elastic Waves ◽

Linear Elastic

Download Full-text

Dispersive Wave Propagation in the Nonlocal Peridynamic Theory

Volume 12: Mechanics of Solids, Structures and Fluids ◽

10.1115/imece2008-67894 ◽

2008 ◽

Cited By ~ 2

Author(s):

Olaf Weckner ◽

Stewart Silling ◽

Abe Askari

Keyword(s):

Elastic Waves ◽

Equation Of Motion ◽

Elastic Problem ◽

Local Problem ◽

Dispersive Wave ◽

Nonlinear Dispersion ◽

Initial Value ◽

Linear Elastic ◽

Nonlinear Dispersion Relation ◽

Nonlocal Formulation

Peridynamics is a nonlocal formulation of continuum mechanics that is oriented toward deformations including discontinuities, especially fractures. However already the linear elastic problem is considerably more complex than the corresponding local problem governed by the NAVIER equations. For example, the presence of long-range forces leads to the dispersion of elastic waves. The amount of dispersion is governed by the peridynamic horizon, a length-scale that naturally appears in in the equation of motion. Another example is the emergence and propagation of discontinuities that can be observed by studying the RIEMANN problem. In this presentation we show how FOURIER transformations can be used to find a representation of the solution of the general inhomogeneous initial value problem for the 3D linear bond-based peridynamic formulation. Several examples illustrate this approach and show the importance of the peridynamic horizon. Finally we demonstrate how the nonlinear dispersion relation can be used to capture experimentally measure dispersion relations.

Download Full-text

Linear elastic waves

Elastic Waves at High Frequencies ◽

10.1017/cbo9780511781094.002 ◽

2010 ◽

pp. 1-22

Author(s):

John G. Harris

Keyword(s):

Elastic Waves ◽

Linear Elastic

Download Full-text

Eigenstrain-Based Algorithm for Viscoelastic Uniaxial Wave Propagation due to Impact

Volume 1D: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-3927 ◽

1997 ◽

Author(s):

Hans Irschik ◽

Alexander K. Belyaev ◽

Peter Raschl

Keyword(s):

Wave Propagation ◽

Numerical Integration ◽

Constitutive Equations ◽

Elastic Waves ◽

Analytic Solution ◽

Present Contribution ◽

Linear Elastic ◽

Background Structure ◽

Physical Background ◽

Multiple Field

Abstract A numerical algorithm for uni-axial inelastic wave propagation due to impact-type loading is presented. The algorithm is based on the linear-elastic multiple-field formulation, in which inelastic parts of strain are considered as eigenstrains acting upon a linear-elastic background structure. The solution thus can be consistently found by superposition of altogether elastic waves, where the fictitious eigenstrains are calculated from the inelastic constitutive equations by numerical integration. Due to the physical background of the method, the procedure turns out to be both, computationally accurate and numerically stable. In the present contribution, the algorithm is realized in C++ and applied to the loading-unloading problem of a semi-infinite rod of Maxwell material. The accuracy of the algorithm is demonstrated by comparing to an analytic solution which is derived in the form suitable for comparison.

Download Full-text

Wave-like solutions in Cosserat micropolar elasticity

10.5194/egusphere-egu21-5241 ◽

2021 ◽

Author(s):

Christian Boehmer

Keyword(s):

Wave Velocity ◽

Elastic Waves ◽

Nonlinear Partial Differential Equations ◽

Coupled System ◽

Material Point ◽

Micropolar Elasticity ◽

Linear Elastic ◽

Cosserat Model ◽

Material Points ◽

Rotational Waves

<p>The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity.&#160; We couple the rotational waves to linear elastic waves to study the behaviour of the coupled system and find wave-like solutions with differing wave speeds. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small.</p>

Download Full-text