• Advances in nano research
• /
• 제6권4호
• /
• pp.377-397
• /
• 2018

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.

• Advances in nano research
• /
• 제4권3호
• /
• pp.197-228
• /
• 2016

In the present study, thermo-electro-mechanical vibration characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and non-linear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FGP nanobeams as compared to some cases in the literature. In following a parametric study is accompanied to examine the effects of several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams.

• Advances in nano research
• /
• 제14권1호
• /
• pp.67-80
• /
• 2023

Economic investigation is one of the main issues regarding the design and production of small-scale structures. This paper concerns the creation, implementation, and economic aspects of the cross-section profile of small-scale structures regarding the dynamic response of the free and forced vibration behavior of spinning nanoscale beams based on big data analysis. According to the financial analysis, the three practical non-uniform functions of cross-sections are compared to the uniform beam in the same weight and the equal material used. The previous studies reported that the uniform beams are more stable and contain a better frequency response based on the mechanical analysis. Still, concerning the economic investigation, which means the considered structures should have equal length and have the same weight in the aspect of material used, the conclusion can be different from the mechanical aspect. Consequently, in the current paper, the dynamic response along with computer technology as well as the big data analysis of the free and forced vibration of the nanobeam regarding the economic shape of the cross-section is scrutinized.

• Coupled systems mechanics
• /
• 제6권3호
• /
• pp.251-272
• /
• 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.

• Structural Monitoring and Maintenance
• /
• 제6권2호
• /
• pp.147-159
• /
• 2019

In present article, a size-dependent refined thick beam element has been established based upon nonlocal elasticity theory. Next, it is used to explore vibration response of porous metal foam nanobeams on elastic medium. The established beam element introduces ten degrees of freedom. Different porosity distributions called uniform, symmetric and asymmetric will be employed. Herein, introduced thick beam element contains shear deformations without using correction factors. Convergence and verification studies of obtained results from finite element method are also provided. The impacts of nonlocality factor, foundation factors, shear deformation, slenderness ratio, porosity kinds and porosity factor on vibration frequencies of metal foam nano-sized beams have been explored.

• Advances in nano research
• /
• 제12권3호
• /
• pp.281-290
• /
• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Steel and Composite Structures
• /
• 제50권4호
• /
• pp.459-474
• /
• 2024

Classical and first-order nonlocal beam theory are employed in this study to assess the thermal buckling performance of a small-scale conical, cylindrical beam. The beam is constructed from functionally graded (FG) porosity-dependent material and operates under the thermal conditions of the environment. Imperfections within the non-uniform beam vary along both the radius and length direction, with continuous changes in thickness throughout its length. The resulting structure is functionally graded in both radial and axial directions, forming a bi-directional configuration. Utilizing the energy method, governing equations are derived to analyze the thermal stability and buckling characteristics of a nanobeam across different beam theories. Subsequently, the extracted partial differential equations (PDE) are numerically solved using the generalized differential quadratic method (GDQM), providing a comprehensive exploration of the thermal behavior of the system. The detailed discussion of the produced results is based on various applied effective parameters, with a focus on the potential application of nanotubes in enhancing sports bikes performance.

• Steel and Composite Structures
• /
• 제42권6호
• /
• pp.805-826
• /
• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.