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1
Content available On the nonlocal interaction range for stability of nanobeams with nonlinear distribution of material properties
Jankowski Piotr
Acta Mechanica et Automatica
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2022
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Vol. 16, no. 2
151--161
EN
The present study analyses the range of nonlocal parameters’ interaction on the buckling behaviour of nanobeam. The intelligent nonhomogeneous nanobeam is modelled as a symmetric functionally graded (FG) core with porosity cause nonlinear distribution of material parameters. The orthotropic face-sheets are made of piezoelectric materials. These kinds of structures are widely used in nanoelectromechanical systems (NEMS). The nanostructure model satisfies the assumptions of Reddy third-order beam theory and higher-order nonlocal elasticity and strain gradient theory. This approach allows to predict appropriate mechanical response of the nanobeam regardless of thin or thick structure, in addition to including nano-sized effects as hardening and softening. The analysis provided in the present study focuses on differences in results for nanobeam stability obtained based on classical and nonlocal theories. The study includes the effect of diverse size-dependent parameters, nanobeams’ length-to-thickness ratio and distributions of porosity and material properties through the core thickness as well as external electro-mechanical loading. The results show a dependence of nonlocal interaction range on geometrical and material parameters of nanobeam. The investigation undertaken in the present study provides an interpretation for this phenomenon, and thus aids in increasing awareness of nanoscale structures’ mechanical behaviour.
2
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.
3
Content available Effect of kerr foundation and in-plane forces on free vibration of fgm nanobeams with diverse distribution of porosity
Jankowski Piotr
Acta Mechanica et Automatica
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2020
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Vol. 14, no. 3
135--143
EN
In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natu-ral vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material pa-rameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse dis-tribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.
4
Content available remote Stability of Timoshenko beams with frequency andinitial stress dependent nonlocal parameters
Glabisz W., Jarczewska K., Holubowski R.
Archives of Civil and Mechanical Engineering
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2019
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Vol. 19, no. 4
1116--1126
EN
This paper presents an analysis of the stability of Timoshenko beams which uses Eringen'snonlocal elasticity theory. A numerical algorithm based on the exact solution for the freevibration of segmental Timoshenko beams was formulated. The algorithm enables one tocalculate, with any degree of accuracy, the critical load levels in the beams on the macro andnanoscale. The beams were subjected to conservative and nonconservative static loads. Thelevels of critical loads in the beams were analysed assuming a functional dependence of thenonlocal parameters on the vibrational frequency and the state of stress.
5
Content available Flexoelectric and surface effects on a cracked piezoelectric nanobeam: Analytical resonant frequency response
Bastanfar M, Hosseini S.A.H., Sourki R., Khosravi F.
Archive of Mechanical Engineering
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2019
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Vol. LXVI, nr 4
417--437
EN
A nanoscale beam model containing defect under the piezoelectricity considering the surface effects and flexoelectricity is established on the framework of Euler-Bernoulli theory. The governing equations of motion and related boundary conditions are derived by using Hamilton’s principle. The imperfect nanobeam is modeled by dividing the beam into two separate parts that are connected by a rotational and a longitude spring at the defect location. Analytical results on the free vibration response of the imperfect piezoelectric nanobeam exhibit that the flexoelectricity and the surface effects are sensitive to the boundary conditions, defect position, and geometry of the nanobeam. Numerical results are provided to predict the mechanical behavior of a weakened piezoelectric nanobeam considering the flexoelectric and surface effects. It is also revealed that the voltage, defect severity, and piezoelectric material have a critical role on the resonance frequency. The work is envisaged to underline the influence of surface effects and flexoelectricity on the free vibration of a cracked piezoelectric nanobeam for diverse boundary conditions. It should be mentioned, despite our R. Sourkiprevious works, an important class of piezoelectric materials used nowadays and called piezoelectric ceramics is considered in the current study.
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 Eigenvalue approach to nanobeam in modified couple stress thermoelastic with three-phase-lag model induced by ramp type heating
Kumar R., Devi S.
Journal of Theoretical and Applied Mechanics
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2017
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Vol. 55 nr 3
1067--1079
EN
This article deals with the study of a thermoelastic nanobeam in a modified couple stress theory subjected to ramp-type heating. The mathematical model is prepared for the nanobeam in thermoelastic three-phase-lag. The Laplace transform and the eigenvalue approach are used to find the displacement component, lateral deflection, temperature change and axial stress of the thermoelastic beam. The general algorithm of the inverse Laplace transform is developed to compute results numerically. The comparison of three-phase-lag, dual-phaselag and GN-III (1993) models are represented, and their illustration is depicted graphically. This study finds the applications in engineering, medical science, sensors, etc.
8
Content available A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method
Ebrahimi F., Nasirzadeh P.
Journal of Theoretical and Applied Mechanics
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2015
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Vol. 53 nr 4
1041--1052
EN
This article presents the solution for free vibration of nanobeams based on Eringen nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is considered in the first theory, and the transverse shear deformation effects as well as rotary inertia are taken into account in the latter one. Through variational formulation and the Hamilton principle, the governing differential equations of free vibration of the nonlocal Timoshenko beam and the boundary conditions are derived. The obtained equations are solved by the differential transformation method (DTM) for various frequency modes of the beams with different end conditions. In addition, the effects of slenderness and on vibration behavior are presented. It is revealed that the slenderness affects the vibration characteristics slightly whilst the small scale plays a significant role in the vibration behavior of the nanobeam.
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