On the Nonlocal Theory of Wave Propagation in Elastic Plates

1984 ◽  
Vol 51 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. L. Nowinski
Keyword(s):  
Lattice Dynamics ◽  
Wave Speed ◽  
Nonlocal Theory ◽  
Short Wave ◽  
Elastic Plates ◽  
Field Equations ◽  
Atomic Lattice ◽  
Longitudinal Waves ◽  
Standard Manner ◽  
The Fourier Transform

Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.

Asymptotics of Flexural Waves in Isotropic Elastic Plates

1997 ◽  
Vol 64 (2) ◽  
pp. 336-342 ◽  
Author(s):  
N. A. Losin
Keyword(s):  
Material Parameter ◽  
Velocity Dispersion ◽  
Three Dimensional ◽  
Analytical Form ◽  
Short Wave ◽  
Frequency Equation ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Explicit Formulas ◽  
Longitudinal Waves

The long and short-wave asymptotics of order O(k6h6) for the flexural vibrations of an infinite, isotropic, elastic plate are studied. The differential equation for the flexural motion is derived from the system of three-dimensional dynamic equations of linear elasticity. All coefficients of the differential operator are presented as explicit functions of the material parameter γ = cs2/cL2, the ratio of the velocities squared of the flexural (shear) and extensional (longitudinal) waves. Relatively simple frequency and velocity dispersion equations for the flexural waves are deduced in analytical form from the three-dimensional analog of Rayleigh-Lamb frequency equation for plates. The explicit formulas for the group velocity are also presented. Variations of the velocity and frequency spectrums depending on Poisson’s ratio are illustrated graphically. The results are discussed and compared to those obtained and summarized by R. D. Mindlin (1951, 1960), Tolstoy and Usdin (1953, 1957), and Achenbach (1973).

scholarly journals Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 87
Author(s):  
Giovanni Tocci Monaco ◽  
Nicholas Fantuzzi ◽  
Francesco Fabbrocino ◽  
Raimondo Luciano
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Scale Effects ◽  
Nonlocal Theory ◽  
Elastic Plates ◽  
Critical Temperatures ◽  
Buckling Behavior ◽  
Linear Vibrations ◽  
Nonlocal Strain Gradient ◽  
Plate Kinematics

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

On the theory of electrohydrodynamically driven capillary jets

1997 ◽  
Vol 335 ◽  
pp. 165-188 ◽  
Author(s):  
ALFONSO M. GAÑÁN-CALVO
Keyword(s):  
Surface Charge ◽  
Electric Fields ◽  
Gas Flow ◽  
Wave Speed ◽  
Propagation Speed ◽  
Field Equations ◽  
Steady Regime ◽  
One Dimensional ◽  
Relaxation Effects ◽  
Capillary Jets

Electrohydrodynamically (EHD) driven capillary jets are analysed in this work in the parametrical limit of negligible charge relaxation effects, i.e. when the electric relaxation time of the liquid is small compared to the hydrodynamic times. This regime can be found in the electrospraying of liquids when Taylor's charged capillary jets are formed in a steady regime. A quasi-one-dimensional EHD model comprising temporal balance equations of mass, momentum, charge, the capillary balance across the surface, and the inner and outer electric fields equations is presented. The steady forms of the temporal equations take into account surface charge convection as well as Ohmic bulk conduction, inner and outer electric field equations, momentum and pressure balances. Other existing models are also compared. The propagation speed of surface disturbances is obtained using classical techniques. It is shown here that, in contrast with previous models, surface charge convection provokes a difference between the upstream and the downstream wave speed values, the upstream wave speed, to some extent, being delayed. Subcritical, supercritical and convectively unstable regions are then identified. The supercritical nature of the microjets emitted from Taylor's cones is highlighted, and the point where the jet switches from a stable to a convectively unstable regime (i.e. where the propagation speed of perturbations become zero) is identified. The electric current carried by those jets is an eigenvalue of the problem, almost independent of the boundary conditions downstream, in an analogous way to the gas flow in convergent–divergent nozzles exiting into very low pressure. The EHD model is applied to an experiment and the relevant physical quantities of the phenomenon are obtained. The EHD hypotheses of the model are then checked and confirmed within the limits of the one-dimensional assumptions.

scholarly journals Large amplitude, short wave peristalsis and its implications for transport

2015 ◽  
Author(s):  
Lindsay D Waldrop ◽  
Laura A. Miller
Keyword(s):  
Fluid Flow ◽  
Large Amplitude ◽  
Compression Wave ◽  
Wave Speed ◽  
Flow Direction ◽  
Short Wave ◽  
Flow Speed ◽  
Biological Pumps ◽  
Flow Speeds ◽  
Flow Compression

Valveless, tubular pumps are widespread in the animal kingdom, but the mechanism by which these pumps generate fluid flow are often in dispute. Where the pumping mechanism of many organs was once described as peristalsis, other mechanisms, such as dynamic suction pumping, have been suggested as possible alternative mechanisms. Peristalsis is often evaluated using criteria established in a technical definition for mechanical pumps, but this definition is based on a small-amplitude, long-wave approximation which biological pumps often violate. In this study, we use a direct numerical simulation of large-amplitude, short-wave peristalsis to investigate the relationships between fluid flow, compression frequency, compression wave speed, and tube occlusion. We also explore how the flows produced differ from the criteria outlined in the technical definition of peristalsis. We find that many of the technical criteria are violated by our model: fluid flow speeds produced by peristalsis are greater than the speeds of the compression wave; fluid flow is pulsatile; and flow speed have a non-linear relationship with compression frequency when compression wave speed is held constant. We suggest that the technical definition is inappropriate for evaluating peristalsis as a pumping mechanism for biological pumps because they too frequently violate the assumptions inherent in these criteria. Instead, we recommend that a simpler, more inclusive definition be used for assessing peristalsis as a pumping mechanism based on the presence of non-stationary compression sites that propagate uni-directionally along a tube without the need for a structurally fixed flow direction.

Bleustein-Gulyaev Waves in an Inhomogeneous Layered Piezoelectric Half-Space

2006 ◽  
Vol 306-308 ◽  
pp. 1223-1228
Author(s):  
Fei Peng ◽  
Hua Rui Liu
Keyword(s):  
Fourier Transform ◽  
Phase Velocity ◽  
Half Space ◽  
Electric Potential ◽  
Piezoelectric Layer ◽  
Field Equations ◽  
Transform Method ◽  
Coupled Field ◽  
Coupled Field Equations ◽  
The Fourier Transform

The propagation of Bleustein-Gulyaev (BG) waves in an inhomogeneous layered piezoelectric half-space is investigated in this paper. Application of the Fourier transform method and by solving the electromechanically coupled field equations, solutions to the mechanical displacement and electric potential are obtained for the piezoelectric layer and substrate, respectively. The phase velocity equations for BG waves are obtained for the surface electrically shorted case. When the layer and the substrate are homogenous, the dispersion equations are in agreement with the corresponding results. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO3 except that they are polarized in opposite directions. Effects of the inhomogeneities induced by either the layer or substrate are discussed in detail.

scholarly journals Buckling analysis of nano-scale magneto-electro-elastic plates using the nonlocal elasticity theory

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879333 ◽  
Author(s):  
Weon-Tae Park ◽  
Sung-Cheon Han
Keyword(s):  
Electric Fields ◽  
Constitutive Relations ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Elastic Plates ◽  
Electric Boundary Condition ◽  
Electric Potentials

Buckling analysis of nonlocal magneto-electro-elastic nano-plate is investigated based on the higher-order shear deformation theory. The in-plane magnetic and electric fields can be ignored for magneto-electro-elastic nano-plates. According to magneto-electric boundary condition and Maxwell equation, the variation of magnetic and electric potentials along the thickness direction of the magneto-electro-elastic plate is determined. To reformulate the elastic theory of magneto-electro-elastic nano-plate, the nonlocal differential constitutive relations of Eringen is applied. Using the variational principle, the governing equations of the nonlocal theory are derived. The relations between local and nonlocal theories are studied by numerical results. Also, the effects of nonlocal parameters, in-plane load directions, and aspect ratio on buckling response are investigated. Numerical results show the effects of the electric and magnetic potentials. These numerical results can be useful in the design and analysis of advanced structures constructed from magneto-electro-elastic materials.

Consolidation analysis for unsaturated soils

2004 ◽  
Vol 41 (4) ◽  
pp. 599-612 ◽  
Author(s):  
Enrico Conte
Keyword(s):  
Fourier Transform ◽  
Unsaturated Soils ◽  
Time Integration ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Spatial Dimension ◽  
Element Approximation ◽  
Field Equations ◽  
Actual Solution ◽  
The Fourier Transform

This paper deals with the multidimensional consolidation of unsaturated soils when both the air phase and water phase are continuous. Following the approach proposed by D.G. Fredlund and his coworkers, the differential equations governing the coupled and uncoupled consolidation are first derived and then solved numerically. The solution is achieved using a procedure that depends on the transformation of the field equations by using the Fourier transform. This transformation has the effect of reducing a two- or three-dimensional problem to a problem involving only a single spatial dimension. The transformed equations are solved using a finite element approximation that makes use of simple one-dimensional elements. Once the solution in the transformed domain is obtained, the actual solution is achieved by inversion of the Fourier transform. The time integration process is formulated in a stepwise form. Results are presented to point out some aspects of the consolidation in unsaturated soils. Moreover, it is shown that the results obtained using the simple uncoupled theory are of sufficient accuracy for practical purposes.Key words: coupled consolidation, uncoupled consolidation, unsaturated soils, Fourier transform.

Simulation of Frictional Sliding Under Impact Shear Loading

2004 ◽  
Author(s):  
Demir Coker ◽  
Alan Needleman ◽  
George Lykotrafitis ◽  
Ares J. Rosakis
Keyword(s):  
Constitutive Relation ◽  
Wave Speed ◽  
Constitutive Relations ◽  
Shear Loading ◽  
Stress And Strain ◽  
Sliding Modes ◽  
Elastic Plates ◽  
Frictional Sliding ◽  
State Dependent ◽  
Dynamic Loading Conditions

Results from recent and ongoing investigations of frictional sliding under dynamic loading conditions are discussed. The configuration analyzed consists of two identical elastic plates with an interface characterized by a rate- and state-dependent frictional law. The calculations are carried out within a framework where two constitutive relations are used: a volumetric constitutive relation between stress and strain and a surface constitutive relation that characterizes the frictional behavior of the interface. The simulations discussed predict a variety of sliding modes including a crack-like mode and several pulse-like modes as well as circumstances where the sliding tip speed can exceed the longitudinal wave speed.

scholarly journals Solubility Property of Baganuur Coal: Performance Assessment by FTIR Spectroscopic Analysis

2021 ◽  
Vol 323 ◽  
pp. 28-41
Author(s):  
Sambuu Munkhtsetseg ◽  
Khandmaa Tsagaanaa ◽  
Erdene Ochir Ganbold ◽  
Galbadrakh Ragchaa ◽  
Enkhtor Sukhbaatar ◽  
...  
Keyword(s):  
Ionic Liquid ◽  
Short Wave ◽  
Imidazolium Chloride ◽  
Acidic Group ◽  
Coal Structure ◽  
Long Wave ◽  
Spectral Integral ◽  
The Fourier Transform ◽  
The Individual

In the present work, the extraction of Mongolian Baganuur coal in solvents as pyridine and ionic liquid with 1-butyl-3-methyl-imidazolium chloride ([Bmim]Cl) anion was first applied. The as recieved coal, its extracts and insoluble residues were then characterized using the Fourier transform infrared (FTIR) spectroscopy. The obtained FTIR spectra have revealed many new features in the field of coal study. An appearance or sharpening of the particular bands after the chemical treatment allow a determination of inactive or weak fundamental vibrations precisely. Some emphasis are as follows, substantial quantitative change, the integrated area decrease of water molecule band at 3260 cm−1 comparing to as received sample and ionic liquid treated extract, can be seen for the extract spectrum in the pyridine treatment. Pyridine react to coal structure particularly in long-wave frequency zone means very susceptible to the oxygen containing functional group. Upon interaction between acidic group of the coal and the basic solvent as pyridine, the inter-fragment hydrogen and ester bonding in the coal structure is breaking, thus increasing the solubility of the individual fragments via producing new components. Towards forming H bond in the short wave zone Cl− anion shows a strong effect on the coal molec-ular structure. A stabilization of hydrogen bonds show well fluidization and a strong intermolecular interaction of the process via its powerful spectral intensity that is followed many new bands and con-siderable strengthening of band spectral integral area in this frequency region. In long-wave vibrational region there are appearances of many new bands, shift in frequency and depletion of the as recieved coal bands. [Bmim]Cl treatment exhibits the highest effect of the disruption on the carboxylic acids dimer.

Buckling and Postbuckling of Electroconducting Elastic Plates in a Magnetic Field

2002 ◽  
Author(s):  
Davresh Hasanyan ◽  
Liviu Librescu ◽  
Damodar R. Ambur
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Ferromagnetic Material ◽  
Electrical Current ◽  
Elastic Plates ◽  
Postbuckling Behavior ◽  
Field Equations ◽  
Flat Plates ◽  
Theory Of Plates ◽  
Basic Equations

The basic equations of a fully nonlinear theory of electromagnetically conducting flat plates carrying an electric current and exposed to a magnetic field of arbitrary orientation are summarized. The relevant equations have been obtained by considering that both the elastic and electromagnetic media are homogeneous and isotropic. The geometrical nonlinearities are considered in the von-Ka´rma´n sense, and the soft ferromagnetic material of the plate is assumed to feature negligible hysteretic losses. Based on the electromagnetic and elastokinetic field equations, by using the standard averaging methods, the 3-D coupled problem is reduced to an equivalent 2-D one, appropriate to the theory of plates. Having in view that the elastic structures carrying an electric current are prone to buckling, by using the presently developed theory, the associated problems of buckling and post-buckling are investigated. In this context, the problem of the electrical current inducing the buckling instability of the plate, and its influence on the postbuckling behavior are analyzed. In the same context, the problem of the natural-frequencies electrical current interaction of flat plates, as influenced by a magnetic field is also addressed.

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