• Steel and Composite Structures
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• v.16 no.4
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• pp.389-415
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• 2014

This study deals with dynamic model of composite sandwich panels with functionally graded flexible cores under low velocity impacts of multiple large or small masses using a new improved higher order sandwich panel theory (IHSAPT). In-plane stresses were considered for the functionally graded core and face sheets. The formulation was based on the first order shear deformation theory for the composite face sheets and polynomial description of the displacement fields in the core that was based on the second Frostig's model. Fully dynamic effects of the functionally graded core and face-sheets were considered in this study. Impacts were assumed to occur simultaneously and normally over the top and/or bottom of the face-sheets with arbitrary different masses and initial velocities. The contact forces between the panel and impactors were treated as internal forces of the system. Nonlinear contact stiffness was linearized with a newly presented improved analytical method in this paper. The results were validated by comparing the analytical, numerical and experimental results published in the latest literature.

• Steel and Composite Structures
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• v.43 no.1
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• pp.79-90
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• 2022

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

• Steel and Composite Structures
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• v.32 no.2
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• pp.225-237
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• 2019

In this research, the dynamic stability and nonlinear vibration behavior of a smart rotating sandwich cylindrical shell is studied. The core of the structure is a functionally graded material (FGM) which is integrated by functionally graded piezoelectric material (FGPM) layers subjected to electric field. The piezoelectric layers at the inner and outer surfaces used as actuator and sensor, respectively. By applying the energy method and Hamilton's principle, the governing equations of sandwich cylindrical shell derived based on first-order shear deformation theory (FSDT). The Galerkin method is used to discriminate the motion equations and the equations are converted to the form of the ordinary differential equations in terms of time. The perturbation method is employed to find the relation between nonlinear frequency and the amplitude of vibration. The main objective of this research is to determine the nonlinear frequencies and nonlinear vibration control by using sensor and actuator layers. The effects of geometrical parameters, power law index of core, sensor and actuator layers, angular velocity and scale transformation parameter on nonlinear frequency-amplitude response diagram and dynamic stability of sandwich cylindrical shell are investigated. The results of this research can be used to design and vibration control of rotating systems in various industries such as aircraft, biomechanics and automobile manufacturing.

• Steel and Composite Structures
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• v.48 no.3
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• pp.335-351
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• 2023

This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

• Earthquakes and Structures
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• v.18 no.4
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• pp.481-492
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• 2020

A New hyperbolic shear deformation theory is developed for the bending analysis of softcore and hardcore functionally graded sandwich beams. This theory satisfies the equilibrium conditions at the top and bottom faces of the sandwich beam and does not require the shear correction factor. The governing equations are derived from the principle of virtual work. Sandwich beams have functionally graded skins and two types of homogenous core (softcore and hardcore). The material properties of functionally graded skins are graded through the thickness according to the power-law distribution. The Navier solution is used to obtain the closed form solutions for simply supported FGM sandwich beams. The accuracy and effectiveness of proposed theory are verified by comparison with previous research. A detailed numerical study is carried out to examine the influence of the deflections, stresses, and sandwich beam type on the bending responses of functionally graded sandwich beams.

• Steel and Composite Structures
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• v.46 no.2
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• pp.263-277
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• 2023

Free vibration analysis of multi-directional porous functionally graded (FG) sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. Hamilton's principle was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The results obtained are validated with those available in the literature. The composition of metal-ceramic-based functionally graded material (FGM) changes in longitudinal and transverse directions according to the power law. Imperfections in the functionally graded material introduced during the fabrication process were modeled with different porosity laws such as evenly, unevenly distributed, and logarithmic uneven distributions. The effect of porosity laws and geometry parameters on the natural frequency was investigated. On comparing the natural frequency of two cases for perfect and imperfect sandwich plates a reverse trend in natural frequency result was seen. The finding shows a multidirectional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters and imperfection types have been identified which will guide experimentalists and researchers in selecting fabrication routes for improving the performance of such structures.

• Steel and Composite Structures
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• v.15 no.2
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• pp.221-245
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• 2013

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1345-1362
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• 2015

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. $1^{st}$ and $2^{nd}$ modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

• Wind and Structures
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• v.23 no.1
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• pp.59-73
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• 2016

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

• Advances in nano research
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• v.16 no.3
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• pp.313-324
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• 2024

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.