Abstract. This article attempts to analyze the Hopf bifurcati on behavior of a railway wheelset i... more Abstract. This article attempts to analyze the Hopf bifurcati on behavior of a railway wheelset in the presence of dead-zone and yaw damper nonline arities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov -Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideration. To solve these nonlinear equations analytically, the integration interval has been divided into three sub-domains. Two-dimens ional bifurcation diagrams are provided to illustrate the mechanism of formation of Hopf bifur cation. These diagrams can be used for design of stable wheelset systems.
This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirect... more This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirectional fiber-reinforced laminated composite on stress distribution around the pin-loaded hole under tensile loading. The Laplace transform is used to prevent the integral form of matrix governing stress-strain relation. Applying a micromechanical model, all equilibrium equations for the fibers are written analytically in the Laplace domain. The numerical algorithm of Gaver–Stehfest is implemented, and the governing equations were solved at any given time to extract the concerned results in the time domain. The obtained results are validated against the Finite Element Method results obtained through ANSYS software. Moreover, a comparison of the results of this study at the time equal zero with elastic solutions of other references showed a good agreement. The results revealed that in the long term, the maximum tensile load in the intact fiber around the pinhole was enlarged and the tensile...
In this paper, two models of elastic metamaterial containing one and two resonators are proposed ... more In this paper, two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. The model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. In the first mechanism, the pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. By obtaining the governing equations of motion for a single cell in each model, the dynamic behavior of two metastructures is thoroughly investigated. Therefore, the equations of motion for the two mode...
On the basis of a theoretical study, this research incorporates an eccentricity into a system of ... more On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.
The conventional modified couple stress theory cannot model the correct behavior of the longitudi... more The conventional modified couple stress theory cannot model the correct behavior of the longitudinal dispersion and acts the same as the classical theory in the face of such problems. In this paper, the micro-inertia-based couple stress theory is used to triumph over this deficiency. The developed theory is imposed to tackle the longitudinal dispersion of aluminum beams in two distinct scales. Convenient available experimental data obtained for a macro-scale aluminum rod and aluminum crystals are utilized to determine the corresponding micro-inertia length scale parameters and show the scale-dependent nature of this parameter for the first time. In addition, a higher order micro-rotation relation is employed to describe the higher order micro-inertia effects. This relation leads to a developed equation of motion containing an additional term compared with the first-order relation. The obtained results indicate that only higher order micro-inertia effect that is proposed in this stud...
Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative bui... more Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with the nonlocal vibrational behavior of carbon/boron-nitride nano-hetero-tubes in the presence of magneto-thermal environment. Euler–Bernoulli beam model in conjunction with the Eringen’s nonlocal theory of elasticity is adopted to derive the governing equation of motion. In order to conduct a nonlinear frequency analysis, the von-Kármán nonlinearity associated with moderate rotations is also considered. It is well known that temperature gradients can significantly change the dynamic behavior of nanotubes. On the other hand, the coefficients of thermal expansio...
Fangzhu, which has been lost for thousands of years, is an ancient device for water collection fr... more Fangzhu, which has been lost for thousands of years, is an ancient device for water collection from air, its mechanism is unknown yet. Here we elucidate its possible surface-geometric and related physical properties by the oldest the Yin-Yang contradiction. In view of modern nanotechnology, we reveal that Fangzhu’s water-harvesting ability is obtained through a hydrophilic-hydrophobic hierarchy of the surface, mimicking spider web’s water collection, lotus or desert beetle’s water intake. The convex-concave hierarchy of Fangzhu’s textured surface enables it to have low wettability(high geometric potential) to attract water molecules from air through the nano-scale convex surface and transfer the attracted water along the concave surface to the collector. A mathematical model is established to reveal three main factors affecting its effectiveness, i.e., the air velocity, the surface temperature and surface structure. The lost technology can play an extremely important role in modern architecture, ocean engineering, transportation and others to catch water from air for everyday use.
Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir ... more Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the
When the size of structures approaches to the sub-micron scale, physical responses of such system... more When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.
Journal of Applied Mechanics and Technical Physics
This paper exhibits the effect of the amplitude of vibrations on the pull-in instability and nonl... more This paper exhibits the effect of the amplitude of vibrations on the pull-in instability and nonlinear natural frequency of a double-sided actuated microswitch by using a nonlinear frequency–amplitude relationship. The nonlinear governing equation of the microswitch pre-deformed by an electric field includes even and odd nonlinearities with a quintic nonlinear term. The study is performed by a new analytical method called the Hamiltonian approach (HA). It is demonstrated that the first term in series expansions is sufficient to produce an acceptable solution. Results obtained by numerical methods validate the soundness of the asymptotic procedure.
Abstract. This article attempts to analyze the Hopf bifurcati on behavior of a railway wheelset i... more Abstract. This article attempts to analyze the Hopf bifurcati on behavior of a railway wheelset in the presence of dead-zone and yaw damper nonline arities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov -Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideration. To solve these nonlinear equations analytically, the integration interval has been divided into three sub-domains. Two-dimens ional bifurcation diagrams are provided to illustrate the mechanism of formation of Hopf bifur cation. These diagrams can be used for design of stable wheelset systems.
This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirect... more This paper aims to investigate the effect of viscoelastic behavior of polymer matrix of unidirectional fiber-reinforced laminated composite on stress distribution around the pin-loaded hole under tensile loading. The Laplace transform is used to prevent the integral form of matrix governing stress-strain relation. Applying a micromechanical model, all equilibrium equations for the fibers are written analytically in the Laplace domain. The numerical algorithm of Gaver–Stehfest is implemented, and the governing equations were solved at any given time to extract the concerned results in the time domain. The obtained results are validated against the Finite Element Method results obtained through ANSYS software. Moreover, a comparison of the results of this study at the time equal zero with elastic solutions of other references showed a good agreement. The results revealed that in the long term, the maximum tensile load in the intact fiber around the pinhole was enlarged and the tensile...
In this paper, two models of elastic metamaterial containing one and two resonators are proposed ... more In this paper, two models of elastic metamaterial containing one and two resonators are proposed to obtain the bandgaps with the aim of providing broadband vibration suppression. The model with one DOF is built by assembling several unite cells in which each unite cell consists of a rectangular frame as the base structure and a rack-and-pinion mechanism that is joined to the frame with a linear spring on both sides. In the second model with two DOF, a small mass is added while its center is attached to the center of the pinion on one side and the other side is connected to the rectangular frame via a linear spring. In the first mechanism, the pinion is considered as the single resonator, and in the 2DOF model, on the other hand, the pinion and small mass acted as multiple resonators. By obtaining the governing equations of motion for a single cell in each model, the dynamic behavior of two metastructures is thoroughly investigated. Therefore, the equations of motion for the two mode...
On the basis of a theoretical study, this research incorporates an eccentricity into a system of ... more On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.
The conventional modified couple stress theory cannot model the correct behavior of the longitudi... more The conventional modified couple stress theory cannot model the correct behavior of the longitudinal dispersion and acts the same as the classical theory in the face of such problems. In this paper, the micro-inertia-based couple stress theory is used to triumph over this deficiency. The developed theory is imposed to tackle the longitudinal dispersion of aluminum beams in two distinct scales. Convenient available experimental data obtained for a macro-scale aluminum rod and aluminum crystals are utilized to determine the corresponding micro-inertia length scale parameters and show the scale-dependent nature of this parameter for the first time. In addition, a higher order micro-rotation relation is employed to describe the higher order micro-inertia effects. This relation leads to a developed equation of motion containing an additional term compared with the first-order relation. The obtained results indicate that only higher order micro-inertia effect that is proposed in this stud...
Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative bui... more Hybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with the nonlocal vibrational behavior of carbon/boron-nitride nano-hetero-tubes in the presence of magneto-thermal environment. Euler–Bernoulli beam model in conjunction with the Eringen’s nonlocal theory of elasticity is adopted to derive the governing equation of motion. In order to conduct a nonlinear frequency analysis, the von-Kármán nonlinearity associated with moderate rotations is also considered. It is well known that temperature gradients can significantly change the dynamic behavior of nanotubes. On the other hand, the coefficients of thermal expansio...
Fangzhu, which has been lost for thousands of years, is an ancient device for water collection fr... more Fangzhu, which has been lost for thousands of years, is an ancient device for water collection from air, its mechanism is unknown yet. Here we elucidate its possible surface-geometric and related physical properties by the oldest the Yin-Yang contradiction. In view of modern nanotechnology, we reveal that Fangzhu’s water-harvesting ability is obtained through a hydrophilic-hydrophobic hierarchy of the surface, mimicking spider web’s water collection, lotus or desert beetle’s water intake. The convex-concave hierarchy of Fangzhu’s textured surface enables it to have low wettability(high geometric potential) to attract water molecules from air through the nano-scale convex surface and transfer the attracted water along the concave surface to the collector. A mathematical model is established to reveal three main factors affecting its effectiveness, i.e., the air velocity, the surface temperature and surface structure. The lost technology can play an extremely important role in modern architecture, ocean engineering, transportation and others to catch water from air for everyday use.
Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir ... more Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the
When the size of structures approaches to the sub-micron scale, physical responses of such system... more When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.
Journal of Applied Mechanics and Technical Physics
This paper exhibits the effect of the amplitude of vibrations on the pull-in instability and nonl... more This paper exhibits the effect of the amplitude of vibrations on the pull-in instability and nonlinear natural frequency of a double-sided actuated microswitch by using a nonlinear frequency–amplitude relationship. The nonlinear governing equation of the microswitch pre-deformed by an electric field includes even and odd nonlinearities with a quintic nonlinear term. The study is performed by a new analytical method called the Hamiltonian approach (HA). It is demonstrated that the first term in series expansions is sufficient to produce an acceptable solution. Results obtained by numerical methods validate the soundness of the asymptotic procedure.
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