Narrow Results

This study aims at investigating the thermal vibration characteristics of sandwich cylindrical shells consisting of two surface layers crafted from functionally graded materials (FGMs) and a central metal core layer. The sandwich cylindrical shells with FGMs surface layers, with and without porosity, are modelled by using the Kirchhoff–Love shell theory. A porosity function composed of three distinct parts is introduced, including the core-to-thickness ratio, porosity volume fraction, and porosity distribution function. Through the function, the significant effects of porosity that varies with the mixing degree of constituent materials can be analyzed. The material properties are assumed to be temperature-dependent and they show continuous graded variation along the thickness direction. A theoretical approach for analyzing thermal strain energy in the cylindrical shells subjected to thermal environments is established by incorporating Green’s nonlinear strains. The governing equations are derived by applying Hamilton’s principle. Subsequently, analytical solutions for the system’s natural frequencies are determined. Further, to validate the analytical results, a comparative analysis is conducted, drawing upon numerical simulations and other data available in the open literature. Additionally, the thermal vibration characteristics of the composite shell structures are examined in a comprehensive study with respect to various parameters such as porosity type, porosity volume fraction, core-to-thickness ratio, power-law exponent, and temperature changes.

The static response of imperfect composites and sandwich laminates subjected to in-plane partial edge loading is studied. An efficient finite element model based on a refined plate theory is developed for the present purpose. In this theory, the transverse shear stresses are continuous at the layer interfaces along with stress free conditions at the top and bottom surfaces of the plate. The imperfection is considered in the form of in-plane displacement jumps at the layer interfaces, which is characterized by a linear spring-layer model. It is quite encouraging to note that the plate model having all these refined features requires unknowns only at the reference plane. However, this theory demands C¹ continuity of transverse displacement at the element edges, which is difficult to accommodate arbitrarily in any existing finite element. To deal with this problem a new triangular element developed by the authors is used in the present study.

A partial discretization formulation with two-noded finite elements (FEs) under plane stress conditions has been developed for flexural analysis of composite and sandwich beams subjected to transverse loading. The methodology consists in defining a two-point boundary value problem (BVP) governed by a set of coupled first-order ordinary differential equations (ODEs) with four degrees of freedom (u, w, τ_xz and σ_z) per node. Continuity of interlaminar transverse stresses and displacements at laminae interfaces is implicitly enforced in the formulation. All the fundamental elasticity relationships between the components of stress, strain and displacement fields are explicitly maintained throughout the elastic continuum. Results have been obtained for cross-ply composite and sandwich beams. Excellent agreement with available analytical, mixed semianalytical and FE solutions is observed. Some new results with clamped support conditions have also been obtained and are presented to serve as benchmark solutions for future reference and to show the generality of the formulation.

This paper introduces a novel approach called the five-unknown trigonometric shear deformation (FTSD) theory for analyzing the flexural and buckling behavior of porous functionally graded (PFG) plates mounted on an elastic foundation. The FTSD theory features a unique trigonometric displacement field distribution that accurately captures the parabolic transverse shear stress distribution and satisfies the zero transverse shear stress conditions on the plate’s top and bottom surfaces while accounting for thickness stretching effects. The elastic foundation is modeled using a three-parameter Kerr-type model, consisting of two spring layers connected by a shear layer. The study considers both isotropic and sandwich PFG plates with various configurations of constituent layers, as well as both regular and irregular porosity types. The validity of the proposed methodology is evaluated by comparing its results with those from previously published research. Additionally, an extensive parametric analysis is conducted to explore the effects of porosity parameters and foundation parameters on the bending and buckling performance of PFG plates.

The conversion of compound 1 [2,4,6-tris(2-oxaphthalonitrile)-s-triazine] into its isoindoline derivative of 2,4,6-tris[2-oxa(1,3-hexaimino isoindoline)]-s-triazine 2 was accomplished by bubbling ammonia gas through a solution in methanol in the presence of sodium methoxide. The cyclization of two different isoindoline derivatives namely, compound 2 and 4,5-bis(hexylthio)-1,2-diimino-isoindoline 3 with lutetium(III) acetate, [Lu(OAc)₃] in refluxed DMF by the method of statistically mixed condensation gave trimeric trilutetium phthalocyanine [(LuOAc)₃(Pc)₃]4. [Lu₃(Pc)₆]5 has been synthesized in situ by the reaction of phthalocyanine 4 and three equivalents of dilithium octakis-hexylsulfanyl phthalocyanine in amyl alcohol.

In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy’s theory, but trigonometric, hyperbolic and exponential functions are first time used in the present displacement field. The present theory is accounted for an accurate distribution of transverse shear stresses through the thickness of plate, therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived from the principle of virtual work. Navier type closed-form solutions are obtained for simply supported boundary conditions. To verify the global response of the present theory it is applied for the bending of both one-dimensional (beams) and two-dimensional (plates) functionally graded, laminated composite and sandwich structures. The present results are compared with exact elasticity solution and other higher order shear deformation theories to verify the accuracy and efficiency of the present theory.

The objective of this study was to investigate 3D woodpile metamaterials for mitigating impact-induced vibrations by leveraging their local resonant and nonlinear contact characteristics. For experimental demonstrations, we designed, fabricated and tested prototypes of sandwich-structured woodpile metamaterials consisting of two plates, slender cylindrical rods and fasteners. We experimentally and numerically obtained impact responses of sandwich-structured woodpile metamaterials under various geometries and boundary conditions. We found that sandwich-structured woodpile metamaterials could efficiently manipulate and attenuate the impact vibrations due to their local bending motions and nonlinear contact between members. In addition, sandwich-structured woodpile metamaterials could have high damping as well as high stiffness by controlling the rod spacing. The findings from this study suggest sandwich-structured woodpile metamaterials can be used as structural components for impact-induced vibration mitigation.