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1
Content available Static analysis of thin-walled beams using two-phase local-nonlocal integral model
Günay M. G.
Archives of Mechanics
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2023
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Vol. 75, nr 6
673--695
EN
A mathematical model is developed for static analysis of small-scale thinwalled beams having arbitrary cross sections. Constitutive relations of the thin-walled beams are defined upon the two-phase local-nonlocal mixture model with integral formulation. The developed model includes flexural-torsional coupling and warping effects. Governing equations of the thin-walled beams having nonlocal property are derived by using the principle of minimum potential energy. The displacement based finite element method is used to solve both local and nonlocal part of the model. The effect of the nonlocal parameters on the static behavior of micro-scale thin-walled beams having closed and open cross-sections is examined and discussed for various nonlocal parameters and boundary conditions.
2
Content available Vibrations of the Euler–Bernoulli Beam Under a Moving Force Based on Various Versions of Gradient Nonlocal Elasticity Theory: Application in Nanomechanics
Śniady Paweł, Misiurek Katarzyna, Szyłko-Bigus Olga, Idzikowski Rafał
Studia Geotechnica et Mechanica
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2020
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Vol. 42, nr 4
306--318
EN
Two models of vibrations of the Euler–Bernoulli beam under a moving force, based on two different versions of the nonlocal gradient theory of elasticity, namely, the Eringen model, in which the strain is a function of stress gradient, and the nonlocal model, in which the stress is a function of strains gradient, were studied and compared. A dynamic response of a finite, simply supported beam under a moving force was evaluated. The force is moving along the beam with a constant velocity. Particular solutions in the form of an infinite series and some solutions in a closed form as well as the numerical results were presented.
3
Content available Effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates
Bahrami Arian, Shiri Hamidreza, Khosravi Nima
Journal of Theoretical and Applied Mechanics
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2020
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Vol. 58 nr 1
87--96
EN
This communication presents the effect of thickness on the frequency ratio of nanobeams and nanoplates using Eringen’s nonlocal theory. Although there exist numerous works regarding the effects of thickness and small scale on the frequency ratio of nanobeams and nanoplates, none has captured and reported the true effects. The main intention of this communication is to correct the misunderstanding regarding this issue. It was found that the frequency ratio is indeed dependent on the thickness to length ratio and its variation with respect to thickness to length ratio is highly dependent on the mode number, combination of boundary conditions, plate aspect ratio, and the nonlocal parameter.
4
Content available Inertial elastic instability of rotating nano disks
Güven Uğur
Journal of Theoretical and Applied Mechanics
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2019
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Vol. 57 nr 4
853--858
EN
In this work, the static inertial-elastic instability of rotating nano disks is investigated with the centrifugal force formulation considering the radial displacement. Thus, Brunelle’s previous local solution is generalized by using Eringen’s nonlocal elasticity theory. The variations of critical rotation speeds with the nonlocal scale parameter are illustrated under different boundary conditions. It is seen that the critical rotation speeds decrease as the nonlocal scale parameters increase for all cases. Also, it is remarkable that the presented results are affected significantly from the boundary conditions.
5
Content available Static resonance in rotating nanobars
Güven U.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 3
887—891
EN
In this study, static resonance that occurs in rotating nanobars is addressed. The analysis is based on Eringen’s nonlocal elasticity theory and is performed in Lagrangian coordinates. Explicit solutions are given for both clamped-free and clamped-clamped boundary conditions. The present study shows that the static resonance phenomenon is largely a critical case requiring attention for rotating nanobars with small lengths.
6
Content available Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory
Nazemnezhad R., Hosseini-Hashemi S.
Journal of Theoretical and Applied Mechanics
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2017
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Vol. 55 nr 2
649--658
EN
In this paper, nonlinear free vibration of nanobeams with various end conditions is studied using the nonlocal elasticity within the frame work of Euler-Bernoulli theory with von K´arm´an nonlinearity. The equation of motion is obtained and the exact solution is established using elliptic integrals. Two comparison studies are carried out to demonstrate accuracy and applicability of the elliptic integrals method for nonlocal nonlinear free vibration analysis of nanobeams. It is observed that the phase plane diagrams of nanobeams in the presence of the small scale effect are symmetric ellipses, and consideration the small scale effect decreases the area of the diagram.
7
Content available remote Free vibration analysis of functionally graded rectangular nanoplates considering spatial variation of the nonlocal parameter
Alipour Ghassabi A., Dag S., Cigeroglu E.
Archives of Mechanics
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2017
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Vol. 69, nr 2
105--130
EN
We present a new nonlocal elasticity-based analysis method for free vibrations of functionally graded rectangular nanoplates. The introduced method allows taking into account spatial variation of the nonlocal parameter. Governing partial differential equations and associated boundary conditions are derived by employing the variational approach and applying Hamilton’s principle. Displacement field is expressed in a unified way to be able to produce numerical results pertaining to three different plate theories, namely Kirchhoff, Mindlin, and third-order shear deformation theories. The equations are solved numerically by means of the generalized differentia quadrature method. Numerical results are generated by considering simply-supported and cantilever nanoplates undergoing free vibrations. These findings demonstrate the influences of factors such as dimensionless plate length, plate theory, power-law index, and nonlocal parameter ratio upon vibration behavior.
8
Content available Analysis of free torsional vibration in carbon nanotubes embedded in a viscoelastic medium
Arda M, Aydogdu M.
Advances in Science and Technology. Research Journal
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2015
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Vol. 9, nr 26
28--33
EN
Carbon Nanotubes (CNTs) have a great potential in many areas like electromechanical systems, medical application, pharmaceutical industry etc. The surrounding physical environment of CNT is very important on torsional vibration behavior of CNT. Damp¬ing and elastic effect of medium to the torsional vibration of CNTs are investigated in the present study. Governing equation of motion of nanotube is obtained using Eringen’s Nonlocal Elasticty Theory. The effects of some parameters like nonlocal parameter, stiffness parameter and nanotube length are studied in detail.
9
Content available Buckling analysis of short carbon nanotubes based on a novel Timoshenko beam model
Hosseini-Ara R., Mirdamadi H. R., Khademyzadeh H.
Journal of Theoretical and Applied Mechanics
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2012
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Vol. 50 nr 4
975-986
EN
In this paper, we present a novel method to investigate the buckling behavior of short clamped carbon nanotubes (CNTs) with small-scale effects. Based on the nonlocal Timoshenko beam kinematics, the strain gradient theory and variational methods, the higher-order governing equation and its corresponding boundary conditions are derived, which are often not considered. Then, we solve the governing differential equation and determine exact critical buckling loads using a linear polynomial plus trigonometric functions different from the purely trigonometric series. We also investigate the influences of the scale coefficients, aspect ratio and transverse shear deformation on the buckling of short clamped CNTs. Moreover, we compare the critical strains with the results obtained from the Sanders shell theory and validate them with molecular dynamic simulations which are found to be in good agreement. The results show that unlike the other beam theories, this model can capture correctly the small-scale effects on buckling strains of short CNTs for the shell-type buckling.
PL
W pracy zaprezentowano nową metodę analizy problemu wyboczenia krótkich, obustronne zamurowanych nanorurek węglowych (tzw. CTN – Carbon NanoTubes) z uwzględnieniem zjawisk małoskalowych. Na podstawie nielokalnego sformułowania kinematyki belki Timoszenki opracowano teorię gradientu odkształcenia oraz metodę analizy wariacyjnej, wyprowadzono równania konstytutywne wyższego rzędu i odpowiadające im warunki brzegowe, do tej pory z rzadka stosowane w tego typu zagadnieniach. Następnie rozwiązano równania modelu, z których wyznaczono dokładną wartość krytycznego obciążenia prowadzącego do wyboczenia. Użyto w tym celu kombinacji funkcji wielomianowych i trygonometrycznych zamiast szeregów wyłącznie trygonometrycznych. Zbadano również wpływ współczynników skali, proporcji oraz odkształcenia postaciowego na wyboczenie utwierdzonych nanorurek CNT. W trakcie symulacji numerycznych dynamiki molekularnej modelu wykazano dobrą zbieżność otrzymanych wyników z powłokowym modelem Sandersa. Potwierdzono, że – w odróżnieniu od innych teorii belek – zastosowany model dokładnie odzwierciedla efekty małoskalowe przy opisie powłokowego wyboczenia krótkich nanorurek CNT.
10
Content available remote Thermal vibration analysis of carbon nanotubes embedded in two-parameter elastic foundation based on nonlocal Timoshenko's beam theory
Amirian B., Hosseini-Ara R., Moosavi H.
Archives of Mechanics
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2012
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Vol. 64, nr 6
581-581
EN
This paper presents a new model to consider the thermal effects, Pasternak’s shear foundation, transverse shear deformation and rotary inertia on vibration analysis of a single-walled carbon nanotube. Nonlocal elasticity theory is implemented to investigate the small-size effect on thermal vibration response of an embedded carbon nanotube. Based on Hamilton’s principle, the governing equations are derived and then solved analytically, in order to determine the nonlocal natural frequencies. Results show that unlike the Pasternak foundation, the influence of Winkler’s constant on nonlocal frequency is negligible for low temperature changes. Moreover, the nonlocal frequencies are always smaller as compared to their local counterparts. In addition, in high shear modulus along with an increase in aspect ratio, the nonlocal frequency decreases.
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