Some approaches to harmonic wave propagation in elastic solids with random microstructure

2018 ◽  
Author(s):  
Alexander K. Belyaev ◽  
Vladimir A. Polyanskiy
Keyword(s):  
Wave Propagation ◽  
Harmonic Wave ◽  
Elastic Solids ◽  
Random Microstructure

Wave Propagation in Two-Dimensional Nonlinear Periodic Lattices

2009 ◽  
Author(s):  
Raj K. Narisetti ◽  
Massimo Ruzzene ◽  
Michael J. Leamy
Keyword(s):  
Wave Propagation ◽  
Linear Models ◽  
Periodic Structures ◽  
Harmonic Wave ◽  
Excitation Amplitude ◽  
Pass Band ◽  
Perturbation Approach ◽  
Nonlinear Stiffness ◽  
Two Dimensional ◽  
Low Amplitude

This paper investigates wave propagation in two-dimensional nonlinear periodic structures subject to point harmonic forcing. The infinite lattice is modeled as a springmass system consisting of linear and cubic-nonlinear stiffness. The effects of nonlinearity on harmonic wave propagation are analytically predicted using a novel perturbation approach. Response is characterized by group velocity contours (derived from phase-constant contours) functionally dependent on excitation amplitude and the nonlinear stiffness coefficients. Within the pass band there is a frequency band termed the “caustic band” where the response is characterized by the appearance of low amplitude regions or “dead zones.” For a two-dimensional lattice having asymmetric nonlinearity, it is shown that these caustic bands are dependent on the excitation amplitude, unlike in corresponding linear models. The analytical predictions obtained are verified via comparisons to responses generated using a time-domain simulation of a finite two-dimensional nonlinear lattice. Lastly, the study demonstrates amplitude-dependent wave beaming in two-dimensional nonlinear periodic structures.

scholarly journals Strains analysis at the wave propagation throught he contact layer of the elastic solids

2020 ◽  
pp. 89-96
Author(s):  
N.B. Chertova ◽  
◽  
Yu.V. Grinyaev ◽  
Keyword(s):  
Wave Propagation ◽  
Strain Distribution ◽  
Strain State ◽  
Strain Analysis ◽  
Contact Layer ◽  
Reflection Coefficients ◽  
Block Medium ◽  
Elastic Solids ◽  
Elastic Parameters ◽  
Analytical Expressions

The stress-strain state on the interface of the elastic solids is investigated. The studied interface presents a contact layer which is characterized by dimension and the set of physics mechanical parameters. The models of layered and block medium are used for the description this boundary. In the framework of these models the problem of elastic wave propagation through the interface is considered. Analytical expressions for the refraction and reflection coefficients allowing us to determine the strains on the interface and strains distribution in the contact layer are found. Corresponding strains amplitudes depending on the layer thickness are calculated at the different elastic parameters of contacting solids and boundary. The strain laws on the interface which is described by the layered and block medium models are analyzed. The regions of equivalent use these models are determined in the case of strain analysis on the boundary and the strain distribution in the contact layer.

Refined Theories for the Dynamic Analysis of Sandwich Structures

2017 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Wave Propagation ◽  
Dynamic Analysis ◽  
Dynamic Loading ◽  
Sandwich Structures ◽  
Harmonic Wave ◽  
Dispersion Relations ◽  
Sandwich Beams ◽  
New Models ◽  
The Individual ◽  
Selection Of

The objective of this study is to give an overview of existing theories for analyzing the behavior of sandwich beams and plates and to develop an approach for evaluating their behavior under dynamic loading. The dispersion relations for harmonic wave propagation through sandwich structures are shown to be a sound basis for evaluating whether the individual layers are modeled properly. The results provide a guide in the selection of existing models or the development of new models.

Lattice Boltzmann Method for Wave Propagation in Elastic Solids

2018 ◽  
Vol 23 (4) ◽  
Author(s):  
J. Surya Narayana J.Murthy ◽  
Praveen Kumar Kolluru ◽  
Vishwanathan Kumaran ◽  
Santosh Ansumali
Keyword(s):  
Wave Propagation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Elastic Solids ◽  
Boltzmann Method

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

1979 ◽  
Vol 46 (1) ◽  
pp. 113-119 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Body ◽  
Harmonic Wave ◽  
Wave Number ◽  
Periodic Medium ◽  
Frequency Wave ◽  
Wave Numbers ◽  
Band Characteristic

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

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