• Smart Structures and Systems
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• v.20 no.3
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• pp.351-368
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• 2017

To peruse the free vibration of curved functionally graded piezoelectric (FGP) nanosize beam in thermal environment, nonlocal elasticity theory is applied for modeling the nano scale effect. The governing equations are obtained via the energy method. Analytically Navier solution is employed to solve the governing equations for simply supported boundary conditions. Solving these equations enables us to estimate the natural frequency for curved FGP nanobeam under the effect of a uniform temperature change and external electric voltage. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocality, uniform temperature changes, external electric voltage, gradient index, opening angle and aspect ratio of curved FGP nanobeam on the natural frequency are successfully discussed. The results revealed that the natural frequency of curved FGP nanobeam is significantly influenced by these effects.

• Coupled systems mechanics
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• v.6 no.3
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

• Advances in nano research
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• v.7 no.4
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• pp.249-263
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• 2019

In the current paper, an exact solution method is carried out for analyzing the thermo-mechanical vibration of curved FG nano-beams subjected to uniform thermal environmental conditions, by considering porosity distribution via nonlocal strain gradient beam theory for the first time. Nonlocal strain gradient elasticity theory is adopted to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field is considered. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Material properties of curved porous FG nanobeam are assumed to be temperature-dependent and are supposed to vary through the thickness direction of beam which modeled via modified power-law rule. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG nano-structures. The governing equations and related boundary condition of curved porous FG nanobeam under temperature 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 nanobeam supposed to thermal loading. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, porosity volume fractions, thermal effect, gradient index, opening angle and aspect ratio on the natural frequency of curved FG porous nanobeam are successfully discussed. It is concluded that these parameters play key 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.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.691-729
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• 2018

In this paper the hygro-thermo-mechanical vibration and buckling behavior of embedded FG nano-plates are investigated. The Eringen's and Gurtin-Murdoch theories are applied to study the small scale and surface effects on frequencies and critical buckling loads. The effective material properties are modeled using Mori-Tanaka homogenization scheme. On the base of RPT and HSDPT plate theories, the Hamilton's principle is employed to derive governing equations. Using iterative and GDQ methods the governing equations are solved and the influence of different parameters on natural frequencies and critical buckling loads are studied.

• Advances in nano research
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• v.8 no.2
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• pp.169-182
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• 2020

This study presents the hygro-thermo-electromagnetic mechanical vibration attributes of elastically restrained piezoelectric nanobeam considering effects of beam surface for various elastic non-ideal boundary conditions. The nonlocal Eringen theory besides the surface effects containing surface stress, surface elasticity and surface density are employed to incorporate size-dependent effects in the whole of the model and the corresponding governing equations are derived using Hamilton principle. The natural frequencies are derived with the help of differential transformation method (DTM) as a semi-analytical-numerical method. Some validations are presented between differential transform method results and peer-reviewed literature to show the accuracy and the convergence of this method. Finally, the effects of spring constants, changing nonlocal parameter, imposed electric potential, temperature rise, magnetic potential and moisture concentration are explored. These results can be beneficial to design nanostructures in diverse environments.

• Smart Structures and Systems
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• v.20 no.6
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• pp.709-728
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• 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
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• v.29 no.3
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• pp.319-332
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• 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.

• Advances in materials Research
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• v.6 no.3
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• pp.279-301
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• 2017

Thermo-mechanical vibration characteristics of in homogeneousporous functionally graded (FG) micro/nanobeam subjected to various types of thermal loadings are investigated in the present paper based on modified couple stress theory with consideration of the exact position of neutral axis. The FG micro/nanobeam is modeled via a refined hyperbolic beam theory in which shear deformation effect is verified needless of shear correction factor. A modified power-law distribution which contains porosity volume fraction is used to describe the graded material properties of FG micro/nanobeam. Temperature field has uniform, linear and nonlinear distributions across the thickness. The governing equations and the related boundary conditions are derived by Extended Hamilton's principle and they are solved applying an analytical solution which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the known data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as thermal loadings, porosity volume fraction, power-law exponents, slenderness ratio, scale parameter and various boundary conditions on natural frequencies of porous FG micro/nanobeams in detail.

• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.351-365
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• 2019

In this paper, free vibration of Cooper-Naghdi micro sandwich cylindrical shell with saturated porous core and reinforced carbon nanotube (CNT) piezoelectric composite face sheets is investigated by using first order shear deformation theory (FSDT) and modified couple stress theory (MCST). The sandwich shell is subjected to magneto-thermo-mechanical loadings with temperature dependent material properties. Energy method and Hamilton's principle are used for deriving of the motion equations. The equations are solved by Navier's method. The results are compared with the obtained results by the other literatures. The effects of various parameters such as saturated porous distribution, geometry parameters, volume fraction and temperature change on the natural frequency of the micro-sandwich cylindrical shell are addressed. The obtained results reveal that the natural frequency of the micro sandwich cylindrical shell increases with increasing of the radius to thickness ratio, Skempton coefficient, the porosity of the core, and decreasing of the length to radius ratio and temperature change.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.7
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• pp.7-12
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• 2010

In this paper, chip-on-glass(COG) interconnection with anisotropic conductive film(ACF) using lateral thermosonic bonding technology is considered. In general, thermo-compression bonding which is used in practice for flip-chip bonding suffers from the low productivity due to the long bonding time. It will be shown that the bonding time can be improved by using lateral thermosonic bonding in which lateral ultrasonic vibration together with thermo-compression is utilized. By measuring the internal temperature of ACF, the fast curing of ACF thanks to lateral ultrasonic vibration will be verified. Moreover, to prove the reliability of the lateral thermosonic bonding, observation of pressured mark by conductive particles, shear test, and water absorption test will be conducted.