Showing papers on "Boundary value problem published in 2020"
TL;DR: In this article, a physics-informed neural network (PINN) was used to approximate the Euler equations that model high-speed aerodynamic flows in one-dimensional and two-dimensional domains.
485 citations
TL;DR: In this article, the authors established exact relations between the winding of energy on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary conditions in non-Hermitian systems.
Abstract: We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary conditions in non-Hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the nonvanishing current through the system.
443 citations
TL;DR: A comparison of several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties, and a collection of benchmark problems to compare different definitions on bounded domains using a sample of state-of-the-art methods.
258 citations
TL;DR: In this article, a boundary control approach is used to control a two-link rigid-flexible wing, which is based on the principle of bionics to improve the mobility and the flexibility of aircraft.
Abstract: A boundary control approach is used to control a two-link rigid-flexible wing in this article. Its design is based on the principle of bionics to improve the mobility and the flexibility of aircraft. First, a series of partial differential equations (PDEs) and ordinary differential equations (ODEs) are derived through the Hamilton's principle. These PDEs and ODEs describe the governing equations and the boundary conditions of the system, respectively. Then, a control strategy is developed to achieve the objectives including restraining the vibrations in bending and twisting deflections of the flexible link of the wing and achieving the desired angular position of the wing. By using Lyapunov's direct method, the wing system is proven to be stable. The numerical simulations are carried out with the finite difference method to prove the effectiveness of designed boundary controllers.
245 citations
TL;DR: In this article, the Mellin-Barnes representation of correlators in Fourier space was used for boundary correlation functions in both the anti-de Sitter and de Sitter spaces.
Abstract: We develop a Mellin space approach to boundary correlation functions in anti-de Sitter (AdS) and de Sitter (dS) spaces. Using the Mellin-Barnes representation of correlators in Fourier space, we show that the analytic continuation between AdSd+1 and dSd+1 is encoded in a collection of simple relative phases. This allows us to determine the late-time tree-level three-point correlators of spinning fields in dSd+1 from known results for Witten diagrams in AdSd+1 by multiplication with a simple trigonometric factor. At four point level, we show that Conformal symmetry fixes exchange four-point functions both in AdSd+1 and dSd+1 in terms of the dual Conformal Partial Wave (which in Fourier space is a product of boundary three-point correlators) up to a factor which is determined by the boundary conditions. In this work we focus on late-time four-point correlators with external scalars and an exchanged field of integer spin-l. The Mellin-Barnes representation makes manifest the analytic structure of boundary correlation functions, providing an analytic expression for the exchange four-point function which is valid for general d and generic scaling dimensions, in particular massive, light and (partially-)massless fields. It moreover naturally identifies boundary correlation functions for generic fields with multi-variable Meijer-G functions. When d = 3 we reproduce existing explicit results available in the literature for external conformally coupled and massless scalars. From these results, assuming the weak breaking of the de Sitter isometries, we extract the corresponding correction to the inflationary three-point function of general external scalars induced by a general spin- l field at leading order in slow roll. These results provide a step towards a more systematic understanding of de Sitter observables at tree level and beyond using Mellin space methods.
179 citations
TL;DR: In this article, free vibration analysis of embedded carbon and silica carbide nanotubes lying on an elastic matrix is performed based on Eringen's nonlocal elasticity theory.
Abstract: In this study, free vibration analyses of embedded carbon and silica carbide nanotubes lying on an elastic matrix are performed based on Eringen’s nonlocal elasticity theory. These nanotubes are modeled as nanobeam and nanorod. Elastic matrix is considered as Winkler–Pasternak elastic foundation and axial elastic media for beam and rod models, respectively. The vibration formulations of the beam and rod are derived by utilizing Hamilton’s principle. The obtained equations of motions are solved by the method of separation of variables and finite element-based Hermite polynomials for various boundary conditions. The effects of boundary conditions, system modeling, structural sizes such as length, cross-sectional sizes, elastic matrix, mode number, and nonlocal parameters on the natural frequencies of these nanostructures are discussed in detail. Moreover, the availability of size-dependent finite element formulation is investigated in the vibration problem of nanobeams/rods resting on an elastic matrix.
157 citations
TL;DR: In this article, the flow and heat transfer characteristics of an electrically conducting Casson fluid past an exponentially stretching curved surface with convective boundary condition were analyzed and suitable transformations were considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like shooting and Runge-Kutta method.
Abstract: This paper presents the flow and heat transfer characteristics of an electrically conducting Casson fluid past an exponentially stretching curved surface with convective boundary condition. The fluid motion is assumed to be laminar and time dependent. The effects of temperature-dependent thermal conductivity, Joule heating, thermal radiation, and variable heat source/sink are deemed. Suitable transformations are considered to transform the governing partial differential equations as ordinary ones and then solved by the numerical procedures like shooting and Runge–Kutta method. Graphs are outlined to describe the influence of various dimensionless parameters on the fields of velocity and temperature and observe that there is an enhancement in the field of temperature with the radiation, temperature-dependent thermal conductivity, and irregular heat parameters. Also, the Casson parameter has a tendency to suppress the distribution of momentum but an inverse development is noticed for the curvature parameter. Attained outcomes are also compared with the existing literature in the limiting case, and good agreement is perceived.
149 citations
TL;DR: In this paper, a unified method is developed to analyze free vibrations of laminated functionally graded shallow shells reinforced by graphene platelets (GPLs) under arbitrary boundary conditions is proposed.
149 citations
TL;DR: The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately and involves both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams.
Abstract: This research develops a nonlocal couple stress theory to investigate static stability and free vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved applying Chebyshev–Ritz method which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation and various boundary conditions on natural frequencies and buckling loads of FG nanobeams in detail.
147 citations
TL;DR: In this article, the size and time-dependent viscoelastic bending analysis of rotating spherical nanostructures made of functionally graded materials (FGMs) is performed, where the structure is assumed to be rotated around two axes with constant angular accelerations.
137 citations
TL;DR: In this paper, a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature is presented.
Abstract: This is a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid Nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature. Carbon fibers (CF) or carbon nanotubes (CNTs) in the macro or nano sizes respectively are responsible for reinforcing the matrix. For prediction of the efficiency of the properties MHCD's modified Halpin-Tsai theory has been presented. The strain-displacement relation in multi-sized laminated disk's nonlinear dynamics through applying Von Karman nonlinear shell-theory and using third-order-shear-deformation-theory (TSDT) is determined. The energy methods called Hamilton's principle is applied for deriving the motion equations along with Boundary Conditions (BCs), which has ultimately been solved using the perturbation approach (PA) and generalized differential quadrature method (GDQM). At the final stage, the outcomes illustrate that patterns of FG, fibers' various directions, the WCNT and VF factors, top surface's applied temperature and temperature gradient have considerable impact on the MHCD's nonlinear dynamics. Another important consequence is that, the influences of the θ, WCNT and VF amounts on the disk's nonlinear vibrations may be taken into account at the larger amounts of the high deflection element and the negative axial load's impact on the structure's nonlinear dynamics is more extreme. A more general conclusion of this study is that for designing the MHCD should be more attention to the nonlinearity parameter.
TL;DR: In this article, a quasi-3D hyperbolic shear deformation theory is proposed to analyze the statics and free vibration of functionally graded porous plates resting on elastic foundations, and the equations of motion are derived from the Hamilton principle.
Abstract: This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to
discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal
deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and
efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.
TL;DR: In this paper, a fundamental study on the buckling temperature and postbuckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation is presented.
Abstract: This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (Ro/Ri), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.
TL;DR: The present investigation shows that strengthening of Weissenberg number uplifts the axial as well transverse fluid velocities while that of Hartmann number turns out to be a reverse trend, which imparts a reasonable, pragmatic and realistic approach to a good absorber of solar energy.
TL;DR: In this paper, the surface charge algebra of generic asymptotically locally (A)dS$4}$ spacetimes without matter is derived without assuming any boundary conditions.
Abstract: The surface charge algebra of generic asymptotically locally (A)dS$_{4}$ spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The Λ-BMS$_{4}$ charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS$_{4}$ charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS$_{4}$ surface charges represent the BMS$_{4}$ algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS$_{4}$ flux algebra admits no non-trivial central extension.
TL;DR: The covariant phase space method of Iyer, Lee, Wald, and Zoupas as discussed by the authors gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance.
Abstract: The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity “B”, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving B emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.
TL;DR: In this paper, the results of steady mixed convection flow of SiO 2 − Al 2 O 3 /water hybrid nanofluid near the stagnation point with the curved surface of radius R and mass suction S.
Abstract: The major focus of this work is to examine the results of steady mixed convection flow of SiO 2 − Al 2 O 3 /water hybrid nanofluid near the stagnation point with the curved surface of radius R and mass suction S . Hybrid nanofluid is taken into consideration by suspending a couple of distinct nanoparticles (SiO 2 and Al 2 O 3 ) into pure water. Depending on similarity variables, the governing equations with associated boundary conditions are modified to formulate a normalized boundary value problem of coupled differential equations and the MATLAB problem solver bvp4c is efficient to resolve the resulting problem. From this study it is determined that the skin friction coefficient and local Nusselt number of hybrid nanofluid improves with high values of mass suction and nanoparticles concentration while increasing curvature K declines the skin friction coefficient and gives rise to a poor performance of heat transfer. Moreover, the improvement of thermal boundary layer and velocity boundary layer take place with powerful concentration of SiO 2 and Al 2 O 3 and greater values of curvature K . Some interesting results for the flat sheet ( K → ∞ ) were also computed.
TL;DR: In this paper, it was demonstrated that the standard non-Bloch band theory breaks down in the symplectic class, in which non-Hermitian Hamiltonians exhibit Kramers degeneracy because of reciprocity.
Abstract: Non-Hermitian Hamiltonians are generally sensitive to boundary conditions, and their spectra and wave functions under open boundary conditions are not necessarily predicted by the Bloch band theory for periodic boundary conditions. To elucidate such a non-Bloch feature, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions. Here, it is demonstrated that the standard non-Bloch band theory breaks down in the symplectic class, in which non-Hermitian Hamiltonians exhibit Kramers degeneracy because of reciprocity. Instead, a modified non-Bloch band theory for the symplectic class is developed in a general manner, as well as illustrative examples. This nonstandard non-Bloch band theory underlies the ${\mathbb{Z}}_{2}$ non-Hermitian skin effect protected by reciprocity.
TL;DR: In this paper, the exact solution is determined by solving only a sequence of linear boundary value problems of fractional-order, and an iterative algorithm that is also computationally efficient.
Abstract: The boundary value problems (BVPs) have attracted the attention of many scientists from both practical and theoretical points of view, for these problems have remarkable applications in different branches of pure and applied sciences Due to this important property, this research aims to develop an efficient numerical method for solving a class of nonlinear fractional BVPs The proposed method is free from perturbation, discretization, linearization, or restrictive assumptions, and provides the exact solution in the form of a uniformly convergent series Moreover, the exact solution is determined by solving only a sequence of linear BVPs of fractional-order Hence, from practical viewpoint, the suggested technique is efficient and easy to implement To achieve an approximate solution with enough accuracy, we provide an iterative algorithm that is also computationally efficient Finally, four illustrative examples are given verifying the superiority of the new technique compared to the other existing results
TL;DR: By employing periodic electrical boundary conditions, an innovative method to generate actively tunable topologically protected interface mode in a "homogeneous" piezoelectric rod system is proposed in this article.
Abstract: By employing periodic electrical boundary conditions, an innovative method to generate actively tunable topologically protected interface mode in a “homogeneous” piezoelectric rod system is proposed. Made of homogeneous material and with uniform structure, each unit cell of the piezoelectric rod system consists of three sub-rods forming an A-B-A structure, where the two A sub-rods have the same geometry and electric boundary conditions. It is discovered that the switch of electrical boundary conditions from A-closed and B-open to A-open and B-closed will yield topological phase inversion, based on which topologically protected interface mode is realized. When capacitors CA and CB are connected to the electrodes of sub-rods A and B, respectively, a variety of physical phenomena is observed. On one hand, varying the capacitance in a certain path leads to topological phase transition. On the other hand, different variation paths of the capacitors give rise to different locations of topological phase transition points. This discovery allows the eigenfrequency of the topologically protected edge mode thus formed be actively controlled by appropriately varying the capacitance. The active topological protected interface mode may find wide engineering applications that require high sensitivity sensing, nondestructive testing, reinforcing energy harvesting, information processing, and others.
TL;DR: In this paper, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation.
Abstract: In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin\'s approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.
TL;DR: In this paper, a dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory is presented, in which the unknowns number is reduced.
Abstract: The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton\' principle and solved by Galerkin\'s approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.
TL;DR: The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
TL;DR: It is found that the velocity increases, while both temperature and nanoparticle volume fraction decrease with increased values of variable thermal conductivity and viscosity, which can find applications in the process involving nanofluid operations.
TL;DR: This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu’s slip (second-order slip) features.
Abstract: This study is carried out to scrutinize the gyrotactic bioconvection effects on modified second-grade nanofluid with motile microorganisms and Wu’s slip (second-order slip) features. The activation energy and thermal radiation are also incorporated. The suspended nanoparticles in a host fluid are practically utilized in numerous technological and industrial products such as metallic strips, energy enhancement, production processes, automobile engines, laptops, and accessories. Nanoparticles with high thermal characteristics and low volume fraction may improve the thermal performance of the base fluid. By employing the appropriate self-similar transformations, the governing set of partial differential equations (PDEs) are reduced into the ordinary differential equations (ODEs). A zero mass flux boundary condition is proposed for nanoparticle diffusion. Then, the transmuted set of ODEs is solved numerically with the help of the well-known shooting technique. The numerical and graphical illustrations are developed by using a collocation finite difference scheme and three-stage Lobatto III as the built-in function of the bvp4c solver via MATLAB. Behaviors of the different proficient physical parameters on the velocity field, temperature distribution, volumetric nanoparticles concentration profile, and the density of motile microorganism field are deliberated numerically as well as graphically.
TL;DR: In this article, a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily shaped regions, and simplified implementation and computation is proposed, where the maximum intensity assumption is removed and the initial solution is further refined iteratively by solving the same Poisson equation.
Abstract: The transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a non-interferometric, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive pre-knowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily shaped regions, and simplified implementation and computation. With the "maximum intensity assumption," we first simplify TIE as a standard Poisson equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Poisson equation, and thus the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. Simulations and experiments with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method.
TL;DR: In this article, the boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform, which can be served as a paradigm for various practical applications.
Abstract: This paper aims to review some effective methods for fully fourth-order nonlinear integral boundary value problems with fractal derivatives.,Boundary value problems arise everywhere in engineering, hence two-scale thermodynamics and fractal calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy of the solution.,An elemental and heuristic explanation of fractal calculus is given, and the main solution process and merits of each reviewed method are elucidated. The fractal boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform.,This paper can be served as a paradigm for various practical applications.
TL;DR: In this paper, a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions.
Abstract: In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton\'s principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.