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Static and free vibration analysis of four-parameter continuous grading elliptical sandwich plates

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Applied Mathematics and Mechanics(English Edition) 2022年第4期43卷 523-536页

作者： M.H.YAS F.AKHLAGHI S.KAMARIAN A.H.YAS Department of Mechanical Engineering Razi UniversityKermanshah ***Iran Department of Mechanical Engineering Ilam BranchIslamic Azad UniversityIlam ***Iran Department of Mechanical Engineering Amir-Kabir University of TechnologyTehran 158754413Iran

In the present study,the static and dynamic analyses of elliptical functionally graded sandwich(FGS)plates are investigated.The constituent materials of the sandwich plates are ceramic and metal so that the core is made of pure metal,while the face sheets consist of a combination of metal and ceramic according to a four-parameter power-law distribution.Different material profiles such as classic,symmetric,and asymmetric can be obtained using the applied generalized power-law distribution relation.The analysis is performed based on the classical laminated plate theory(CLPT)and the Ritz method.The effects of four parameters in the material distribution relation as well as different geometric parameters on the deflection and natural frequencies of elliptical FGS plates are studied.The results of this study show that with a proper distribution of materials,the optimal static and dynamic behavior can be achieved.The results also indicate that the generalized power-law distribution has significant effects on the natural frequencies of elliptical FGS plates.For example,although the frequency parameter of a plate with ceramic face sheets is more than the one with metal face sheets,the use of larger amounts of ceramic does not necessarily increase the natural frequency of the structure.

关键词： elliptical plate sandwich plate four-parameter power-law distribution static analysis free vibration analysis Ritz method

Vibration and Buckling Analyses of sandwich plates Containing Functionally Graded Metal Foam Core

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Acta Mechanica Solida Sinica 2022年第4期35卷 587-602页

作者： A.Garg H.D.Chalak L.Li M.-O.Belarbi R.Sahoo T.Mukhopadhyay Department of Civil Engineering National Institute of TechnologyKurukshetraHaryana136119India Department of Aerospace Engineering Indian Institute of TechnologyKanpurUttar Pradesh208016India State Key Lab of Digital Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan430074China Laboratoire de Génie Energétique et Matériaux LGEMFacultéde la science et de lo TechnologieUniversitéde BiskraB.P.145R.P.07000BiskraAlgeria Department of Civil Engineering Indian Institute of TechnologyBanaras Hindu UniversityVaranasiUttar Pradesh221005India

In the present work,free vibration and buckling analyses of sandwich plates with various functionally graded foam cores are carried out.Foam cores are assumed to be made of metal,and three different configurations of the porous distribution in the core layer are taken into consideration.To carry out a comparative study between the distributions of pores in the core foam,the mass of foam in all three cases is kept the same.The vibration and buckling behaviors of skew plates are also analyzed as a part of the current investigation.The principle of minimization of potential energy and Hamilton’s principle are used for the derivation of the governing equations,while a C-0 finite element-based higher-order zigzag formulation is developed to solve the free vibration and buckling problems.The influences of gradation laws,boundary conditions,skew angle and geometry of plates are studied in detail for the dynamic and stability characteristics.It is found that both the non-dimensional natural frequency and buckling load decrease with the increase in the thickness of the metal foam cores,while they show an increasing trend as the skew angle of the plate increases.

关键词： sandwich plate Metal foam core Functionally graded core Finite element Skew plate

Higher-order vibration of thick composite and sandwich plates based on an alternative higher-order model

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Chinese Journal of Aeronautics 2023年第3期36卷 406-420页

作者： Jinghui DENG Tangzhen WU Zhen WU Zhengliang LIU Xiaohui REN China Helicopter Research and Development Institute Jingdezhen 333001China School of Aeronautics Northwestern Polytechnical UniversityXi’an 710072China School of Mechanical Engineering Xi’an Aeronautical UniversityXi’an 710065China

The transverse stretching vibration of thick sandwich plates,which is attributed to largely different stiffness at the adjacent layers,is a challenging issue,and efficient approach for such issue is less reported in the published literature.Thus,natural frequencies corresponding to stretching vibration modes are generally neglected in engineering design,which might impact structural safety as frequencies of the exciting force are close to transverse stretching vibration frequencies.This paper proposes an alternative higher-order model for dynamic analysis corresponding to the higher-order vibration modes.The proposed model is classified in the displacement-based equivalent single-layer theory,as the number of displacement parameters in the proposed model is independent of the layer number.The continuity of displacements and transverse shear stresses can be fulfilled at the interfaces between the adjacent layers of structures.To demonstrate the capability of the proposed model,typical examples are analyzed by utilizing the proposed model,the threedimensional finite element method and the chosen higher-order models.By comparing with the exact three-dimensional elasticity solutions,it is found that the proposed model can yield more accurate natural frequencies corresponding to the higher-order displacement modes than the selected models.Moreover,the factors influencing reasonable prediction of the higher-order frequencies are investigated in detail,which can provide a reference for the accurate prediction of the higher-order frequencies.

关键词： Analytical solution Higher-order theory Natural frequency sandwich plate Transverse stretching vibration

Free vibration of functionally graded sandwich plates in thermal environments

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International Journal of Mechanical System Dynamics 2023年第1期3卷 39-47页

作者： Dongdong Li Zongbai Deng Guoping Chen State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjingChina

This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to obtain the solution.Two types of sandwich plates are examined in this study:one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets.The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method.The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature.The effects of volume fraction distribution,geometrical parameters,and temperature increments on the free vibration characteristics are discussed in detail.

关键词： functionally graded material sandwich plate equivalent‐single‐layer theory free vibration

BENDING OF ORTHOTROPIC sandwich plateS WITH A FUNCTIONALLY GRADED CORE SUBJECTED TO DISTRIBUTED LOADINGS

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Acta Mechanica Solida Sinica 2013年第3期26卷 292-301页

作者： Huadong Li Xi Zhu Zhiyuan Mei Jiabo Qiu Yingjun Zhang College of Naval Architecture and Power Naval University of Engineering

Based on the Reissner assumptions, this paper is concerned with the bending analy- sis of simply supported sandwich plates with functionally graded core and orthotropic face sheets subjected to transverse distributed loadings. First, the expressions of the displacements, stresses and internal forces of the sandwich plate are presented according to the constitutive relations and stress states of the core and face sheets. Then, the solutions of bending equilibrium equa- tions are derived by expanding the deflection w, transverse shearing forces Q~ and Qv with double trigonometric series that satisfy the simply supported boundary conditions. Finally, the proposed solution is validated by comparing the results with available elasticity solutions for a square sand- wich plate with an isotropie core and finite element simulations for one with functionally graded core. The Young＇s modulus of the functionally graded core is assumed to be graded by a power law distribution of volume fractions of the constituents, and the Poisson＇s ratio is held constant. And the effects of the core＇s top-bottom Young＇s modulus ratio A and volume fraction exponent no on the variation of the displacements of the functionally graded sandwich plate are also examined.

关键词： functionally graded materials orthotropic sandwich plate distributed loading,simply supported

NONLINEAR VIBRATION OF CIRCULAR sandwich plateS UNDER CIRCUMJACENT LOAD

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Applied Mathematics and Mechanics(English Edition) 2006年第10期27卷 1417-1424页

作者：杜国君马建青 Yanshan University Qinhuangdao 066004Hebei ProvinceP.R.China

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

关键词： sandwich plate nonlinear vibration critical load buckling amplitude frequency-load characteristic relation

ELASTIC-PLASTIC DYNAMIC RESPONSE OF FULLY BACKED sandwich plateS UNDER LOCALIZED IMPULSIVE LOADING

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Acta Mechanica Solida Sinica 2010年第4期23卷 324-335页

作者： Hua Liu Wuchao Chen Jialing Yang (The Solid Mechanics Research Center, Beijing University of Aeronautics and Astronautics, Beijing 100191, China) The Solid Mechanics Research Center Beijing University of Aeronautics and Astronautics Beijing China

An analytical model is developed to assess the elastic-plastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elastic-perfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elastic-plastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulse-induced local effect on fully backed sandwich plates.

关键词： sandwich plate elastic plastic localized impulse plastic dissipation

THE BUCKLED STATES OF ANNULAR sandwich plateS

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Applied Mathematics and Mechanics(English Edition) 1992年第7期13卷 623-628页

作者：何录武程昌钧 Department of Mechanics Lanzhou University Lanzhou

In this paper, the axisymmetric buckled states of an annular sandwich plate ( Reissner-type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled slates in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.

关键词： sandwich plate shooting method critical load buckled state

PERIODICITY OF A 1:3 INTERNAL RESONANCE sandwich plate

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PERIODICITY OF A 1:3 INTERNAL RESONANCE SANDWICH PLATE