scholarly journals Fundamental Frequency Analysis of Sandwich Beams with Functionally Graded Face and Metallic Foam Core

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lin Mu ◽  
Guiping Zhao
Keyword(s):  
Fundamental Frequency ◽  
Plate Theory ◽  
Order Theory ◽  
Functionally Graded ◽  
Face Sheet ◽  
Metallic Foam ◽  
Sandwich Beams ◽  
Classical Plate Theory ◽  
The Core ◽  
The Face

This study is interested in assessing a way to analyze fundamental frequency of sandwich beams with functionally graded face sheet and homogeneous core. The face sheet, which is an exponentially graded material (EGM) varying smoothly in the thickness direction only, is composed of a mixture of metal and ceramic. The core which is made of foam metal is homogeneous. The classical plate theory (CPT) is used to analyze the face sheet and a higher-order theory (HOT) is used to analyze the core of sandwich beams, in which both the transverse normal and shear strains of the core are considered. The extended Galerkin method is used to solve the governing equations to obtain the vibration equations of the sandwich beams suitable for numerical analysis. The fundamental frequency obtained by the theoretical model is validated by using the finite element code ABAQUS and comparison with earlier works. The influences of material and geometric properties on the fundamental frequency of the sandwich beams are analyzed.

Buckling and Postbuckling of Sandwich Beams With Delaminated Faces Based on Higher Order Core Theory

1999 ◽  
Author(s):  
R. F. Li ◽  
Y. Frostig ◽  
G. A. Kardomateas
Keyword(s):  
Nonlinear Distortion ◽  
Variational Principles ◽  
Vertical Direction ◽  
Initial Imperfection ◽  
Order Theory ◽  
Sandwich Beams ◽  
Postbuckling Behavior ◽  
The Core ◽  
Core Theory ◽  
The Face

Abstract Delaminations within the face sheets are often observed when a sandwich structure is exposed to impact loads. The buckling and postbuckling behavior of sandwich beams with delaminated faces is investigated in this work. The governing nonlinear equations, boundary conditions, and continuity conditions are formulated through variational principles. The beam construction consists of upper and lower, metallic or composite laminated symmetric skins, and a soft core of a foam or low strength honeycomb type. A high order theory is used for the core that accounts for the nonlinear distortion of the plane of section of the core and the compressibility in the vertical direction. The delamination considered is an interface crack, in which the substrate includes the transversely flexible core. The case of a debond at one of the skin-core interfaces is also included. The effects of the delamination length and location on the overall and local behavior are examined with an arbitrary initial imperfection.

Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets

2019 ◽  
Vol 22 (3) ◽  
pp. 866-895 ◽  
Author(s):  
S Jedari Salami
Keyword(s):  
Sandwich Panel ◽  
Sandwich Beam ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Face Sheet ◽  
Sandwich Beams ◽  
Nonlinear Bending ◽  
Graphene Platelet ◽  
The Face ◽  
Graphene Platelets

This study investigates the nonlinear bending response of a novel class of sandwich beams with flexible core and face sheets reinforced with graphene platelets that are functionally graded distributed through the thickness. Nonlinear governing equations are established based on extended high-order sandwich panel theory and Von Kármán type of geometrical nonlinearity. In this theory, the face sheets follow the first-order shear deformation theory, and the two-dimensional elasticity is adopted for the core. These nonlinear differential equations are discretized into algebraic systems by means of the Ritz-based method from which the static bending solution can be achieved. The effective Young’s modulus of functionally graded graphene platelet-reinforced composite (GPLRC) face sheets is determined through the modified Halpin–Tsai micromechanics model, and associated Poisson’s ratio is evaluated by employing the rule of mixture. Comparison studies are provided for a sandwich beam with graphene-reinforced face sheets and conventional nanocomposite beam reinforced by graphene platelets due to lack of results for introduced sandwich beams. Besides, three-point bending test was carried out in order to assure the validity of nonlinear bending analysis of a sandwich beam based on extended high-order sandwich panel theory. Afterwards, parametric studies are given to examine the influences of graphene platelet distribution pattern, weight fraction, and core-to-face sheet thickness ratio together with the total number of layers on the linear and nonlinear bending performances of the sandwich beams. Numerical results demonstrate that distributing more graphene platelets near the upper and lower surface layers of the face sheets, named X-GPLRC, is capable to improve the bending strength and decrease the local deflection of the top face sheet, and this recovery effect becomes more significant as graphene platelet weight fraction increases. The results also reveal that the graphene platelet distribution pattern of the face sheets plays an important role to decrease the transverse shear stress of the core by dispersing more graphene platelets near surfaces of the face sheets (X-GPLRC). So, reducing the local deflection of the top face sheet tends to be much more safety of the soft core from any failure. Besides, sandwich beams with a lower weight fraction of graphene platelets in face sheets that are symmetrically distributed in such a way, called O-GPLRC, are also less sensitive to the nonlinear deformation.

Analytical Modeling on Vibration Analysis of Cracked Functionally Graded Plate Submerged in Fluid

2019 ◽  
Vol 12 (3) ◽  
pp. 240-247
Author(s):  
Shashank Soni ◽  
Nitin K. Jain ◽  
Prasad V. Joshi
Keyword(s):  
Fundamental Frequency ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Plate Theory ◽  
Fluid Medium ◽  
Fluid Forces ◽  
Bernoulli’S Equation ◽  
Submerged Plate ◽  
Line Spring Model

Background: It is established that the vibration response of submerged structures is quite different than that calculated in vacuum. Therefore, the study of vibration characteristics of submerged plate structures is important for safety and its designing purpose. Objective: To investigate the fundamental frequency of partially cracked Functionally Graded (FG) submerged plate based on analytical approach. Methods: The governing differential equation of the cracked-submerged plate is derived based on Kirchhoff’s thin classical plate theory in conjunction with the potential flow theory. The line spring model is used to incorporate the effect of crack in the form of additional bending whereas the effect of fluid medium is incorporated in form fluids forces associated with inertial effects of its surrounding fluids. The Bernoulli’s equation and velocity potential function are used to define the fluid forces acting on plate surface. Results: An approximate solution for governing equation of coupled fluid-plate system is obtained by using the Galerkin’s method. For validation of the present results, they are compared with the existing results of the previous published work, which are in good agreements. New results for natural frequencies as affected by gradient index, crack length, level of submergence and immersed depth of plate are presented for Simply Supported (SSSS) boundary condition. Conclusion: It has been concluded that the presence of crack and fluidic medium significantly affect the natural frequencies of the plate. It is observed that the increase in the length of crack and level of submergence decreases the fundamental frequency. In this paper, few patents have been discussed.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

Effect of Core Plasticity on the Post-Buckling Behavior of Debonded Sandwich Beams

2000 ◽  
Author(s):  
Bhavani V. Sankar ◽  
Manickam Narayanan ◽  
Abhinav Sharma
Keyword(s):  
Plastic Material ◽  
Maximum Load ◽  
Face Sheet ◽  
Compression Tests ◽  
Element Analysis ◽  
The Core ◽  
Perfectly Plastic ◽  
The Face ◽  
Post Buckling ◽  
Elastic Perfectly Plastic

Abstract Nonlinear finite element analysis was used to simulate compression tests on sandwich composites containing debonded face sheets. The core was modeled as an elastic-perfectly-plastic material, and the face-sheet as elastic isotropic. The effects of core plasticity, face-sheet and core thickness, and debond length on the maximum load the beam can carry were studied. The results indicate that the core plasticity is an important factor that determines the maximum load.

On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-PlaneForce Via GDQR

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Roshan Lal ◽  
Rahul Saini
Keyword(s):  
Mechanical Properties ◽  
Plate Theory ◽  
Elastic Equilibrium ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Axisymmetric Vibration ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a nonlinear temperature distribution (NTD) along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent (TD). At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule (GDQR), the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force, and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

Finite Elements for Curved Sandwich Beams

1977 ◽  
Vol 28 (2) ◽  
pp. 123-141 ◽  
Author(s):  
P J Holt ◽  
J P H Webber
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Test Cases ◽  
Sandwich Beams ◽  
Honeycomb Core ◽  
The Core ◽  
The Face ◽  
Core Thickness ◽  
Displacement Approach ◽  
Circular Sandwich Ring

SummaryThe formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

Geometrical Nonlinear Effects in the Dynamic Response of Sandwich Beams

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Itay Odessa ◽  
Oded Rabinovitch ◽  
Yeoshua Frostig
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
High Order ◽  
Theory Approach ◽  
Nonlinear Frequency ◽  
Sandwich Beams ◽  
Nonlinear Dynamic Response ◽  
The Core ◽  
Geometrical Nonlinear ◽  
The Face

Abstract The geometrical nonlinear dynamic response of sandwich beams is studied using a dynamic high-order nonlinear model. The model is derived using the variational principle of virtual work and uses the Extended High-Order Sandwich Panel Theory approach with consideration of two interfaces between the three layers. A first-order shear deformation theory is adopted for the face sheets, while the kinematic assumption of high-order small deformations that account for out-of-plane compressibility are considered for the core layer. The nonlinearity of the dynamic model is introduced by considering geometrically nonlinear kinematic relations in the face sheets. The nonlinear kinematic relations and the dynamic modeling aim to evaluate the effects of the two features and their coupling on the response. The nonlinear dynamic response of sandwich beams is studied through two numerical cases and comparison of the nonlinear results with their linear counterparts. The first case looks into the coupling of the global geometrical nonlinear behavior with the dynamic behavior. The second case focuses on the local instability of the face sheets and its interaction with the compressibility of the core in the dynamic response of soft core sandwich beams. The comparison of linear and nonlinear dynamic response in the two cases sheds light on the coupling of the geometrical nonlinear and dynamic behaviors. Among other features, the latter is expressed by nonlinear attractors, higher modes response, nonlinear frequency response, and significant wrinkling response.

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