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This paper has developed the Levy solution of a size-dependent model for free vibration analysis functionally graded thin rectangular plate according to the theories of first-order shear deformation as well as modified couple stress. The couple stress theory is used to calculate the effects of small-scale parameter, while the first-order shear deformation theory is employed to calculate the effects of shear deformation. By taking the displacement field according to the Mindlin plate theory, application of the Hamilton principle aims at obtaining five governing equations of motion and desired six boundary conditions. The governing equations of motion have been solved based on Levy boundary conditions by using four auxiliary functions. Numerical findings have been used to determine the impacts of various parameters including small-scale parameter changes, power-law index changes, as well as aspect ratios changes with different boundary conditions. As the results show, an increase in the size effects makes that plate tougher and consequently the natural frequency is increased. Also, it can be seen that in little thicknesses of plate, the effects of small-scale parameter are noticeable, but as the plate becomes thicker, the effects will be insignificant.

The tubule occlusion of two newly developed herbal toothpastes was examined. They were prepared based on the mixture of pomegranate peel and Equisetum arvense extracts with strontium acetate. The antimicrobial activity of pomegranate peel and E. arvense were determined using minimum inhibitory concentration (MIC). Then, 30 mid-coronal dentin discs from the human third molars were etched for 30 s with the lemon juice (pH = 2.4). The specimens divided into the three groups. While the control group had 6 specimens, Groups 1 and 2 were including 12 specimens. Group 1 brushed with toothpaste containing 10% strontium acetate and 5% hydroalcoholic extracts of pomegranate peel, and Group 2 brushed with 5% strontium acetate, 5% hydroalcoholic extracts of E. arvense, and 5% hydroalcoholic extracts of pomegranate peel. Brushing was simulated for 6 months with 2 N loading. Then, 50% of discs in each group were immersed in lemon juice for 1 min. Moreover, specimens in control group were brushed with distilled water. Finally, all 30 discs were analyzed using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDXS). The occluded dentin tubules were counted and statistically evaluated. It was found that the number of open dentin tubules decreases significantly after brushing with both tested toothpastes compared with control group (p < .001). Moreover, a significant difference was observed between two toothpastes before and after acid immersion process (p < .001). The SEM micrographs confirmed the dentin tubule occlusion of both herbal dentifrices. Besides, EDXS analysis approved the strontium and silica presence on the dentin tubules for the toothpaste which was based on E. arvense.

In this paper, energy harvesting from a thin annular sectorial plate, which consists of an elastic layer bonded with two layers of piezoelectric materials, is studied analytically. The Rayleigh damping assumption is used in the model to consider the structural damping. To derive the governing equations, the Hamilton principle for an electro-elastic body is employed based on the classical plate theory, and to solve the derived equations, the Rayleigh–Ritz method is used. The modeling approach is verified against analytical solutions as well as experimental results for rectangular and annular sectorial plates. Finally, the impact of changing some parameters (material properties, electrical boundary conditions, geometrical parameters) on the performance of the system is investigated extensively. It is shown that the annular sector plate energy harvesters can deliver better performance compared to rectangular plate energy harvesters.

Roller screen is a key device in pelletizing plants employed to size classification of green pellets. Realistic observations showed that some pellets with size slightly larger than the gap were tra...

The effects of a nonthermal atmospheric plasma jet with argon and argon/oxygen (Ar/O2) gases on live human dental pulp stem cells (hDPSCs) were studied to verify tooth vitality in the pulp-capping process. Using MTT assay, the surviving hDPSCs after plasma jet exposure for 1, 2, and 3 min were counted. First, for the pulsed plasma jet the frequency varied from 10 to 50 kHz for 5 groups with Ar and 5 groups with Ar/O2 plasma jet. Later, with the alternating current (AC) plasma jet, the voltage was changed between 5.5 and 16.05 kV for 13 groups. The cells in the control group were only exposed to Ar and Ar/O2 gases. To control thermal damage to hDPSCs, optical emission spectroscopy was used. For data analysis, the ANOVA repeated measure was used. There were significant differences between the various frequencies and exposure durations (p < 0.05) for the Ar plasma. For the Ar/O2 gas, there were significant differences between frequencies (p < 0.001). For the AC plasma jet with Ar gas, there were significant differences between voltages (p < 0.001). At the higher pulsed jet frequencies, temperatures increased. Eventually, the suitable durations for root canal disinfection and hDPSC survival with the Ar pulsed jet were 2 and 3 min at 10 and 30 kHz, respectively. Since cold plasma disinfection keeps hDPSCs alive, it can be helpful in promoting tooth survival and durability for pulp capping in clinical treatments.

In this study, the free vibration of a composite sandwich plate reinforced with graphene nanoplatelets (GPLs) enclosed by piezoelectric layers is investigated using an analytical solution. In the framework of the first-order shear deformation plate theory, multilayer functionally graded graphene platelets-reinforced composite plate is assumed. Applying modified Halpin–Tsai model and rule of mixtures, the effective Young’s modulus, mass density and Poisson’s ratio of nanocomposites are predicted. In each individual layer, the weight fraction of GPL nanofillers illustrates a layer-wise variation along the thickness direction either uniformly or non-uniformly GPLs dispersed. Based on Maxwell’s equation, the electric potential in a piezoelectric layer is considered for open and closed circuit boundary conditions. Coupled governing equations of motion and boundary conditions are derived by using the Hamilton’s principle. Four auxiliary scalar functions are introduced to decouple the governing equations of motion and boundary conditions, which are solved analytically by employing Levy-type boundary conditions. The effects of GPLs weight fraction, GPLs distribution patterns, number of layers and aspect ratio are examined in detail. The results show that the best way to predict the most effective reinforcement is to distribute more GPLs with a larger surface area near the top and bottom surfaces of the plate. Besides, adding a small amount of GPLs as reinforcing nanofillers can significantly improve the stiffness of the plate.

In this article, the flutter vibrations of fluid-conveying thin-walled nanotubes subjected to magnetic field is investigated. For modeling fluid structure interaction, the nonlocal strain gradient thin-walled Timoshenko beam model, Knudsen number and magnetic nanoflow are assumed. The Knudsen number is considered to analyze the slip boundary conditions between the fluid-flow and the nanotube's wall, and the average velocity correction parameter is utilized to earn the modified flow velocity of nano-flow. Based on the extended Hamilton's principle, the size-dependent governing equations and associated boundary conditions are derived. The coupled equations of motion are transformed to a general eigenvalue problem by applying extended Galerkin technique under the cantilever end conditions. The influences of nonlocal parameter, strain gradient length scale, magnetic nanoflow, longitudinal magnetic field, Knudsen number on the eigenvalues and critical flutter velocity of the nanotubes are studied.

This paper is concerned with influence of porosity and mechanical/electrical boundary conditions on buckling of moderately thick, porous sector and annular sector plates integrated with piezoelectric layers. Presence of both porous and piezoelectric elements in a configuration provides new opportunities for manipulating the buckling load broadly. To demonstrate these possibilities, across the thickness of the core plate, varying porosity profiles are considered, yet the network of pores is assumed to be free of fluid. The governing equations of the sandwich plate under uniform in-plane mechanical loading are obtained by taking the Mindlin plate theory and von Karman assumptions into account; and later the nonlinear nature of the problem is simplified through the use of the adjacent equilibrium criterion. Next, decoupled formulae for all the unknown kinematic variables are reached by introducing two transformation functions. The critical buckling loads are computed analytically by assuming simply supported radial edges and classical boundary conditions for the circumferential edges. Eventually, the effect of the mechanical/electrical boundary conditions, geometrical parameters and porosity is realized by comprehensive parametric studies.

The vibration and stability analyses of functionally graded (FG) reinforced porous plates with piezoelectric layers under supersonic flow are investigated. The plate has a FG core reinforced by nanocomposite graphene platelets (GPLs) which surrounded by two piezoelectric layers. The GPLs are distributed thorough the thickness direction both uniformly and non-uniformly. The first-order shear deformation plate theory (FSDT) and first-order piston theory are applied to analyze the stability of FG porous plates. Using Hamilton's principle and Maxwell's equation, the governing equations of motion as well as electrical and mechanical boundary conditions are obtained. Applying the Galerkin approach, the partial differential governing equations are converted to the ordinary differential equations. The numerical results show that the flutter aerodynamic pressure and natural frequencies decrease as the porosity coefficient increases. Besides, the symmetric porosity distribution together with GPL pattern A predicts the highest flutter aerodynamic pressure and natural frequencies. Also, the best efficient way to increase the stability region is considering GPL pattern A, with dispersing more GPLs fillers near the top and bottom surfaces of FG porous plate along with symmetric porosity distribution. Furthermore, FG porous plate enclosed by piezoelectric layers in open circuit condition predicts higher flutter aerodynamic pressure and natural frequencies than similar plate in closed circuit condition.

In this study, the aerothermoelastic flutter analysis of pre-twisted tapered rotating blades reinforced with functionally graded carbon nanotubes (FG-CNTs) under supersonic flow is investigated. Based on the thin-walled Timoshenko beam theory and quasi-steady supersonic linear piston theory, the dynamic model of the supersonic rotating blades reinforced with FG-CNTs has been developed. The CNTs are considered to be either uniformly or non-uniformly distributed in the matrix along the thickness direction. Three various CNTs distribution patterns namely, UD, FG-X and FG-O have been assumed. The properties of CNTs and polymer matrix are considered to be temperature-dependent. Based on the extended Hamilton's principle , the equations of motion as a system of coupled linear partial deferential equations are found. The extended Galerkin method (EGM) is utilized to transform these coupled partial deferential equations to a set of coupled ordinary deferential equations. The influences of rotating speed, CNTs distribution, CNTs weight fraction, temperature, pre-twist and pre-setting angels, hub radius ratio, taper ratios and Mach number on the aerothermoelastic flutter responses of the system have been analyzed. The results indicate that the FG-X distribution pattern have predicted more strengthening the total bending of blade and the greatest flutter frequency for the composite blades. Furthermore, the pre-twist and pre-setting angles as well as taper ratio have significant effects on the flutter frequency of the thin-walled blade reinforced with CNTs.

In this paper, Reddy’s higher-order and Mindlin’s first-order plate theories are used for buckling analysis of porous rectangular plates subjected to various types of mechanical loading. The condition of the internal pores is considered to be either free of or saturated by fluid. Biot’s theory of poroelasticity is thereby employed to model the behaviour of fluid. Distribution of pores is assumed to vary through the thickness according to an asymmetric distribution. For each displacement field considered, five highly coupled partial differential equations are derived by means of variational principle. These systems of equations are first decoupled through an efficient method, and then solved analytically for Levy-type boundary conditions. Accuracy of the approach is examined by comparing the obtained results with those available in literature. Eventually, comprehensive parametric studies are provided to investigate the effects of geometrical parameters, boundary conditions, loading conditions, porosity coefficient and pore fluid compressibility on the buckling response of the system. The results suggest that a structure with higher equivalent rigidity is met, when its corresponding internal pores are saturated by fluid. The results of the current work can be considered as a benchmark for future studies.

In the current study, the stability analysis of functionally graded (FG) thin-walled porous beams reinforced by nanocomposite graphene platelets (GPLs) under compressive axial load is investigated. It is assumed that the thin-walled porous beam is spinning along its longitudinal axis and both symmetric and asymmetric distributions of porosity are considered. Furthermore, the GPLs are distributed thorough the thickness direction both uniformly and non-uniformly. The effective material properties such as Young's modulus, mass density and Poisson's ratio of the porous beams are computed based on the Halpin-Tsai micromechanics model and the rule of mixture. The extended Hamilton's principle is utilized to establish the governing equations and they are discretized by the extended Galerkin method (EGM). The effects of various parameters such as GPL porous distribution patterns, GPL weight fraction, geometry of GPL nanofillers and porosity coefficient on the frequencies as well as flutter and divergence instabilities of the thin-walled porous beams have been studied. Numerical results demonstrate that the best efficient way to increase the stability region is considering GPL pattern A, with dispersing more GPL fillers near the top and bottom surfaces of the thin-walled porous beam along with symmetric porosity distribution.

The divergence and flutter instabilities of the thin-walled spinning pipes reinforced by single-walled carbon nanotubes in thermal environment are investigated. The material properties of carbon nanotube-reinforced composites are assumed to be uniform distribution as well as two types of functionally graded distribution patterns. The thermal effects are also considered and the material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent. The cantilever pipe conveying fluid is spinning along its longitudinal axis and subjected to an axial force at the free end. Based on the thin-walled Timoshenko beam theory, the governing equations of motion are derived using the extended Hamilton's principle and discretized via the Galerkin method. The resulting thermal-structural-fluid eigenvalue problem is solved and the frequency and the critical fluid velocities are calculated. The effects of carbon nanotubes distributions, volume fraction of carbon nanotubes, compressive axial force, spinning speed, gravity and fluid mass ratio on the critical divergence and flutter velocities of the thin-walled spinning pipe conveying fluid are studied.

In this study, vibration and dynamic stability of fluid-conveying thin-walled rotating pipes reinforced with functionally graded carbon nanotubes are studied. The pipe is modeled based on thin-walled Timoshenko beam theory and reinforced by single-walled carbon nanotubes with uniform distribution as well as three types of functionally graded distribution patterns. The governing equations of motion and the associated boundary conditions are derived via Hamilton’s principle. The governing equations of motion are discretized via the Galerkin method, and the eigenfrequency and the stability region of the pipe are found using the eigenvalue analysis. Some numerical examples are presented to study the effects of length–radius ratio, carbon nanotubes distribution, volume fraction of carbon nanotubes, rotational speed and mass ratio on the non-dimensional eigenfrequency and critical flutter velocity of the thin-walled rotating pipe conveying fluid. The results show that the carbon nanotubes distribution has a significant effect on the non-dimensional eigenfrequency and critical flutter velocity. Also, it is found that the rotational speed has a stabilizing effect on the dynamic behavior of the system.

In this study, the aeroelastic analysis of functionally graded (FG) multilayer graphene platelet reinforced polymer composite (GPLRPC) rotating blades under supersonic flow is investigated. It is considered that the graphene platelet (GPL) nanofillers are distributed in the matrix either uniformly or non-uniformly along the thickness direction. Four GPL distribution patterns namely, U-GPLRPC, Λ-GPLRPC, X-GPLRPC and O-GPLRPC are considered. The effective material properties of GPLRPC layers are obtained via the modified Halpin–Tsai micromechanics model and the rule of mixture. Based on the first-order shear deformation theory, the dynamic equations of thin-walled blades reinforced with GPL are obtained using extended Hamilton's principle. The aerodynamic pressure is assumed in accordance with the quasi-steady supersonic piston theory. The extended Galerkin method (EGM) is employed to transform the coupled equations of motion to a general eigenvalue problem. The influences of rotating speed, GPL distribution, GPL weight fraction, geometry of GPL nanofillers, geometric parameters and Mach number on the natural frequencies of the system are studied. The results indicate that the Λ-GPLRPC distribution pattern predicts the highest natural frequencies for the composite blade. Also, the natural frequencies of the composite blade significantly increase by adding a small amount of GPL to the polymer matrix.

In this paper, an orthotropic elastic shell model is developed for the buckling analysis of protein microtubules subjected to an axial force in living cells. Surface effects are taken into consideration based on the Gurtin–Murdoch elasticity theory. To incorporate the small scale effects, the nonlocal elasticity theory is also used. The influences of the viscoelastic surrounding cytoplasm are taken into account employing standard linear solid model. The governing differential equations are derived using the first-order shear deformation theory and the principle of virtual work. A numerical solution is obtained for the governing equations by employing differential quadrature method. To verify the accuracy of the numerical results, the present results for the axial buckling of microtubules stabilized with microtubule-associated proteins and taxol are compared with those of experimental observations in the literature. It is found that the orthotropic shell model with both surface and nonlocal effects can describe the buckling behavior of microtubules accurately, while the nonlocal shell model without surface effects fails to predict the buckling loads.

A nonlocal strain gradient Timoshenko beam model is developed to study the vibration and instability analysis of the carbon nanotubes conveying nanoflow. The governing equations of motion and boundary conditions are derived by employing Hamilton’s principle, including the effects of moving fluid, material length scale and nonlocal parameters, Knudsen number and gravity force. The material length scale and nonlocal parameters are considered, in order to take into account the size effects. Also, to consider the small-size effects on the flow field, the Knudsen number is used as a discriminant parameter. The Galerkin approach is chosen to analyze the governing equations under clamped–clamped, clamped–hinged and hinged–hinged boundary conditions. It is found that the natural frequency and critical fluid velocity can be decreased by increasing the nonlocal parameter or decreasing the material length scale parameter. Furthermore, it is revealed that the critical flow velocity does not affected by two size-dependent parameters and various boundary conditions in the free molecular flow regime.

This paper develops a micro-scale vibration analysis of micro-plates using higher-order shear and normal deformable plate theory in conjunction with modified couple stress theory. The present model includes one material length scale parameter which takes into account the size effects. The equations of motions and boundary conditions are derived using Hamilton’s principle. Analytical solutions for the free vibration problem of simply supported rectangular micro-plates are obtained. Numerical results are presented to illustrate the effect of small scale on the dynamic response of functionally graded micro-plates. The results show that the size-dependent effect increases the stiffness of the micro-plate and consequently increases the natural frequencies.

In this study, a size-dependent Timoshenko beam model is used for free vibration and instability analysis of a nanotube conveying nanoflow. To capture the size effects, nonlocal strain gradient theory and Knudsen number are applied. The extended Hamilton's principle is employed to obtain the size-dependent governing equations of motion and associated boundary conditions. The Galerkin approach is utilized to convert the partial differential equation into a set of ordinary differential equations. The resulting eigenvalue problem is solved for cantilever Timoshenko nanotubes. Some numerical instances are presented to study the effects of various parameters such as strain gradient length scale, small length scale, length-diameter ratio, nanotube's thickness, Knudsen number and gravity on the eigenfrequencies, critical flutter velocities and instability of the system. The results reveal that the natural frequencies and critical flutter velocities are closer to the ones from Euler-Bernoulli beam model just for long nanotubes and low mode numbers. Furthermore, it is shown that by increasing the length-diameter ratio, the critical flutter velocity increases. Moreover, by increasing the strain gradient length scale and decreasing the small length scale, the critical flutter velocity and stability region increase.

In post-core crown restorations, the significant mismatch between stiffness of artificial crowns and dental tissues leads to stress concentration at the interfaces. The aim of the present study was to reduce the destructive stresses by using a class of inhomogeneous materials called functionally graded materials (FGMs). For the purpose of the study, a 3-dimentional computer model of a premolar tooth and its surrounding tissues were generated. A post-core crown restoration with various crown materials, homogenous and FGM materials, were simulated and analyzed by finite element method. Finite element and statistical analysis showed that, in case of oblique loading, a significant difference (p

In this paper, the aeroelastic analysis of both symmetric and non-symmetric trapezoidal sandwich plates with various boundary conditions in supersonic airflow is studied. The trapezoidal sandwich plate is composed of an orthotropic honeycomb core and two functionally graded (FG) porous face sheets. The fluid structure interaction equations of the sandwich plates under supersonic airflow are derived based on the first-order shear deformation theory (FSDT) and first-order piston theory. Using the Hamilton's principle, the governing equations of motion and the associated boundary conditions are derived in the Cartesian coordinates. Then, applying a transformation of coordinates, the partial differential equations of motion and the associated boundary conditions are converted from Cartesian coordinates into new computational coordinates. The transferred partial differential equations of motion and the associated boundary conditions are discretized by using the generalized differential quadrature (GDQ) method and solved using the state space method. Consequently, the influences of geometry of hexagonal cells in the honeycomb core, porosity, power-law index, geometry of trapezoidal plates, boundary conditions and bending effects of honeycomb core on the critical flutter aerodynamic pressure and stability boundaries of trapezoidal sandwich plates are studied in detail.

Aeroelastic analysis of functionally graded spinning cylindrical shells reinforced with graphene nanoplatelets in supersonic flow is studied. Multilayer functionally graded graphene platelets reinforced composite cylindrical shell based on the first-order shear deformation theory are examined. The supersonic flow is modeled through the use of first order piston theory. The effective Young’s modulus, mass density and Poisson’s ratio of nanocomposites are calculated based on the modified Halpin-Tsai model and rule of mixture. The coupled governing equations of motion and associated boundary conditions are developed by applying extended Hamilton principle. Galerkin technique is utilized to convert the coupled equations of motion to a general eigenvalue problem. In this investigation, four graphene platelets distribution patterns through the thickness of shell, i.e., UD, FG- Λ , FG- X and FG-O are considered. The effects of weight fraction, distribution patterns, number of layers, aspect ratio and spinning velocity on the flutter boundary are expressed. The results point out that the larger surface area related to more distributing graphene platelets near the inner and outer surfaces of the cylindrical shell predicts the most effective reinforcing effect. Furthermore, to improve significantly the stiffness of cylindrical shell, a small amount of extra graphene nanoplatelets as reinforcing nanofillers is an efficient way.

Statement of problem In post-and-core crown restorations, the use of flexible posts concentrates stresses at the dentin and the use of stiff posts concentrates stresses at the interfaces. A class of inhomogeneous materials (called functionally graded materials) has been proposed for posts to resolve the weaknesses of both flexible and rigid posts. Purpose The purpose of this in vitro study was to design an inhomogeneous post and investigate its influence on the stress distribution of post-and-core crown restorations. Material and methods An extracted tooth was mounted, sectioned, and photographed to create a 3-dimensional model of the first premolar tooth. The post-and-core crown restoration was modeled with and without a ferrule. The surrounding tissues of the mandibular tooth, periodontal ligament, and cortical and trabecular bones were modeled. Fiber-reinforced composite (FRC), metallic, and inhomogeneous posts were investigated by finite element analysis and the stress distribution results compared. Results FRC posts resulted in the highest maximum tensile stress (MTS) at the remaining dentin (90.4 to 93.2 MPa), while inhomogeneous posts graded by index n=10 (FGM10) caused the lowest MTS, both with and without a ferrule (72.3 to 74.8 MPa). Conclusions The use of FRC posts concentrated more MTS at the dentin and less MTS at the dentin-adhesive interface than metallic posts. Inhomogeneous posts (FGM10) resolved the weaknesses of both flexible and rigid posts by simultaneously reducing stresses at the dentin and interface. The ferrule effect resulted in fewer dentin and interface stresses.

In this paper, an analytical solution for free vibration of rectangular porous-cellular plates enclosed by piezoelectric layers is presented by using third-order shear deformation plate theory. Using Hamilton’s principle and Maxwell equation, the governing equations of the system are obtained for both closed and open circuit conditions. Due to the coordinate dependency of mechanical properties of porous materials, the governing equations of motion are highly coupled. By using four auxiliary functions, these equations convert into two independent partial differential equations. The decoupled equations are solved analytically by employing Levy-type boundary conditions for the plate. Finally, after validation of the obtained results, the effects of various parameters such as porosity and geometrical dimensions on the natural frequencies of plate are investigated for different electrical and mechanical boundary conditions. It is found that the natural frequencies of the plate decrease as the coefficient of plate porosity increases. Also, the piezoelectric layers cause the natural frequency of the plate to increase in various vibrating modes.

In the present article, the buckling of a fluid-infiltrated porous plate is investigated using Mindlin plate theory and an analytical procedure. A cosine rule for the pore distribution across the plate thickness is assumed with a coefficient defining porosity level. The governing stability equations are rewritten in terms of four auxiliary functions and decoupled with the aid of some mathematical manipulations. The decoupled partial differential equations are solved analytically by assuming simply supported radial edges for the plate. The critical buckling loads are calculated by considering fluid-saturated and fluid free conditions for the interconnected network of pores for different sector angles, thickness–radius ratios, coefficients of plate porosity, aspect ratios, and boundary conditions. It is found that the pore fluid compressibility affects the buckling load significantly.

An exact analytical approach based on Mindlin plate theory is considered for free vibration analysis of fluid-saturated porous annular sector plates. The interconnected network of pores is saturated by inviscid fluid and the fluid is trapped in the network. The plate’s radial edges are considered to be simply supported and four auxiliary functions are used to evaluate the natural frequencies of porous plates under undrained condition. The mechanical properties of the material are considered to vary through the thickness by expressing shear modulus and density in terms of a simple cosine rule in case of plates with pores free of fluid. The present method is validated by comparing it with the results of other accurate solutions found in the literature. The influence of the coefficient of plate porosity, geometrical parameters as well as the effect of fluid on natural frequency response of porous annular sector plates under various boundary conditions are comprehensively investigated. It is found that the presence of fluid in the interconnected network of pores causes the fundamental natural frequency to increase. The method proposed in this paper may provide useful information for the future assessments of the dynamic response of porous structures when fluid–solid interaction effects are fully taken into account.

In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one.

This article reviews conventional nonlocal elasticity constitutive relation which is frequently used for mechanical analyses of nanostructures. It is shown here that since this constitutive relation has been essentially derived based on infinite-body assumption, it cannot consider the nonlocal effects at all points of a nanoscale body accurately. Also, it is shown that although the nonlocal constitutive relations can potentially consider the surface effects, that constitutive relation has been obtained substantially by ignoring those effects. So, it cannot also consider the surface effects accurately. Therefore, the conventional nonlocal constitutive relation generally is not accurate for material-behavior modeling and consequently mechanical analysis of nanostructures. Furthermore, common nonlocal constitutive law is examined in buckling problem of Timoshenko beam-columns to show another limitation of that constitutive law. Finally, some special cases for which that constitutive relation can be used more accurately are proposed.

This paper is concerned with the effect of deformation coupling between solid and fluid on the free vibration characteristics of isotropic rigid porous rectangular plates under undrained condition. Mindlin plate theory is employed to model the moderately thick porous plate. The problem addressed is formulated by using Hamilton's principle, which leads to a set of partial differential equations dealing with frequency response of the plate. The governing equations of motion are solved analytically for Levy-type porous plates by introducing some auxiliary functions. The fluid viscosity is assumed to be very low so that it cannot cause energy dissipation in system. Numerical results are obtained in non-dimensional form. The accuracy of the solution is confirmed by making some comparisons of the obtained frequencies with those available in literature. It is found that the effect of coupled solid-fluid deformation cannot be neglected when the Biot-Willis constants are considerable compared to mechanical properties of solid skeleton of the plate. It is also observed that the plate's effective stiffness increases as fluid is trapped in pore network of the porous medium.

In the present article, higher-order shear and normal deformable plate theory together with modified couple stress theory are developed to study the bending analysis of thick functionally graded rectangular micro-plates. One material length scale parameter is used for capturing the size effects. Utilizing the variational approach and also a principle of virtual displacement, a new form of equilibrium equations and the corresponding boundary conditions are derived. It is assumed that material properties vary through the thickness according to the power law function. Finally, an analytical solution for the bending problem of a simply supported FG rectangular micro-plate is presented.

Carrera Unified Formulation (CUF) is used for free vibration analysis of Levy-type thick rectangular porous–cellular plates. The variation of porosity through the thickness causes mechanical properties to change along the thickness. Properties are modeled by a simple cosine rule. The equations of motion are solved analytically for Levy-type rectangular porous–cellular plates using state space method. The correctness of this approach is confirmed through comparison studies with published results based on highly accurate approaches. Different orders of model are used to enhance the accuracy of the method in order to obtain the exact frequencies of thick and very thick porous–cellular plates. The effects of the coefficient of plate porosity and the thickness–length ratio as well as the aspect ratio, on the frequencies are investigated for Levy-type boundary conditions. It is found that natural frequencies of the porous–cellular thick plates decrease as the coefficient of plate porosity increases in all studied boundary conditions.

In this paper, a nonlinear Timoshenko beam model is considered to analytically investigate post-buckling and nonlinear vibration of flexible fluid-conveying pipes made of functionally graded materials. Closed-form expressions are presented to study the effects of shear deformation and rotary inertia on the post-buckling behavior and nonlinear vibration of fluid-conveying functionally graded pipes for the first time. It is assumed that the material property of the functionally graded material pipe is changed continuously along the direction of the pipe wall thickness based on a simple power law. Considering the Von-Karman nonlinear strain components and using the Hamilton's principle, the nonlinear governing equations for vibration and buckling of the functionally graded pipe conveying fluid are derived. These nonlinear governing equations are discretized by applying the Galerkin's procedure. The homotopy analysis method is employed to determine the closed-form expressions for the nonlinear frequency and the time history of vibration of the functionally graded pipe. The influences of rotary inertia and shear deformation on the buckling behavior, critical fluid velocity, nonlinear frequency and non-dimensional amplitude of the system are investigated and discussed in detail. The effects of physical parameters of the pipe conveying fluid on the divergence fluid velocity are studied by considering polypropylene random and functionally graded polymer pipes. The numerical results attest to the importance of considering rotary inertia and shear deformation in analyzing of short functionally graded material pipes especially for stiffer materials with higher initial amplitudes.

The focus of this article is on analytical solution for stress and deformation of human arteries. The artery is considered as a long homogeneous isotropic cylinder. Hyperelastic, incompressible stress-strain behavior is used by adopting a classical Mooney-Rivlin material model. The elastic constants of the arteries are calculated by using the reported results of biaxial test. The analysis is based on both single and double layer arterial wall models and. Radial and circumferential stress distribution on the minimum and maximum blood pressure is calculated. Variation of radii due to internal pressure within the arteries is found which is in a good accordance with the experimental results. The results containing the changes in diameter and thickness together with the stress distribution for both single and double layer models have been plotted. It is shown that the major difference between the single and double layer models is in their stress distributions. The circumferential stress distribution for different human’s ages is plotted which shows that the stress increases by increasing the age due to decreasing the flexibility of the artery. It is also shown that despite the artery’s inner layer is softer than the outer layer, the maximum stresses occur at the inner layer.

As a first endeavor, the effect of nonlinear elastic foundation on the postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanotubes is investigated. The composite nanotube is affected by a non-uniform thermal environment. A typical MEE composite nanotube consists of microtubules (MTs) and carbon nanotubes (CNTs) with a MEE cylindrical nanoshell for smart control. It is assumed that the nanoscale layers of the system are coupled by a polymer matrix or filament network depending on the application. In addition to thermal loads, magneto-electro-mechanical loads are applied to the composite nanostructure. Length scale effects are taken into account using the nonlocal elasticity theory. The principle of virtual work and von Karman’s relations are used to derive the nonlinear governing differential equations of MEE CNT-MT nanotubes. Using Galerkin’s method, nonlinear critical buckling loads are determined. Various types of non-uniform temperature distribution in the radial direction are considered. Finally, the effects of various parameters such as the nonlinear constant of elastic medium, thermal loading factor and small scale coefficient on the postbuckling of MEE CNT-MT nanotubes are studied.

The eigenvibration characteristics of a smart plate with piezoelectric layers and porous-cellular core are investigated in the present article. The core plate is assumed to be composed of materials that contain pores and the porosities may be distributed according to different mathematical rules. Variational principle is applied in order to derive the continuous system equations on the basis of Mindlin plate theory. A highly efficient analytical modeling for eigenfrequency analysis of the smart plate is presented under the assumption that both Skempton’s pore pressure coefficient and normal elongation through the thickness are negligible. Unlike numerical methods that require huge computational cost, this approach enables us to find the system’s response for rectangular plates with arbitrary dimensions. To examine the validity of the present framework, multiple comparison studies are made between the extracted results and those available in the literature. It is shown that the type of porosity distribution influences strongly on the way that frequency changes. Furthermore, it is found out that it is necessary to consider electrical effects for plates with open circuit condition unlike the other electrical condition.

In this paper, buckling analysis of thick functionally graded piezoelectric rectangular plates is investigated based on the higher-order shear and normal deformable plate theory. Two cases consisting of closed and open–closed circuits are considered as electrical conditions. Using the principle of minimum total potential energy and utilizing the variational approach, nonlinear governing equations for buckling analysis of thick functionally graded rectangular plates are derived. Applying the adjacent equilibrium criterion, the linear form of the governing stability equations is determined. The electric potential function is assumed to be quadratic in terms of the thickness variable. Also, it is supposed that material properties of the functionally graded plates vary through the thickness according to the power law function. Finally, the Maxwell and stability equations are solved analytically for a simply supported thick plate to obtain the critical buckling loads. Consequently, the effects of loading conditions, aspect ratio, thickness and material properties on the critical buckling loads are investigated in detail.

In this paper, conventional nonlocal constitutive equations are examined in the three-dimensional buckling problem of rectangular nanoplates. Those constitutive equations that are frequentl...

In this paper, the free vibration analysis of rectangular plates composed of functionally graded materials with porosities is investigated based on a simple first-order shear deformation plate theory. The network of pores in assumed to be empty or filled by low pressure air and the material properties of the plate varies through the thickness. Using Hamilton's principle and utilizing the variational method, the governing equations of motion of FG plates with porosities are derived. Considering two boundary layer functions, the governing equations of the system are rewritten and decoupled. Finally, two decoupled equations are solved analytically for Levy-type boundary conditions so as to obtain the eigenfrequencies of the plate. The effects of porosity parameter, power law index, thickness-side ratio, aspect ratio, porosity distribution and boundary conditions on natural frequencies of the plate are investigated in detail.

This article studies nonlocal postbuckling behavior of both uniaxially and biaxially loaded graphene sheets (GSs) in a polymer environment based on an orthotropic nano-plate model. The van der Waals interaction force between the graphene sheets and the polymer medium is considered as a nonlinear function of the graphene’s deflection. Considering the small scale effect and using the thin plate theory, postbuckling equilibrium equations are derived with the von Karman-type geometrical nonlinearity. These equations are solved using the Galerkin method for GSs with different boundary conditions. Finally, postbuckling equilibrium path is plotted and the effects of nonlocal parameter, polymer medium, linear and nonlinear coefficients of the vdW interaction, boundary and loading conditions and geometric properties are studied in detail.

The aeroelastic flutter analysis of thick porous plates surrounded with piezoelectric layers in supersonic flow is studied. In order to aeroelastic analysis of the thick porous-cellular plate, Reddy’s third-order shear deformation plate theory and first-order piston theory are used. Furthermore, the plate is composed of two face piezoelectric layers and three functionally graded porous distributions core. Applying the extended Hamilton’s principle and Maxwell’s equation, the governing equations of motion are obtained. The partial differential governing equations are transformed into a set of ordinary differential equations by applying Galerkin’s approach. The effects of porosity coefficient, porosity distributions, piezoelectric layers, geometric dimensions, electrical and mechanical boundary conditions on the flutter aerodynamic pressure and natural frequencies of porous-cellular plates are investigated.