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This study addresses a critical gap in the literature by investigating the static and natural frequency characteristics of functionally graded (FG) auxetic metamaterial annular plates reinforced with graphene origami (GOri), a novel area previously unexplored in the context of composite constructions, particularly for circular plates. The governing equations are derived utilizing higher-order shear deformation theory along with Hamilton’s principle, and solved using the finite element approach. For the first time, a comprehensive parametric study including the folding degree and mass fraction, and distribution pattern of GOri, is investigated on the static and natural frequency properties of annular plates. It is found that the natural frequency generally increased with higher mass fractions and decreased with greater folding degrees, though the X and V patterns at a 3% mass fraction showed an atypical increase in frequency with higher folding degrees. The impact of distribution patterns varied with weight fraction: the X-pattern caused the highest deflection at 1% weight fraction but the lowest at 3%, while the O-pattern caused the least deflection overall.

It has been observed that undulating periodic patterns formed on an initial flat annular plate that model the leaves of plants are a physical response to the expansion of the surface under a lateral restraint. They are not visible at the beginning but become apparent only when the plants continue to grow. The behavior can be explained via the inhomogeneous deformation of gel materials that behave in a similar manner to hyperelastic materials in solid mechanics.This paper compares the stability of thin annular plates clamped along the inner edge and free along the outer periphery using numerical simulations of the swelling of thin gel annular plate held along the inner edge as well as analysis of a similar class of structures by solid mechanics concept via energy principle. The trends of results from both approaches compare favorably. The buckling patterns of annular plates with various values of inner radius to outer radius ratio illustrate the relationship between the geometry of the annular plate and the inhomogeneous deformation of gels or buckling patterns of solid mechanics materials. The undulating patterns on leaves such as those of flowering cabbage can thus be explained via the buckling behavior of annular plates, which can be regarded as thin soft materials adhered to a stiffer core. The study can also be extended to cover other stimuli under different environmental conditions and the outcome may bring further insights into the evolution of plants.

Steady-state and transient acoustic radiation characteristics of clamped-free annular plate with tuned mass damper (TMD) device is studied. Galerkin’s procedure is employed to obtain the transverse vibration of the annular disk. Based on the Rayleigh integral approach, acoustic pressure radiation is obtained and subsequently the modal sound power and modal radiation efficiency are obtained. A new formulation for the transient acoustic pressure in Laplace domain is presented for the first time in this paper. Durbin’s numerical Laplace transform inversion scheme is employed to obtain the response spectrum. The optimum parameters of vibration absorbers are proposed for suppressing the dynamic vibration and acoustic pressure. A parametric study is carried out and the effects of vibration absorber characteristics are investigated using the analytical procedure. Limiting cases are considered and good agreements with the finite element solution, as well as with those available in the literature, are achieved.

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

The paper presents a solution to the dynamic response of three-layered, annular plates that are thermo-mechanically loaded. Time-dependent forces are considered to act on the facings of the plate. The thermal loading is defined by a flat, axisymmetric temperature field whose profile is expressed by the stationary or increase in time temperature differences between the plate edges. The cases of the plates loaded only thermally or mechanically have been examined. The problem has been solved analytically and numerically using the approximation methods: orthogonalization and finite difference. The selected reactions of an exemplar plate have been compared with the results obtained for the plate analyzed by the finite element method (FEM). The critical temperature differences and critical loads and corresponding dynamic buckling modes have been analyzed in detail. The numerous results presented for the dynamic responses have an important and practical meaning in the design process of plate structures subjected to complex thermo-mechanical loads.

The porous material is an emerging lightweight material, which is able to reduce structural weight and also keeps the superiority of the structure. Therefore, this work is devoted to the investigation of the functionally graded porous (FGP) annular and circular plates with general boundary conditions. The unified modeling method is proposed by combining the first-order shear deformation theory, the virtual spring technology, the multi-segment partition method, and the semi-analysis Rayleigh–Ritz approach. Afterwards, the convergency and correctness of the proposed method are verified, respectively. The frequency parameters, modal shapes, and forced vibration responses are uniformly calculated based on the proposed method. Finally, the dynamic analyses of the FGP annular and circular plates with different parameters, such as the porosity distribution types, porosity ratios, boundary condition types, geometry parameters, and load types, are conducted in detail. It is found that the reasonable porous design is able to keep the dynamic stability of the structure under different parameter variations.

This study investigates the axisymmetric postbuckling of functionally graded graphene platelets reinforced composite (FG-GPLRC) annular plates resting on nonlinear elastic medium in thermal environment. Five kinds of graphene platelets (GPLs) distribution patterns including $U$-pattern, $X$-pattern, $O$-pattern, $A$-pattern, and $V$-pattern have been considered. The nonlinear equilibrium equations and associated boundary conditions are obtained based upon the Mindlin plate theory. The governing equations are solved via the generalized differential quadrature method (GDQM). Afterwards, the direct iterative method is implemented to accomplish postbuckling loads using the buckling mode deflection. In order to confirm the accuracy of the present model, comparisons between our data with those published in the available literature are put forth. Eventually, this paper emphasizes the impact of diverse parameters such as geometrical parameters of the structure, GPLs patterns and their geometric, GPLs weight fraction, boundary conditions, elastic medium’s parameters and temperature change on the buckling and postbuckling response of nanocomposite annular plates. It can be found that elastic medium overshadows the applicability of distribution patterns and weight fraction of GPLs.

In this paper, a semi-analytical technique based on Taylor’s series method namely DTM has been used to solve the differential equation which governs the motion of three types of annular FGM plates. The differential equation has been obtained using Hamilton principle and classical plate theory. The mechanical properties of the plate (Young’s modulus and density) are considered to be graded in thickness direction and vary following the power-law. The behaviour of volume fraction index and radii ratio has been investigated onto first three modes of frequency parameter for all three plates. Moreover, the novelty of this paper is the application of the versatile technique DTM to study the effect of radii ratio and volume fraction index on three different types of annular FGM plates. A comparison has been made between the obtained numerical results and the results are available in the literature. A good agreement of the results verifies the accuracy of the present technique. Three-dimensional mode shapes for all three plates are also presented.

This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic substrate besides describing the kinematics on the basis of HSDT makes the results closer to real condition. Numerical results are compared with those published in the literature to examine the accuracy and validity of the applied approach. A comprehensive parametric study is accomplished to reveal the influence of stiffness of the substrate, patterns of temperature rise, temperature gradient, axial load, weight fraction and distribution patterns of GPLs, outer radius to inner radius ratio, inner radius to thickness ratio of the plate and geometric dimensions of GPLs on the response of the structure. This study provides essential information to engineers seeking innovative ways to promote the composite structures in a practical way.