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Journal articles on the topic 'Metamaterials. Elasticity. Wave-motion, Theory of'

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Published: 4 June 2021

Last updated: 12 February 2022

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1

MEI, CHIANG C., and YING-HUNG LIU. "Approximate theory of acoustic waveguide of metamaterials." Journal of Fluid Mechanics 678 (April 12, 2011): 203–20. http://dx.doi.org/10.1017/jfm.2011.106.

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We theoretically examine the propagation of sound in a waveguide bounded by a metamaterial formed by an array of small Helmholtz resonators. The field equation is shown to be similar to that governing sound in a bubbly liquid. The effects of dissipation on the wave dispersion are examined. In particular, it is shown that the energy in a monochromatic wave train is not transported by the real part of the complex group velocity unless dissipation is absent. We further derived the envelope equation and show that in a one-dimensional waveguide, energy is transported forward despite the backward mo

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2

Norris, A. N., and W. J. Parnell. "Hyperelastic cloaking theory: transformation elasticity with pre-stressed solids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2146 (2012): 2881–903. http://dx.doi.org/10.1098/rspa.2012.0123.

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Transformation elasticity, by analogy with transformation acoustics and optics, converts material domains without altering wave properties, thereby enabling cloaking and related effects. By noting the similarity between transformation elasticity and the theory of incremental motion superimposed on finite pre-strain, it is shown that the constitutive parameters of transformation elasticity correspond to the density and moduli of small-on-large theory. The formal equivalence indicates that transformation elasticity can be achieved by selecting a particular finite (hyperelastic) strain energy fun

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3

Gaygusuzoglu, Guler, Metin Aydogdu, and Ufuk Gul. "Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 7-8 (2018): 709–19. http://dx.doi.org/10.1515/ijnsns-2017-0225.

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AbstractIn this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical in

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ISLAM, Z. M., P. JIA, and C. W. LIM. "TORSIONAL WAVE PROPAGATION AND VIBRATION OF CIRCULAR NANOSTRUCTURES BASED ON NONLOCAL ELASTICITY THEORY." International Journal of Applied Mechanics 06, no. 02 (2014): 1450011. http://dx.doi.org/10.1142/s1758825114500112.

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The presence of size effects represented by a small nanoscale on torsional wave propagation properties of circular nanostructure, such as nanoshafts, nanorods and nanotubes, is investigated. Based on the nonlocal elasticity theory, the dynamic equation of motion for the structure is formulated. By using the derived equation, simple analytical solutions for the relation between wavenumber and frequency via the differential nonlocal constitutive relation and the numerical solutions for a discrete nonlocal model via the integral nonlocal constitutive relation have been obtained. This results not

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5

Mishra, B. K., and P. C. Upadhyay. "Dynamic Response of Buried Pipelines—An Elasticity Solution." Journal of Pressure Vessel Technology 112, no. 3 (1990): 291–95. http://dx.doi.org/10.1115/1.2928628.

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This paper presents a theory of elasticity solution of the axisymmetric steady-state dynamic response of a buried pipeline excited by a plane longitudinal wave (P-wave) traveling in the surrounding soil. Both the pipeline and the ground have been assumed to be linearly elastic, homogeneous and isotropic. Linear elasticity equations of motion have been solved simultaneously for the pipeline and the surrounding soil. A perfect bond between the pipeline and the ground has been assumed. The midplane deformations of the pipeline have been plotted against the nondimensional wave number of the incide

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6

Rousseau, Martine, and Gérard A. Maugin. "Rayleigh surface waves and their canonically associated quasi-particles." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (2010): 495–507. http://dx.doi.org/10.1098/rspa.2010.0229.

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Inspired by soliton theory and exploiting the conservation law of wave momentum, it is shown that one can associate with the surface Rayleigh wave of macroscopic elasticity a quasi-particle, a ‘surface phonon’, which is in inertial motion for the standard boundary conditions. The ‘mass’ of this ‘particle’ is determined in terms of the wave properties. Different types of alteration in the boundary conditions are shown to result in perturbations of this inertial motion in various ways. The essential tool in the presented derivation is the exploitation of the canonical equations of conservation,

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7

MICHELITSCH, THOMAS M., GÉRARD A. MAUGIN, MUJIBUR RAHMAN, SHAHRAM DEROGAR, ANDRZEJ F. NOWAKOWSKI, and FRANCK C. G. A. NICOLLEAU. "A continuum theory for one-dimensional self-similar elasticity and applications to wave propagation and diffusion." European Journal of Applied Mathematics 23, no. 6 (2012): 709–35. http://dx.doi.org/10.1017/s095679251200023x.

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We analyse some fundamental problems of linear elasticity in one-dimensional (1D) continua where the material points of the medium interact in a self-similar manner. This continuum with ‘self-similar’ elastic properties is obtained as the continuum limit of a linear chain with self-similar harmonic interactions (harmonic springs) which was introduced in [19] and (Michelitsch T.M. (2011) The self-similar field and its application to a diffusion problem. J. Phys. A Math. Theor.44, 465206). We deduce a continuous field approach where the self-similar elasticity is reflected by self-similar Laplac

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8

Norris, A. N., and D. L. Johnson. "Nonlinear Elasticity of Granular Media." Journal of Applied Mechanics 64, no. 1 (1997): 39–49. http://dx.doi.org/10.1115/1.2787292.

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The finite and incremental elasticity of a random packing of identical spheres is derived using energy methods. We consider different models for the contact forces between spheres, all of which are based upon or related to the fundamental Hertz theory; we consider only the special cases of perfect friction (no tangential slip) or no tangential friction. The existence of a strain energy function for the medium depends critically upon the type of contact. If the tangential contact stiffness is independent of the normal force, then the energy is well defined for all values of the macroscopic stra

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9

Kalderon, Moris, Andreas Paradeisiotis, and Ioannis Antoniadis. "2D Dynamic Directional Amplification (DDA) in Phononic Metamaterials." Materials 14, no. 9 (2021): 2302. http://dx.doi.org/10.3390/ma14092302.

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Phononic structures with unit cells exhibiting Bragg scattering and local resonance present unique wave propagation properties at wavelengths well below the regime corresponding to bandgap generation based on spatial periodicity. However, both mechanisms show certain constraints in designing systems with wide bandgaps in the low-frequency range. To face the main practical challenges encountered in such cases, including heavy oscillating masses, a simple dynamic directional amplification (DDA) mechanism is proposed as the base of the phononic lattice. This amplifier is designed to present the s

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10

Gerasik, Vladimir, and Marek Stastna. "Poroelastic acoustic wave trains excited by harmonic line tractions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2090 (2007): 491–511. http://dx.doi.org/10.1098/rspa.2007.0107.

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A two-dimensional boundary-value problem for a porous half-space with an open boundary, described by the widely recognized Biot's equations of poroelasticity, is considered. Using complex analysis techniques, a general solution is represented as a superposition of contributions from the four different types of motion corresponding to P1, P2, S and Rayleigh waves. Far-field asymptotic solutions for the bulk modes, as well as near-field numerical results, are investigated. Most notably, this analysis reveals the following: (i) a line traction generates three wave trains corresponding to the bulk

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11

Ponnusamy, Palaniyandi. "Elastic Waves in Generalized Thermo-Piezoelectric Transversely Isotropic Circular Bar Immersed in Fluid." Advances in Applied Mathematics and Mechanics 8, no. 1 (2015): 82–103. http://dx.doi.org/10.4208/aamm.2013.m428.

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AbstractIn this paper, a mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of circular cross-sections immersed in inviscid fluid. The present study is based on the use of the three-dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied based on Lord-Shulman, Green-Lindsay and Classical theory t

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12

Ejaz, K., and M. Shams. "Love waves in compressible elastic materials with a homogeneous initial stress." Mathematics and Mechanics of Solids 24, no. 8 (2018): 2576–90. http://dx.doi.org/10.1177/1081286518771726.

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In this paper, the motion of Love waves is considered in hyperelastic materials with an initially stressed reference configuration. Here, the Love wave is directed by a compressible layer on a compressible half-space and both are considered to be initially stressed. For the basic formulation of the problem, we make use of the nonlinear theory of elasticity and invariants of the stress tensor and deformation tensor. The equations governing a finite deformation superimposed by infinitesimal motions are used to the study the composite effect of finite deformation and initial stress on wave speed.

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13

LIU, ZHANFANG, XIAOYONG SUN, and YUAN GUO. "ON ELASTIC STRESS WAVES IN AN IMPACTED PLATE." International Journal of Applied Mechanics 06, no. 04 (2014): 1450047. http://dx.doi.org/10.1142/s1758825114500471.

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Elastic stress wave theory is developed and the stress waves in the impacted plate are examined in the paper. Generalized linear elasticity is adopted where the couple stress and curvature tensor are both deviatoric tensors and they meet a linear constitutive relation. It is found that there exist volumetric, rotational, and deviatoric waves in the generalized elastic solids. However, for macro-scale elastic solids only two wave modes, namely a volumetric wave and a deviatoric wave should be taken into account. Wave motion in plate impact tests is studied that a volumetric wave and a deviatori

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14

Li, Yueqiu, Peijun Wei, and Changda Wang. "Propagation of thermoelastic waves across an interface with consideration of couple stress and second sound." Mathematics and Mechanics of Solids 24, no. 1 (2017): 235–57. http://dx.doi.org/10.1177/1081286517736999.

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The reflection and transmission of thermoelastic waves across an interface between two different couple stress solids are studied based on the thermoelastic Green–Naghdi theory with consideration of second sound. First, some thermodynamic equations of a couple stress elastic solid are formulated and the function of free energy density is postulated. Second, equations of thermal motion and heat conduction of the couple stress elasticity are derived and constitutive relations with thermoelastic coupled effects are obtained. From these equations, four kinds of dispersive waves, namely, thermal-me

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15

Tomar, S. K., N. Goyal, and A. Szekeres. "Plane Waves in Thermo-Viscoelastic Material with Voids Under Different Theories of Thermoelasticity." International Journal of Applied Mechanics and Engineering 24, no. 3 (2019): 691–708. http://dx.doi.org/10.2478/ijame-2019-0043.

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Abstract Propagation of time harmonic plane waves in an infinite thermo-viscoelastic material with voids has been investigated within the context of different theories of thermoelasticity. The equations of motion developed by Iesan [1] have been extended to incorporate the Lord-Shulman theory (LST) and Green-Lindsay theory (GLT) of thermoelasticity. It has been shown that there exist three coupled dilatational waves and an uncoupled shear wave propagating with distinct speeds. The presence of thermal, viscosity and voids parameters is responsible for the coupling among dilatational waves. All

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16

Yang, Yang, Qihui Lin, and Rongxin Guo. "Axisymmetric Wave Propagation Behavior in Fluid-Conveying Carbon Nanotubes Based on Nonlocal Fluid Dynamics and Nonlocal Strain Gradient Theory." Journal of Vibration Engineering & Technologies 8, no. 5 (2020): 773–80. http://dx.doi.org/10.1007/s42417-019-00194-1.

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Abstract Purpose Goal for the present research is investigating the axisymmetric wave propagation behaviors of fluid-filled carbon nanotubes (CNTs) with low slenderness ratios when the nanoscale effects contributed by CNT and fluid flow are considered together. Method An elastic shell model for fluid-conveying CNTs is established based on theory of nonlocal elasticity and nonlocal fluid dynamics. The effects of stress non-locality and strain gradient at nanoscale are simulated by applying nonlocal stress and strain gradient theories to CNTs and nonlocal fluid dynamics to fluid flow inside the

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17

Hull, Andrew J., Daniel Perez, and Donald L. Cox. "A Comprehensive Analytical Dynamic Model of a T-Beam." March 24, No 1 (2019): 139–49. http://dx.doi.org/10.20855/ijav.2019.24.11382.

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This paper derives a comprehensive analytical dynamic model of a T-shaped beam that includes in-plane and outof-plane vibrations for mid-frequency range analysis, defined here as approximately 1 kHz to 10 kHz. The web, right part of the flange, and left part of the flange of the T-beam are modelled independently with two-dimensional elasticity equations for the in-plane motion and the classical flexural plate equation for the out-of-plane motion. The differential equations are solved with unknown wave propagation coefficients multiplied by circular spatial domain functions, which are inserted

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18

Losin, N. A. "Asymptotics of Extensional Waves in Isotropic Elastic Plates." Journal of Applied Mechanics 65, no. 4 (1998): 1042–47. http://dx.doi.org/10.1115/1.2791898.

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The long and short-wave asymptotics of order O(η6),η=kh, for free extensional vibrations of an infinite isotropic elastic plate are studied. The asymptotic model for flexural and extensional wave motion applicable for both long and short-wave approximations and for any materials is developed. The velocity and frequency dispersion relations for extensional waves are derived in analytical form from the system of three-dimensional dynamic equations of linear elasticity. All dispersion equations and the group velocity formula are presented as explicit functions in material parameter γ=cs2/cL2 (the

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19

Jani, S. M. H., and Y. Kiani. "Symmetric Thermo-Electro-Elastic Response of Piezoelectric Hollow Cylinder Under Thermal Shock Using Lord–Shulman Theory." International Journal of Structural Stability and Dynamics 20, no. 05 (2020): 2050059. http://dx.doi.org/10.1142/s0219455420500595.

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The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These

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20

Hull, Andrew J., Daniel Perez, and Donald L. Cox. "A High-Frequency Model of a Rectilinear Beam with a T-Shaped Cross Section." Acoustics 1, no. 3 (2019): 726–48. http://dx.doi.org/10.3390/acoustics1030043.

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This paper derives an analytical model of a straight beam with a T-shaped cross section for use in the high-frequency range, defined here as approximately 1 to 35 kHz. The web, the right part of the flange, and the left part of the flange of the T-beam are modeled independently with two-dimensional elasticity equations for the in-plane motion and Mindlin flexural plate equation for the out-of-plane motion. The differential equations are solved with unknown wave propagation coefficients multiplied by circular spatial domain functions. These algebraic equations are then solved to yield the wave

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21

Turchyn, Ihor, and Olga Turchyn. "TRANSIENT PLANE WAVES IN MULTILAYERED HALF-SPACE." Acta Mechanica et Automatica 7, no. 1 (2013): 53–57. http://dx.doi.org/10.2478/ama-2013-0010.

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Abstract Considered the dynamic problem of the theory of elasticity for multilayered half-space. Boundary surface of inhomogeneous half-space loaded with normal load, and the boundaries of separation layers are in conditions of ideal mechanical contact. The formulation involves non-classical separation of equations of motion using two functions with a particular mechanical meaning volumetric expansion and function of acceleration of the shift. In terms of these functions obtained two wave equation, written boundary conditions and the conditions of ideal mechanical contact of layers. Using the

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22

TAKAGI, D., and N. J. BALMFORTH. "Peristaltic pumping of rigid objects in an elastic tube." Journal of Fluid Mechanics 672 (February 24, 2011): 219–44. http://dx.doi.org/10.1017/s0022112010005926.

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A mathematical model is developed for long peristaltic waves propelling a suspended rigid object down a fluid-filled axisymmetric tube. The fluid flow is described using lubrication theory and the deformation of the tube using linear elasticity. The object is taken to be either an infinitely long rod of constant radius or a parabolic-shaped lozenge of finite length. The system is driven by a radial force imposed on the tube wall that translates at constant speed down the tube axis and with a form chosen to generate a periodic wave train or a solitary wave. These waves exert a traction on the e

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23

Tchonkova, Maria. "Solution of two-dimensional vector wave equations via a mixed least squares method." Engineering Computations 32, no. 7 (2015): 1893–907. http://dx.doi.org/10.1108/ec-07-2014-0161.

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Purpose – The purpose of this paper is to present an original mixed least squares method for the numerical solution of vector wave equations. Design/methodology/approach – The proposed approach involves two different types of unknowns: velocities and stresses. The approximate solution to the dynamic elasticity equations is obtained via a minimization of a least squares functional, consisting of two terms: a term, which includes the squared residual of a weak form of the time rate of the constitutive relationships, expressed in terms of velocities and stresses, and a term, which depends on the

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Tchonkova, Maria. "Solution of problems in dynamic elasticity via a mixed least squares method." Engineering Computations 32, no. 3 (2015): 687–704. http://dx.doi.org/10.1108/ec-08-2013-0215.

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Purpose – The purpose of this paper is to present an original mixed least squares method for solving problems in dynamic elasticity. Design/methodology/approach – The proposed approach involves two different types of unknowns: velocities and stresses. The approximate solution to the dynamic elasticity equations is obtained via a minimization of a least squares functional, consisting of two terms: a term, which includes the squared residual of a weak form of the time rate of the constitutive relationships, expressed in terms of velocities and stresses, and a term, which depends on the squared r

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Daneshjou, K., R. Talebitooti, and A. Tarkashvand. "Investigation on sound transmission through thick-wall cylindrical shells using 3D- theory of elasticity in the presence of external and mean air-gap flow." Journal of Vibration and Control 24, no. 5 (2016): 975–1000. http://dx.doi.org/10.1177/1077546316655723.

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This paper studies the effects of an external mean flow and an internal air-gap mean flow on sound transmission through a double-wall thick cylindrical shell. Due to the major influence of some effective terms such as membrane, bending, transverse shearing and rotational inertia on thick-walled shell, three-dimensional theory of elasticity is used to obtain the governing equations of motion. Therefore, Newton’s second law is utilized to develop the equilibrium equations for an infinitesimal element in cylindrical coordinates. Then, the equations of motion related to the circular hollow cylinde

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Chanda, Ayan, and Swaroop Nandan Bora. "Propagation of Oblique Waves Over a Small Undulating Elastic Bottom Topography in a Two-Layer Fluid Flowing Through a Channel." International Journal of Applied Mechanics 12, no. 02 (2020): 2050023. http://dx.doi.org/10.1142/s1758825120500234.

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A hydrodynamic model, with the incorporation of elasticity, is considered to study oblique incident waves propagating over a small undulation on an elastic bed in a two-layer fluid, where the upper layer fluid is bounded above by a rigid lid, which is an approximation to the free surface. Following the Euler–Bernoulli beam equation, the elastic bed is approximated as a thin elastic plate. The surface tension at the interface of the layers is completely ignored since its contribution will be minimal. The behavior and properties of the roots of the dispersion relation are analyzed using counting

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LOKTEVA, Natalia A., and Nguyen Duong PHUNG. "Unsteady dynamics of a sandwich plate under the influence of a cylindrical wave in an elastic medium." INCAS BULLETIN 13, S (2021): 117–32. http://dx.doi.org/10.13111/2066-8201.2021.13.s.12.

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The interaction of a sandwich plate with a damped cylindrical wave in the ground has been investigated. A sandwich plate is considered as a model of a barrier in the ground, described by a system of equations by V. N. Paimushin, placed in the ground dividing it into two parts. The plane problem formulation is considered. The boundary conditions correspond to the hinge attachment of the barrier, and the initial conditions are zero. A cylindrical damped wave is considered as an external influence. To describe the ground movement, the equations of the elasticity theory, the Cauchy relations and t

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Ponnusamy, Palaniyandi. "Stress wave analysis of thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid." Multidiscipline Modeling in Materials and Structures 10, no. 4 (2014): 537–61. http://dx.doi.org/10.1108/mmms-12-2013-0076.

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Purpose – The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle, square, pentagon and hexagon) cross-section immersed in fluid is using Fourier expansion collocation method, with in the frame work of linearized, three-dimensional theory of thermo-piezoelectricity. Design/methodology/approach – A mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sections immersed

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Qiu, Shaoyang, Hongxiang Ren, and Haijiang Li. "Computational Model for Simulation of Lifeboat Free-Fall during Its Launching from Ship in Rough Seas." Journal of Marine Science and Engineering 8, no. 9 (2020): 631. http://dx.doi.org/10.3390/jmse8090631.

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In order to improve the accuracy of the freefall of lifeboat motion simulation in a ship life-saving simulation training system, a mathematical model using the strip theory and Kane’s method is established for the freefall of the lifeboat into the water from a ship. With the boat moving on a skid, the model of the ship’s maneuvering mathematical group (MMG) is used to model the motion of the ship in the waves. Based on the formula of elasticity and friction theory, the forces of the skid acting on the boat are calculated. When the boat enters the water, according to the analytical solution the

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Achenbach, Jan D. "Reciprocity and Related Topics in Elastodynamics." Applied Mechanics Reviews 59, no. 1 (2006): 13–32. http://dx.doi.org/10.1115/1.2110262.

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Reciprocity theorems in elasticity theory were discovered in the second half of the 19th century. For elastodynamics they provide interesting relations between two elastodynamic states, say states A and B. This paper will primarily review applications of reciprocity relations for time-harmonic elastodynamic states. The paper starts with a brief introduction to provide some historical and general background, and then proceeds in Sec. 2 to a brief discussion of static reciprocity for an elastic body. General comments on waves in solids are offered in Sec. 3, while Sec. 4 provides a brief summary

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NG, CHIU-ON, and XUEYAN ZHANG. "Mass transport in water waves over a thin layer of soft viscoelastic mud." Journal of Fluid Mechanics 573 (February 2007): 105–30. http://dx.doi.org/10.1017/s0022112006003508.

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A theory is presented for the mass transport induced by a small-amplitude progressive wave propagating in water over a thin layer of viscoelastic mud modelled as a Voigt medium. Based on a sharp contrast in length scales near the bed, the boundary-layer approximation is applied to the Navier–Stokes equations in Lagrangian form, which are then solved for the first-order oscillatory motions in the mud and the near-bed water layers. On extending the analysis to second order for the mass transport, it is pointed out that it is inappropriate, as was done in previous studies, to apply the complex vi

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KUMAR, S., J. N. SHARMA, and Y. D. SHARMA. "GENERALIZED THERMOELASTIC WAVES IN MICROSTRETCH PLATES LOADED WITH FLUID OF VARYING TEMPERATURE." International Journal of Applied Mechanics 03, no. 03 (2011): 563–86. http://dx.doi.org/10.1142/s1758825111001135.

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In the present paper, the theory of generalized thermo-microstretch elasticity has been employed to study the propagation of straight and circular crested waves in microstretch thermoelastic plates bordered with inviscid liquid layers (or half-spaces), with varying temperature on both sides. The secular equations governing the wave motion in both rectangular and cylindrical plates have been investigated. The results in the case of thin (long wavelength) and thick (short wavelength) plates have also been obtained and discussed as special cases of this work. The secular equation in the case of m

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Bagno, O. M. "On the influence of finite initial deformations on the surface instability of the incompressible elastic layer interacting with the half-space of an ideal fluid." Reports of the National Academy of Sciences of Ukraine, no. 1 (February 2021): 24–32. http://dx.doi.org/10.15407/dopovidi2021.01.024.

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The problem of the propagation of quasi-Lamb waves in a pre-deformed incompressible elastic layer that interacts with the half-space of an ideal compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory of finite deformations for the incompressible elastic layer and on the basis of the three-dimensional linearized Euler equations for the half-space of an ideal compressible fluid. The problem is formulated, and the approach based on the utilization of representations of the general solutions of the linearized equatio

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Musayev, Vyacheslav K. "Mathematical modeling of unsteady elastic stress waves in a console with a base (half-plane) under fundamental seismic action." Structural Mechanics of Engineering Constructions and Buildings 15, no. 6 (2019): 477–82. http://dx.doi.org/10.22363/1815-5235-2019-15-6-477-482.

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The aim of the work is to consider the problems of numerical modeling of seismic safety of the console with the base in the form of an elastic half-plane under unsteady wave influences. Stress waves of different nature, propagating in the deformed body interact with each other. After three or four times the passage and reflection of stress waves in the body, the process of propagation of disturbances becomes steady, the body is in oscillatory motion. The problem of modeling problems of the transition period is an actual fundamental and applied scientific problem. Methods. The finite element me

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Sandanbata, Osamu, Shingo Watada, Tung-Cheng Ho, and Kenji Satake. "Phase delay of short-period tsunamis in the density-stratified compressible ocean over the elastic Earth." Geophysical Journal International 226, no. 3 (2021): 1975–85. http://dx.doi.org/10.1093/gji/ggab192.

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SUMMARY Tsunamis are often modelled as surface gravity waves of incompressible homogenous water propagating over a rigid seafloor. Previous studies have noted that when computing long-period tsunamis travelling at trans-oceanic distances with dominant periods of thousands of seconds, we need to consider four factors that are not included in the surface gravity wave theory: compressibility of seawater, density stratification of oceans, elasticity of the Earth and gravitational potential change associated with the tsunami motion. However, their effects on short-period tsunamis with dominant peri

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Liu, Liao, and Mahmoud I. Hussein. "Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance." Journal of Applied Mechanics 79, no. 1 (2011). http://dx.doi.org/10.1115/1.4004592.

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Band gaps appear in the frequency spectra of periodic materials and structures. In this work we examine flexural wave propagation in beams and investigate the effects of the various types and properties of periodicity on the frequency band structure, especially the location and width of band gaps. We consider periodicities involving the repeated spatial variation of material, geometry, boundary and/or suspended mass along the span of a beam. In our formulation, we implement Bloch’s theorem for elastic wave propagation and utilize Timoshenko beam theory for the kinematical description of the un

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Soltani, P., J. Saberian, and R. Bahramian. "Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube With Shell Model Based on the Nonlocal Elasticity Theory." Journal of Computational and Nonlinear Dynamics 11, no. 1 (2016). http://dx.doi.org/10.1115/1.4030753.

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In this paper, nonlinear vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is investigated based on von Karman's geometric nonlinearity and nonlocal shell theory. The SWCNT is designated as an individual shell, and the Donnell's formulations of a cylindrical shell are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial differential equations (PDEs) into the ordinary differential equations (ODEs) of motion, and the method of averaging is applied to obtain an analytical solution of the nonlinear vibration of (10,0), (20,0)

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Singh, Baljeet. "Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid." Vietnam Journal of Mechanics, July 31, 2021. http://dx.doi.org/10.15625/0866-7136/15533.

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In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medium is assumed rotating about an axis perpendicular to the plane. The transverse isotropy axis is taken perpendicular to the surface. The specialized governing equations are first applied to derive a velocity equation for homogeneous plane wave. The s

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Kang, B., and C. H. Riedel. "Coupling of In-Plane Flexural, Tangential, and Shear Wave Modes of a Curved Beam." Journal of Vibration and Acoustics 134, no. 1 (2011). http://dx.doi.org/10.1115/1.4004676.

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In this paper, the coupling effects among three elastic wave modes, flexural, tangential, and radial shear, on the dynamics of a planar curved beam are assessed. Two sets of equations of motion governing the in-plane motion of a curved beam are derived, in a consistent manner, based on the theory of elasticity and Hamilton’s principle. The first set of equations retains all resulting linear coupling terms that includes both static and dynamic coupling among the three wave modes. In the derivation of the second set of equations, the effects of Coriolis acceleration and high-order elastic coupli

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Zimmerman, Jonathan A., Farid F. Abraham, and Huajian Gao. "Atomistic Simulation of Transonic Dislocations." MRS Proceedings 578 (1999). http://dx.doi.org/10.1557/proc-578-229.

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AbstractRecent work has been done on the analysis of elastic stress singularities, such as cracks and dislocations, which propagate at supersonic speeds. Gumbsch and Gao have performed atomistic simulations in which dislocations are created and travel at transonic velocities (speeds which are greater than the material's shear wave speeds but less than the longitudinal wave speed) close to the theoretical value corresponding to the radiation-free state for glide motion. Gao et al. have derived expressions for this radiation-free velocity in both isotropic and anisotropic media. We have performe

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