• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.207-223
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• 2019

Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• Steel and Composite Structures
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• v.38 no.3
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• pp.257-270
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• 2021

This paper presents a displacement-based numerical methodology following the Euler-Bernoulli theory to simulate the 2 nonlinear behavior of steel structures. It is worth emphasizing the adoption of co-rotational finite element formulations considering large displacements and rotations and an inelastic material behavior. The numerical procedures proposed considers plasticity concentrated at the finite elements nodes, and the simulation of the steel nonlinear behavior is approached via the Strain Compatibility Method (SCM), where the material constitutive relation is used explicitly. The SCM is also applied in determining the sections bearing capacity. Moreover, the present numerical approach is not limited to a specific structural member cross-sectional typology, with the residual stress models introduced explicitly in subareas of steel cross-sections generated by a 2D discretization. Finally, results consistent with the literature and with low processing time are presented.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.747-756
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• 2022

This study presents the nonlinear free and forced vibrations of a cracked atomic force microscopy (AFM) cantilever by using the modified couple stress. The cracked section of the AFM cantilever is considered and modeled as rotational spring. In the frame work of Euler-Bernoulli beam theory, Von-Karman type of geometric nonlinear equation and the modified couple stress theory, the nonlinear equation of motion for the cracked AFM is derived by Hamilton's principle and then discretized by using the Galerkin's method. The semi-inverse method is utilized for analysis nonlinear free oscillation of the system. Then the method of multiple scale is employed to investigate primary resonance of the system. Some numerical examples are presented to illustrate the effects of some parameters such as depth of the crack, length scale parameter, Tip-Mass, the magnitude and the location of the external excitation force on the nonlinear free and forced vibration behavior of the system.

• Steel and Composite Structures
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• v.43 no.2
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• pp.185-200
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• 2022

A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.

• Geomechanics and Engineering
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• v.32 no.5
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• pp.541-551
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• 2023

Snap-buckling is one of the main failure modes of structures, because it will lead to the reduction of structural bearing capacity, durability loss and even structural damage. Boundary condition plays an important role in the research of engineering mechanics. Further discussion on the boundary conditions problems will help to analyze the dynamic and static behavior of structures more accurately. Therefore, in order to understand the dynamic and static behavior of curved beams more comprehensively, this paper mainly studies the nonlinear snap-through buckling and forced vibration characteristics of functionally graded graphene reinforced composites (FG-GPLRCs) curved beams with two different boundary conditions (including clamped-hinged and hinged-hinged) using Euler-Bernoulli beam theory (E-BBT). In addition, the effects of the curved beam radius, the GLPs distributions, number of GLPs layers, the mass fraction of GLPs and elastic foundation parameters on the nonlinear snap-through buckling and forced vibration behavior are discussed respectively.

• Advances in nano research
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• v.14 no.3
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• pp.285-294
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• 2023

The dynamic and sensing performances of nanomechanical resonators with their different boundary conditions are studied based on surface elasticity-based modeling and simulation. Specifically, the effect of surface stress is included in Euler-Bernoulli beam model for different boundary conditions. It is shown that the surface effect on the intrinsic elastic property of nanowire is independent of boundary conditions, while these boundary conditions affect the frequency behavior of nanowire resonator. The detection sensitivity of nanowire resonator is remarkably found to depend on the boundary conditions such that double-clamping boundary condition results in the higher mass sensitivity of the resonator in comparison with simple-support or cantilever boundary condition. Furthermore, we show that the frequency shift of nanowire resonator due to mass adsorption is determined by its length, whereas the frequency shift is almost independent of its thickness. This study enables a design principle providing an insight into how the dynamic and sensing performances of nanomechanical resonator is determined and tuned.

• Steel and Composite Structures
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• v.46 no.5
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• pp.637-647
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• 2023

Nonlinear free vibration and stability responses of a carbon nanotube reinforced composite beam under temperature rising are investigated in this paper. The material of the beam is considered as a polymeric matrix by reinforced the single-walled carbon nanotubes according to different distributions with temperature-dependent physical properties. With using the Hamilton's principle, the governing nonlinear partial differential equation is derived based on the Euler-Bernoulli beam theory. In the nonlinear kinematic assumption, the Von Kármán nonlinearity is used. The Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The critical buckling temperatures, the nonlinear natural frequencies and the nonlinear free response of the system is obtained. The effect of different patterns of reinforcement on the critical buckling temperature, nonlinear natural frequency, nonlinear free response and phase plane trajectory of the carbon nanotube reinforced composite beam investigated with temperature-dependent physical property.

• Coupled systems mechanics
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• v.12 no.1
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• pp.21-40
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• 2023

In thisstudy, the vibration problem ofthermo elastic carbon nanotubes conveying pulsating viscous nano fluid subjected to a longitudinal magnetic field is investigated via Euler-Bernoulli beam model. The controlling partial differential equation of motion is arrived by adopting Eringen's non local theory. The instability domain and pulsation frequency of the CNT is obtained through the Galerkin's method. The numerical evaluation of thisstudy is devised by Haar wavelet method (HWM). Then, the proposed model is validated by analyzing the critical buckling load computed in presentstudy with the literature. Finally, the numerical calculation ofsystem parameters are shown as dispersion graphs and tables over non local parameter, magnetic flux, temperature difference, Knudsen number and viscous parameter.

• Advances in materials Research
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• v.11 no.4
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• pp.279-298
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• 2022

In this paper, the important novelty and the defining a physical phenomenon of the resent research is the development of nonlocal stress and strain parameters on the porous sandwich beam with functionally graded materials in the top and bottom face sheets.Also, various beam models including Euler-Bernoulli, Reddy and the generalized formulation of two-variable beam theories are obtained in this research. According to a nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Thus, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It can be seen that the critical buckling load and transverse deflection of sandwich beam by considering both nonlocal stress-strain parameters is higher than the nonlocal stress parameter. On the other hands, it is noted that by considering the nonlocal stress-strain parameters simultaneously becomes the actual case.