scholarly journals TWO-SCALE MICROSTRUCTURE DYNAMICS

2011 ◽  
Vol 03 (03) ◽  
pp. 177-188
Author(s):  
ARKADI BEREZOVSKI ◽  
MIHHAIL BEREZOVSKI ◽  
JÜRI ENGELBRECHT
Keyword(s):  
Wave Propagation ◽  
Equations Of Motion ◽  
Dispersion Curves ◽  
Linear Momentum ◽  
Internal Variables ◽  
Type Model ◽  
Length Scale ◽  
Scale Separation ◽  
Dual Internal Variables

Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.

Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko’s sandwich piezoelectric microbeam

2017 ◽  
Vol 21 (4) ◽  
pp. 1243-1270 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M Zenkour
Keyword(s):  
Wave Propagation ◽  
Free Vibration ◽  
Equations Of Motion ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Governing Equations ◽  
Scale Parameters ◽  
Material Length Scale ◽  
Material Length

In this study, the strain gradient theory is employed to derive governing equations of motion of a functionally graded Timoshenko’s sandwich microbeam resting on Pasternak’s foundation. The microbeam is including a micro-core and two piezoelectric face-sheets on top and bottom. The plate is actuated with applied electric potential at top of piezoelectric face-sheets. The governing equations of motion are derived using Hamilton’s principle and strain gradient theory. After derivation of governing equations of motion, the problem is solved for three classes of analysis including wave propagation, free vibration and bending analysis. The numerical results are presented to reflect the effect of important parameters such as wave number, applied voltage, inhomogeneous index, parameters of foundation and material length-scale parameters on the different responses. The obtained results indicated that changing material length-scale parameters leads to a stiffer structure that increase natural frequencies and decreases transverse deflection and maximum electric potential.

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

scholarly journals Calculation of Wave Dispersion Curves in Multilayered Composite-Metal Plates

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ameneh Maghsoodi ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Transfer Matrix ◽  
Equations Of Motion ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Metal Plate ◽  
Material Symmetry ◽  
Major Purpose ◽  
Characteristic Equations ◽  
Multilayered Composite ◽  
Metal Plates

The major purpose of this paper is the development of wave dispersion curves calculation in multilayered composite-metal plates. At first, equations of motion and characteristic equations for the free waves on a single-layered orthotropic plate are presented. Since direction of wave propagation in composite materials is effective on equations of motion and dispersion curves, two different cases are considered: propagation of wave along an axis of material symmetry and along off-axes of material symmetry. Then, presented equations are extended for a multilayered orthotropic composite-metal plate using the transfer matrix method in which a global transfer matrix may be extracted which relates stresses and displacements on the top layer to those on the bottom one. By satisfying appropriate boundary conditions on the outer boundaries, wave characteristic equations and then dispersion curves are obtained. Moreover, presented equations may be applied to other materials such as monoclinic, transversely isotropic, cubic, and isotropic materials. To verify the solution procedure, a number of numerical illustrations for a single-layered orthotropic and double-layered orthotropic-metal are presented.

Locally resonant effective phononic crystals for subwavelength vibration control of torsional cylindrical waves

2021 ◽  
pp. 1-30
Author(s):  
Ignacio Arretche ◽  
Kathryn Matlack
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Effective Properties ◽  
Equations Of Motion ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Unit Cell ◽  
Periodic Coefficients ◽  
Bloch Theorem ◽  
Plane Wave Propagation

Abstract Locally resonant materials allow for wave propagation control in the sub-wavelength regime. Even though these materials do not need periodicity, they are usually designed as periodic systems since this allows for the application of the Bloch theorem and analysis of the entire system based on a single unit cell. However, geometries that are invariant to translation result in equations of motion with periodic coefficients only if we assume plane wave propagation. When wave fronts are cylindrical or spherical, a system realized through tessellation of a unit cell does not result in periodic coefficients and the Bloch theorem cannot be applied. Therefore, most studies of periodic locally resonant systems are limited to plane wave propagation. In this paper, we address this limitation by introducing a locally resonant effective phononic crystal composed of a radially-varying matrix with attached torsional resonators. This material is not geometrically periodic but exhibits effective periodicity, i.e. its equations of motion are invariant to radial translations, allowing the Bloch theorem to be applied to radially propagating torsional waves. We show that this material can be analyzed under the already developed framework for metamaterials. To show the importance of using an effectively periodic system, we compare its behavior to a system that is not effectively periodic but has geometric periodicity. We show considerable differences in transmission as well as in the negative effective properties of these two systems. Locally resonant effective phononic crystals open possibilities for subwavelength elastic wave control in the near field of sources.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Propagation of a nonlinear seismic pulse in an anelastic homogeneous medium

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 949-963 ◽  
Author(s):  
Dan W. Kosik
Keyword(s):  
Wave Propagation ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Homogeneous Medium ◽  
Seismic Surveys ◽  
Linear Elastic ◽  
Cylindrically Symmetric ◽  
Unconsolidated Material ◽  
Linear Pulse ◽  
Implicit Finite Difference

Seismic surveys are often conducted using dynamite charges buried near the surface in unconsolidated material. In such material a large zone near the source should exist wherein nonlinear anelastic wave propagation, can be expected to take place, and have a significant impact on the way in which a seismic pulse forms and how its energy gets distributed into the surrounding medium. To obtain a solution for a propagating pulse in this zone, the equations of motion for nonlinear anelastic wave propagation, good to second order in the displacements, are solved numerically for the problem of a Gaussian pressure pulse acting on the interior cavity of a cylindrically symmetric hole in the medium. An implicit finite‐difference algorithm is used for the solution to the equations of motion for this problem. The anelastic medium is characterized by multivalued stress‐strain relations that exhibit hysteresis, and therefore a loss of energy per cycle, corresponding to a medium with a constant Q factor. Several numerical examples are calculated contrasting the nonlinear anelastic, linear anelastic, and linear elastic propagating pulses to one another. The nonlinear anelastic propagating pulse is found to have an amplitude that is several times larger than would be expected for a pulse in a linear medium and has a peak propagation velocity that is slightly less than that for a linear pulse. Dispersive effects are also evident for the nonlinear pulse.

A Methodology for the Analysis of Physical Model Scale Effects on the Simulation of Wave Propagation up to Wave Breaking: Preliminary Physical Model Results

2008 ◽  
Author(s):  
Conceic¸a˜o Fortes ◽  
Maria da Grac¸a Neves ◽  
Joa˜o Alfredo Santos ◽  
Rui Capita˜o ◽  
Artur Palha ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Physical Model ◽  
Scale Effects ◽  
National Laboratory ◽  
Physical Models ◽  
Type Model ◽  
Research Activity ◽  
Joint Research ◽  
Common Structure ◽  
Constant Slope

This paper describes the experiments performed at the National Laboratory for Civil Engineering (LNEC) aiming at simulating, in a flume, the wave propagation along a constant slope bottom that ends on a sea wall coastal defence structure, a common structure employed in the Portuguese coast. The objective of these tests is to calibrate the parameters of FUNWAVE, a Boussinesq type model, for wave propagation in coastal regions. This is the first step in the validation of a methodology to combine numerical and physical models in the study of the interactions between beaches and structures. This work is performed in the framework of the Composite Modelling of the Interactions between Beaches and Structures (CoMIBBs) project, a joint research activity of the HYDRALAB III European project.

scholarly journals Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

2018 ◽  
Vol 8 (11) ◽  
pp. 2319 ◽  
Author(s):  
Evgeny Glushkov ◽  
Natalia Glushkova ◽  
Bernard Bonello ◽  
Lu Lu ◽  
Eric Charron ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Elastic Constants ◽  
Acoustic Waves ◽  
Composite Structures ◽  
Elastic Moduli ◽  
Surface Acoustic Waves ◽  
Dispersion Curves ◽  
Effective Elastic Moduli ◽  
Asymptotic Representations

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties.

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