• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.55-66
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• 2019

This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

• Advances in nano research
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• v.7 no.2
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• pp.109-123
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• 2019

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.

• Steel and Composite Structures
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• v.31 no.2
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• pp.187-199
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• 2019

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

• Structural Engineering and Mechanics
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• v.78 no.5
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• pp.557-572
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• 2021

The current study considers free vibration of the spherical panel with magnetorheological (MR) fluids core and magneto-electro-elastic face sheets. The panel is subjected to electro-magnetic loads and also is located on an orthotropic visco-Pasternak elastic foundation. To describe the displacement components of the structure, the first-order shear deformation theory (FSDT) is used and the motion equations are extracted by employing Hamilton's principle. To solve the motion differential equations, Navier's method is selected as an exact analytical solution for simply supported boundary conditions. Effect of the most important parameters such as magnetic field intensity, loss factor, multi-physical loads, types of an elastic medium, geometrical properties of the panel, and also different material types for the face sheets on the results is considered and discussed in details. The outcomes of the present work may be used to design more efficient smart structures such as sensors and actuators.

• Advances in nano research
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• v.10 no.1
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• pp.43-57
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• 2021

In this study, thermally induced bifurcation buckling of shallow composite cylindrical panels reinforced with aligned single-walled carbon nanotubes is investigated. Distribution of carbon nanotubes across the thickness of the cylindrical panel as reinforcements may be either uniform or functionally graded. Thermo-mechanical properties of the matrix and reinforcements are considered to be temperature dependent. Properties of the cylindrical panel are obtained using a refined micromechanical approach which introduces the auxiliary parameters into the rule of mixtures. The governing equations are obtained by using the static version of the Hamilton principle based on the first-order shear deformation theory and considering the linear strain-displacement relation. An energy-based Ritz method and an iterative process are used to obtain the critical buckling temperature of composite cylindrical panel with temperature dependent material properties. In addition, the effect of various parameters such as the boundary conditions, different geometrical conditions, distribution pattern of CNTs across the thickness and their volume fraction are studied on the critical buckling temperature and buckled pattern of cylindrical panels. It is shown that FG-X type of CNT dispersion is the most influential type in thermal stability.

• Advances in nano research
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• v.10 no.2
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• pp.175-189
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• 2021

In this article, frequency characteristics, and sensitivity analysis of a size-dependent laminated composite cylindrical nanoshell under bi-directional thermal loading using Nonlocal Strain-stress Gradient Theory (NSGT) are presented. The governing equations of the laminated composite cylindrical nanoshell in thermal environment are developed using Hamilton's principle. The thermodynamic equations of the laminated cylindrical nanoshell are obtained using First-order Shear Deformation Theory (FSDT) and Fourier-expansion based Generalized Differential Quadrature element Method (FGDQM) is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The novelty of the current study is to consider the effects of bi-directional temperature loading and sensitivity parameter on the critical temperature and frequency characteristics of the laminated composite nanostructure. Apart from semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the laminated cylindrical shell. The results created from finite element simulation illustrates a close agreement with the semi-numerical method results. Finally, the influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature, sensitivity, and frequency of the laminated composite nanostructure are investigated, in details.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.729-742
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• 2023

It is a recent attraction to the mechanical scientists to investigate state of wave propagation, buckling and vibration in the sport balls to observe the importance of different parameters on the performance of the players and the quality of game. Therefore, in the present study, we aim to investigate the wave propagation in handball game ball in term of mass of the ball and geometrical parameters wit incorporation of the viscoelastic effects of the ball material into account. In this regard, the ball is modeled using thick shell structure and classical elasticity models is utilized to obtain the equation of motion via Hamilton's principle. The displacement field of the ball model is obtained using first order shear deformation theory. The resultant equations are solved with the aid of generalized differential quadrature method. The results show that mass of the ball and viscoelastic coefficient have considerable influence on the state of wave propagation in the ball shell structure.

• 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.

• Advances in nano research
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• v.14 no.3
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• pp.261-271
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• 2023

The present study follows three main goals. First, an analytical solution with high accuracy is developed to assess the effects of embedding pre-strained shape memory alloy (SMA) wires on the critical buckling temperatures of rectangular sandwich plates made of soft core and graphite fiber/epoxy (GF/EP) face sheets based on piecewise low-order shear deformation theory (PLSDT) using Brinson's model. As the second goal, this study compares the effects of SMAs on the thermal buckling of sandwich plates with those of carbon nanotubes (CNTs). The glass transition temperature is considered as a limiting factor. For each material, the effective ranges of operating temperature and thickness ratio are determined for real situations. The results indicate that depending on the geometric parameters and thermal conditions, one of the SMAs and CNTs may outperform the other. The third purpose is to study the thermal buckling of sandwich plates with advanced hybrid SMA/CNT/GF/EP composite face sheets. It is shown that in some circumstances, the co-incorporation of SMAs and CNTs leads to an astonishing enhancement in the critical buckling temperatures of sandwich plates.

• Advances in nano research
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• v.14 no.6
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• pp.575-590
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• 2023

Many of small-scale devices should be designed to tolerate high temperature changes. In the present study, the states of buckling and stability of nano-scale cylindrical shell structure integrated with piezoelectric layer under various thermal and electrical external loadings are scrutinized. In this regard, a multi-layer composite shell reinforced with graphene nano-platelets (GNP) having different patterns of layer configurations is modeled. An outer layer of piezoelectric material receiving external voltage is also attached to the cylindrical shell for the aim of observing the effects of voltage on the thermal buckling condition. The cylindrical shell is mathematically modeled with first-order shear deformation theory (FSDT). Linear elasticity relationship with constant thermal expansion coefficient is used to extract the relationship between stress and strain components. Moreover, minimum virtual work, including the work of the piezoelectric layer, is engaged to derive equations of motion. The derived equations are solved using numerical method to find out the effects of temperature and external voltage on the buckling stability of the shell structure. It is revealed that the boundary condition, external voltage and geometrical parameter of the shell structure have notable effects on the temperature rise required for initiating instability in the cylindrical shell structure.