• International Journal of Aeronautical and Space Sciences
• /
• 제18권2호
• /
• pp.255-269
• /
• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.

• Steel and Composite Structures
• /
• 제22권4호
• /
• pp.889-913
• /
• 2016

Vibration analysis of embedded functionally graded (FG)-carbon nanotubes (CNT)-reinforced piezoelectric cylindrical shell subjected to uniform and non-uniform temperature distributions are presented. The structure is subjected to an applied voltage in thickness direction which operates in control of vibration behavior of system. The CNT reinforcement is either uniformly distributed or functionally graded (FG) along the thickness direction indicated with FGV, FGO and FGX. Effective properties of nano-composite structure are estimated through Mixture low. The surrounding elastic foundation is simulated with spring and shear constants. The material properties of shell and elastic medium constants are assumed temperature-dependent. The motion equations are derived using Hamilton's principle applying first order shear deformation theory (FSDT). Based on differential cubature (DC) method, the frequency of nano-composite structure is obtained for different boundary conditions. A detailed parametric study is conducted to elucidate the influences of external applied voltage, elastic medium type, temperature distribution type, boundary conditions, volume percent and distribution type of CNT are shown on the frequency of system. In addition, the mode shapes of shell for the first and second modes are presented for different boundary conditions. Numerical results indicate that applying negative voltage yields to higher frequency. In addition, FGX distribution of CNT is better than other considered cases.

• Steel and Composite Structures
• /
• 제49권4호
• /
• pp.361-380
• /
• 2023

A size dependent bending behavior of piezoelectrical flexoelectric layered perforated functionally graded (FG) composite nanobeam rested on an elastic foundation is investigated analytically. The composite beam is composed of regularly cutout FG core and two piezoelectric face sheets. The material characteristics is graded through the core thickness by power law function. Regular squared cutout perforation pattern is considered and closed forms of the equivalent stiffness parameters are derived. The modified nonlocal strain gradient elasticity theory is employed to incorporate the microstructure as well as nonlocality effects into governing equations. The Winkler as well as the Pasternak elastic foundation models are employed to simulate the substrate medium. The Hamiltonian approach is adopted to derive the governing equilibrium equation including piezoelectric and flexoelectric effects. Analytical solution methodology is developed to derive closed forms for the size dependent electromechanical as well as mechanical bending profiles. The model is verified by comparing the obtained results with the available corresponding results in the literature. To demonstrate the applicability of the developed procedure, parametric studies are performed to explore influences of gradation index, elastic medium parameters, flexoelectric and piezoelectric parameters, geometrical and peroration parameters, and material parameters on the size dependent bending behavior of piezoelectrically layered PFG nanobeams. Results obtained revealed the significant effects both the flexoelectric and piezoelectric parameters on the bending behavior of the piezoelectric composite nanobeams. These parameters could be controlled to improve the size dependent electromechanical as well as mechanical behaviors. The obtained results and the developed procedure are helpful for design and manufacturing of MEMS and NEMS.

• Smart Structures and Systems
• /
• 제20권6호
• /
• pp.709-728
• /
• 2017

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Steel and Composite Structures
• /
• 제29권3호
• /
• pp.319-332
• /
• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Structural Engineering and Mechanics
• /
• 제34권4호
• /
• pp.449-474
• /
• 2010

A smart hollow cylinder consisting of a host functionally graded elastic core layer and two surface homogeneous piezoelectric layers is presented in this paper. The bonding between the layers can be perfect or imperfect, depending on the parameters taken in the general linear spring-layer interface model. The effect of such weak interfaces on free vibration and steady-state response is then investigated. Piezoelectric layers at inner and outer surfaces are polarized axially or radially and act as a sensor and an actuator respectively. For a simply supported condition, the state equations with non-constant coefficients are obtained directly from the formulations of elasticity/piezoelasticity. An approximate laminated model is then introduced for the sake of solving the state equations conveniently. It is further assumed that the hollow cylinder is embedded in an elastic medium and is simultaneously filled with compressible fluid. The interaction between the structure and its surrounding media is taken into account. Numerical examples are finally given with discussions on the effect of some related parameters.

• Steel and Composite Structures
• /
• 제38권3호
• /
• pp.337-353
• /
• 2021

Micro-electro-mechanical systems (MEMS) are widely employed in sensors, biomedical devices, optic sectors, and micro-accelerometers. New reinforcement materials such as carbon nanotubes as well as graphene platelets provide stiffer structures with controllable mechanical specifications by changing the graphene platelet features. This paper deals with buckling analyses of functionally graded graphene platelets micro plates with two piezoelectric layers subjected to external applied voltage. Governing equations are based on Kirchhoff plate theory assumptions beside the modified couple stress theory to incorporate the micro scale influences. A uniform temperature change and external electric field are regarded along the micro plate thickness. Moreover, an external in-plane mechanical load is uniformly distributed along the micro plate edges. The Hamilton's principle is employed to extract the governing equations. The material properties of each composite layer reinforced with graphene platelets of the considered micro plate are evaluated by the Halpin-Tsai micromechanical model. The governing equations are solved by the Navier's approach for the case of simply-supported boundary condition. The effects of the external applied voltage, the material length scale parameter, the thickness of the piezoelectric layers, the side, the length and the weight fraction of the graphene platelets as well as the graphene platelets distribution pattern on the critical buckling temperature change and on the critical buckling in-plane load are investigated. The outcomes illustrate the reduction of the thermal buckling strength independent of the graphene platelets distribution pattern while meanwhile the mechanical buckling strength is promoted. Furthermore, a negative voltage, -50 Volt, strengthens the micro plate stability against the thermal buckling occurrence about 9% while a positive voltage, 50 Volt, decreases the critical buckling load about 9% independent of the graphene platelet distribution pattern.

• Advances in nano research
• /
• 제4권2호
• /
• pp.65-84
• /
• 2016

This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electro-magnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electro-magnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.

• Steel and Composite Structures
• /
• 제19권3호
• /
• pp.713-733
• /
• 2015

In this paper, viscous fluid induced nonlinear free vibration and instability analysis of a functionally graded carbon nanotube-reinforced composite (CNTRC) cylindrical shell integrated with two uniformly distributed piezoelectric layers on the top and bottom surfaces of the cylindrical shell are presented. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC cylindrical shell are assumed to be graded through the thickness direction and are estimated through the rule of mixture. The elastic foundation is modeled by temperature-dependent orthotropic Pasternak medium. Considering coupling of mechanical and electrical fields, Mindlin shell theory and Hamilton's principle, the motion equations are derived. Nonlinear frequency and critical fluid velocity of sandwich structure are calculated based on differential quadrature method (DQM). The effects of different parameters such as distribution type of SWCNTs, volume fractions of SWCNTs, elastic medium and temperature gradient are discussed on the vibration and instability behavior of the sandwich structure. Results indicate that considering elastic foundation increases frequency and critical fluid velocity of system.

• Structural Engineering and Mechanics
• /
• 제68권2호
• /
• pp.203-213
• /
• 2018

This paper presents a study of geometric nonlinear forced vibration of carbon nano-tubes (CNTs) reinforcement composite plates on nonlinear elastic foundations. The plate is bonded with piezoelectric layers. The von Karman geometric nonlinearity assumptions with classical plate theory are employed to obtain the governing equations. The Galerkin and homotopy perturbation method (HPM) are utilized to investigate the effect of carbon nano-tubes volume fractions, large amplitude vibrations, elastic foundation parameters, piezoelectric applied voltage on frequency ratio and primary resonance. The results indicate that the carbon nano-tube volume fraction, applied voltage and elastic foundation parameters have significant effect on the hardening response of carbon nanotubes reinforced composite (CNTRC) plates.