## What is/are Isotropic Plate?

Isotropic Plate - The anisotropic plate-like grains were observed across all the samples, which decreased in size with an increase in La3+ content.^{[1]}The proposed PIL method has the following advantages: (a) it can be applied to isotropic/anisotropic plate structures; (b) it doesn’t require any signal interpretation, making it attractive for active impact monitoring systems; (c) for anisotropic materials it doesn’t require the accurate knowledge of the wave velocity in all directions of propagation; (d) it doesn’t need a reference database; and (e) it remains effective even in the presence of noise.

^{[2]}There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates.

^{[3]}The newly mechanical models of materially anisotropic plate and geometrically orthotropic combined plate at ship double bottom in large deflection have been formulated.

^{[4]}Recently, the plate bending analysis has been interpreted in terms of the tensor's components of curvatures and bending moments by presenting the conceptual perspectives of the Hydrostatic Method of Analysis (HM) and theoretical formulations that combine the continuum mechanics with the graphical statics analysis, the theory of thin orthotropic and isotropic plates, and the elasticity theory.

^{[5]}This paper presents dispersion curve regression-assisted local wavenumber analysis method, which can analyze the time–space wavefield containing wideband information of wave-damage interaction and further extract the structural information carried by such wavefield for characterizing hidden corrosion damage in an isotropic plate.

^{[6]}An increase in the thickness of the anisotropic plate intensified the effect of wave interference in it - all changes in the polarization parameters with a change in the angle of incidence of radiation occurred more often than with a thinner plate.

^{[7]}That is why the present work is dedicated to determine the stress field of finite dimensions bolted joints with isotropic plate material by means of the Airy stress function.

^{[8]}The design problems show that a considerable decrease of sound power can be accomplished with the optimal design of FGM plates in comparison with the isotropic plates.

^{[9]}In order to determine the stress fields in an anisotropic plate, the pan-complex variable means must be utilized.

^{[10]}Several examples including isotropic plates with various cutouts and complex shapes without thermal conditions are presented to justify the correctness and convergence of IGA-FSDT approach.

^{[11]}Ice is modeled by an isotropic plate of infinite extent, the behavior of which is described by the rheological viscoelastic Kelvin-Voigt model.

^{[12]}The pan-complex function and the polar coordinate replace approach are utilized with the aim of solving the stress boundary problems for the anisotropic plate.

^{[13]}: Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.

^{[14]}SEM images reveal anisotropic plate-like grains, which increase in size with the presence of Ln3+ ions.

^{[15]}We study the problem of combined bending and tension of an isotropic plate containing a through crack by distributed bending moments and forces at infinity in the absence of contact between the crack faces and external loads applied to the crack but in the presence of plastic zones at its tips.

^{[16]}In this phase, the VSC laminate is modelled as an equivalent homogeneous anisotropic plate whose behaviour is described in terms of polar parameters (PPs), which vary locally over the structure.

^{[17]}Both simulation and experiment are performed to validate F-MUSIC when used for imaging single and multiple sites of damage in an isotropic plate waveguide with a sparse sensor network.

^{[18]}With aid of the Stroh octet formalism, we obtain the elastic field in an infinite Kirchhoff laminated anisotropic plate containing a parabolic Eshelby inclusion undergoing uniform mid-plane in-plane eigenstrains and eigencurvatures.

^{[19]}Various techniques have emerged in the past few years for localizing the acoustic source in an anisotropic plate.

^{[20]}In addition to the extraction of nonisotropic resistivities, the resistance matrix can be used to analyze the Hall effect for anisotropic plates.

^{[21]}Our study has shown that the method of time-domain filtering in multi-band combining with frequency-domain TFM can realize non-contact and accurate damage detection in isotropic plate structures, and it is a potential effective method for application in engineering practice.

^{[22]}SEM images of the prepared thin film exhibited an anisotropic plate-like grained structure.

^{[23]}The general framework of this study is the Corrected Force Analysis Technique (CFAT), which was previously used on isotropic plates.

^{[24]}Shear horizontal (SH) waves are of great importance in structural health monitoring (SHM) and nondestructive testing (NDT), since the lowest order SH wave in isotropic plates is non-dispersive.

^{[25]}The present study proposes an anisotropic formulation of the acoustic forward model to map velocity variations induced by defects in anisotropic plates.

^{[26]}, two independent constants for the isotropic plate and four constants for the transversely isotropic plate) can thus be determined.

^{[27]}Three-dimensional exact solutions for temperature and thermoelastic stresses in multilayered anisotropic plates are derived for advanced boundary-value problems with general boundary conditions.

^{[28]}This study aims to extend the radiative energy transfer method (RETM) to anisotropic plates loaded by transverse point force at high frequencies.

^{[29]}Localization of solution of the problem of isotropic plate analysis with the use of B-spline discrete-continual finite element method (specific version of wavelet-based discrete-continual finite element method) is under consideration in the distinctive paper.

^{[30]}This element is implemented, for the first time in the commercial computer code ABAQUS, by using the subroutine (UEL), for the static and dynamic analysis of isotropic plates, whatever thin or thick.

^{[31]}Both approaches are validated with compliance measurements previously reported, observing good agreement ( less than 10 % difference with respect to experiments ) for most orthotropic and isotropic plates.

^{[32]}The solution of this urgent problem for composite anisotropic plates can be found in this article, where the author continues the research in this area, extending them to the bending of anisotropic composite plates.

^{[33]}Moreover, static and steady state dynamic antiplane problems of flexoelectric and couple stress elastic materials can be modeled as anisotropic plates with a non-equal biaxial pre-stress.

^{[34]}Explicit formulas of the fundamental tone of the frequency of the transverse vibration of an anisotropic plate lying on an inhomogeneous viscoelastic base are determined.

^{[35]}The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work.

^{[36]}Propagation of harmonic Lamb waves in plates made of functionally graded materials with transverse inhomogeneity is analyzed by applying Cauchy six-dimensional formalism previously developed for the study of Lamb wave propagation in homogeneous or stratified anisotropic plates.

^{[37]}The road deck bridge was considered to be made from reinforced concrete and is considered to be modelled by isotropic plates with varying boundary conditions.

^{[38]}The design principle is based on the field transformation theory and the anisotropic plate is made with high/low permittivity strip metamaterials.

^{[39]}Finally, the displacement and stress profiles of fundamental modes of the guided waves in an arbitrary lay-up quasi-isotropic plate at a given frequency is discussed in details.

^{[40]}In this chapter we give the solution of a problem of bending of a transversally-isotropic plate of variable thickness.

^{[41]}As for the anisotropic plates, there are no such tables, with the exception of one Huber table compiled for a freely supported rectangular orthotropic plate, depending on the relationship between the stiffness values.

^{[42]}A material independent technique, that needs neither a priori knowledge of the material properties even for anisotropic plates nor a dense array of sensors, will be used to locate the impact.

^{[43]}It is well understood that in an isotropic plate, the energy velocity of a backward wave is directed opposite to the phase velocity.

^{[44]}A comparison with the exact solution, which is known for the case of one inclusion in the plane, shows that the error of the asymptotic solution does not exceed 9% at case of an isotropic plate.

^{[45]}113902], we show that the effect is actually an example of the regular spin-Hall effect that occurs at tilted anisotropic plates [Optica3, 1039 (2016) OPTIC82334-253610.

^{[46]}This paper investigates the buckling of isotropic plates with circular cutout subjected to non-uniform in-plane loading.

^{[47]}In this work, we proposed a baseline-free sparse array system for SHM of isotropic plates based on the fundamental shear horizontal (SH0) wave, which is totally non-dispersive.

^{[48]}Moreover, static and steady state dynamic anti-plane problems of flexoelectric or couple stress elastic materials can be modeled as anisotropic plates with a non-equal biaxial pre-stress.

^{[49]}Properties of isotropic plates in terms of material constants and thickness are characterized by making use of dispersion characteristics of propagating Lamb waves.

^{[50]}

## acoustic source localization

This paper discusses how silicon dampers on edges affect the acoustic source localization on an isotropic plate using low SRD.^{[1]}In this paper new developments for acoustic source localization in an anisotropic plate is first reviewed briefly.

^{[2]}In recent years some progresses have been made in acoustic source localization (ASL) in highly anisotropic plates when the plate material properties are not known.

^{[3]}Development of acoustic source localization techniques in anisotropic plates has gained attention in the recent past and still has scope of improvement.

^{[4]}This study presents acoustic source localization techniques for anisotropic plates based on the analysis of the wave front shapes typically observed in anisotropic plates and presents experimental verification of the techniques.

^{[5]}

## order shear deformation

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates.^{[1]}In this paper, three high-order shear deformation theories are presented to investigate in-plane dominated vibrations for circular transversely isotropic plates.

^{[2]}

## first order shear

A variant of the first-order shear deformation theory is presented for the flexure of shear deformable linear isotropic plates undergoing small deformations.^{[1]}Bending and membrane components of transverse forces in a fixed square isotropic plate under simultaneous compression and transverse loading were established within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), and the classical plate theory (CPT).

^{[2]}

## Thin Isotropic Plate

To investigate the wave behaviour, a plate-droplet inspection system comprising a thin isotropic plate loaded with water droplets and a pitch–catch transducer configuration was modelled and studied experimentally.^{[1]}An analytical model is presented for the generation, sensing, and time-reversible process of Lamb waves in thin isotropic plates with surface-bonded piezoelectric wafer transducers, incorporating the shear-lag effect of the bonding layer and inertia effects of the system in transducer modeling.

^{[2]}Two- and one-dimensional Kirchhoff models of thin isotropic plates and rods are combined into a single problem describing the deformation of the joint of these elastic objects.

^{[3]}Numerical results, obtained using the proposed method for thin isotropic plates and plate assemblies, show that the proposed method is accurate and rapidly convergent.

^{[4]}By calculating a proper separation to locate the transducers on both sides of a thin isotropic plate, the Lamb waves excited from the plate generated its leaky waves into the air domain and the leaky waves detected by the receiver successfully in the simulation.

^{[5]}Classical plate theory is used to derive the governing differential equation for the transverse deflection of the thin isotropic plate.

^{[6]}

## Transversely Isotropic Plate

In this paper, the consistent second-order plate theory is developed for transversely isotropic plates.^{[1]}In this paper, three high-order shear deformation theories are presented to investigate in-plane dominated vibrations for circular transversely isotropic plates.

^{[2]}A method for solving the boundary value problems of a variant of the mathematical theory of thick transversely isotropic plates has been developed.

^{[3]}The Fourier–Legendre series expansion and the boundary-shape perturbation method are used to determine the stress state of an unbounded transversely isotropic plate with a curved hole under constant shear forces at infinity.

^{[4]}An analytical three-dimensional effective elastic constant of transversely isotropic plates that include ply cracks is proposed using a continuum damage mechanics approach.

^{[5]}

## Rectangular Isotropic Plate

The effectiveness of the proposed approach was tested for a mechanical system consisting of a rectangular isotropic plate of medium thickness, hinged-supported along the contour, and an additional concentrated viscoelastic support, taking into account its mass-inertial characteristics.^{[1]}This paper presents an analytical solution for free vibration analysis of thick rectangular isotropic plates coupled with a bounded fluid for various boundary conditions.

^{[2]}In a previous work, we showed that starting with the Kts for rectangular isotropic plates with circular holes the Kts for rectangular orthotropic plates with elliptic holes can be easily and accurately predicted, using a double scaling procedure (a geometric scaling and a material scaling) together with a basic Kt curve employed as a master curve.

^{[3]}Computed results for simply supported, clamped, and clamped-free rectangular isotropic plates agree well with the corresponding analytical frequencies of simply supported plates and with those found using the commercial software, ABAQUS, for other edge conditions.

^{[4]}

## Infinite Isotropic Plate

It is found that laminates can be designed with SCF ( 3 ) that is lower than even an infinite isotropic plate.^{[1]}The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate.

^{[2]}

## Thick Isotropic Plate

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates.^{[1]}In present study, a novel refined hyperbolic shear deformation theory is proposed for the buckling analysis of thick isotropic plates.

^{[2]}

## Circular Isotropic Plate

In this article, a new closed solution of the axisymmetric dynamic problem of the theory of thermoelasticity is constructed for a rigidly fixed circular isotropic plate in the case of temperature changes on its face surfaces.^{[1]}A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind).

^{[2]}

## Square Isotropic Plate

A comparative study of the proposed approach and the FEM or analytical solutions on a square isotropic plate and a three-dimensional rectangular block under uniaxial tension shows that this proposed approach can well investigate the behavior of elastic solids under both two and three dimensional conditions.^{[1]}Bending and membrane components of transverse forces in a fixed square isotropic plate under simultaneous compression and transverse loading were established within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), and the classical plate theory (CPT).

^{[2]}

## Homogeneou Isotropic Plate

Computer simulation of the stress-strain state of a thin rectangular homogeneous isotropic plate with a circular hole, reinforced by an annular inclusion made of a functional-gradient material (FGM) has been carried out.^{[1]}This article explores the effects of two temperatures on the combined problem of wave propagation and thermomechanical loading in a homogeneous isotropic plate.

^{[2]}

## isotropic plate containing

We study the problem of combined bending and tension of an isotropic plate containing a through crack by distributed bending moments and forces at infinity in the absence of contact between the crack faces and external loads applied to the crack but in the presence of plastic zones at its tips.^{[1]}With aid of the Stroh octet formalism, we obtain the elastic field in an infinite Kirchhoff laminated anisotropic plate containing a parabolic Eshelby inclusion undergoing uniform mid-plane in-plane eigenstrains and eigencurvatures.

^{[2]}The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate.

^{[3]}

## isotropic plate loaded

To investigate the wave behaviour, a plate-droplet inspection system comprising a thin isotropic plate loaded with water droplets and a pitch–catch transducer configuration was modelled and studied experimentally.^{[1]}To implement the task, the Lekhnitsky theory of calculating the stability of anisotropic plates is used, in particular, the energy method for determining the critical force for a flat anisotropic plate loaded along the edges by tangential efforts.

^{[2]}

## isotropic plate structure

The proposed PIL method has the following advantages: (a) it can be applied to isotropic/anisotropic plate structures; (b) it doesn’t require any signal interpretation, making it attractive for active impact monitoring systems; (c) for anisotropic materials it doesn’t require the accurate knowledge of the wave velocity in all directions of propagation; (d) it doesn’t need a reference database; and (e) it remains effective even in the presence of noise.^{[1]}Our study has shown that the method of time-domain filtering in multi-band combining with frequency-domain TFM can realize non-contact and accurate damage detection in isotropic plate structures, and it is a potential effective method for application in engineering practice.

^{[2]}