Effects Of Small Scale Parameter Research Articles

Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model

A mathematical model is proposed to investigate the dynamic response of an inclined single-walled carbon nanotube (SWCNT) subjected to a viscous fluid flow. The tangential interaction of the inside fluid flow with the equivalent continuum structure (ECS) of the SWCNT is taken into account via a slip boundary condition. The dimensionless equations of motion describing longitudinal and lateral vibrations of the fluid-conveying ECS are obtained in the context of nonlocal elasticity theory of Eringen. The unknown displacement fields are expressed in terms of admissible mode shapes associated with the ECS under simply supported conditions with immovable ends. Using Galerkin method, the discrete form of the equations of motion is derived. The time history plots of the normalized longitudinal and transverse displacements as well as the nonlocal axial force and bending moment of the midspan point of the SWCNT are provided for different levels of the fluid flow speed, small-scale parameter, and inclination angle of the SWCNT. The effects of small-scale parameter, inclination angle, speed and density of the fluid flow on the maximum dynamic amplitude factors of longitudinal and transverse displacements as well as those of nonlocal axial force and bending moment of the SWCNT are then studied in some detail.

Magneto-elasto-dynamic analysis of an elastically confined conducting nanowire due to an axial magnetic shock

Vibration of a conducting nanowire embedded in an elastic matrix due to an axial magnetic shock is of concern. Based on Maxwellʼs and Cauchyʼs equations, a model is proposed to study the problem in the context of nonlocal continuum theory. For solving the equations of motion of the nanowire, an analytical approach and a semi-analytical technique are proposed for low and high levels of small-scale parameter, respectively. The effects of small-scale parameter, stiffness of the surrounding matrix, and duration of the applied magnetic shock on the maximum dynamic elastic fields are examined.

Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory

The vibration of elastic thin nanoplates traversed by a moving nanoparticle involving Coulomb friction is investigated using the nonlocal continuum theory of Eringen. The eigen function technique and the Laplace transform method are employed to solve the governing equations of the nanoplate. The explicit expressions of the in-plane and transverse displacements are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight line. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. The effects of small-scale parameters and velocity of the moving nanoparticle on the dynamic response as well as the dynamic amplitude factors (DAFs) of the in-plane and transverse displacements are then explored in some detail. The results indicate that the magnitude of DAF of the transverse displacement of the nanoplate (i.e., DAF w ) increases with the first small-scale effect parameter, irrespective of the values of the second small-scale effect parameter and the velocity of the moving nanoparticle. As the first small-scale effect parameter grows, the maximum values of DAF w as a function of the moving nanoparticle velocity increase and generally occur in the lower levels of the moving nanoparticle velocity.

Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects

A nonlocal Timoshenko beam model is developed to study the nonlinear vibrations of embedded multiwalled carbon nanotubes (MWCNTs) in thermal environments. The Timoshenko beam model, unlike its Bernoulli–Euler beam counterpart, takes the effects of transverse shear deformation and rotary inertia into consideration. These effects become more significant for short-length nanotubes that are normally encountered in applications such as nanoprobes. The nested nanotubes are coupled via the van der Waals (vdW) force that considers interactions between adjacent and non-adjacent nested nanotubes. The set of coupled nonlinear equations are then analytically solved using the harmonic balance approach. The effects of small-scale parameter, nanotube geometries, temperature change and the elastic medium are investigated.

Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixed–fixed and fixed–free boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results reveal that the proposed methodology is a capable one in capturing the free longitudinal dynamic response of tapered nanowires with different boundary conditions. However, the differences of the results of the perturbation technique and those of the exact solution increase with the rate of radii change. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. It is also observed that for higher values of the small scale effect parameter, the variation of the rate of radii change has a more effect on the variation of the natural frequencies and phase velocities, irrespective of the boundary conditions of the tapered nanowire. Additionally, a scrutiny of the presented dispersion curves indicates that for a constant wavenumber, the value of the phase velocity decreases with the small scale effect parameter, particularly for higher wavenumbers.

A meshless approach for free transverse vibration of embedded single-walled nanotubes with arbitrary boundary conditions accounting for nonlocal effect

A single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal Euler–Bernoulli, Timoshenko, and higher order beams. The beams are assumed to be elastically supported and attached to continuous lateral and rotational springs to take into account the effects of the surrounding matrix. The discrete equations of motion associated with free transverse vibration of each model are established in the context of the nonlocal continuum mechanics of Eringen using Hamilton's principle and an efficient meshless method. The effects of slenderness ratio of the nanotube, small scale effect parameter, initial axial force and the stiffness of the surrounding matrix on the natural frequencies of various beam models are investigated for different boundary conditions. The capabilities of the proposed nonlocal beam models in capturing the natural frequencies of the nanotube are also addressed.

Longitudinal and transverse vibration of a single-walled carbon nanotube subjected to a moving nanoparticle accounting for both nonlocal and inertial effects

Single-walled carbon nanotubes (SWCNTs) can be promising delivery nanodevices for a diverse range of applications, however, little is known about their dynamical interactions with moving nanoscale particles. In this paper, dynamic response of a SWCNT subjected to a moving nanoparticle is examined in the framework of the nonlocal continuum theory of Eringen. The inertial effects of the moving nanoparticle and the existing friction between the nanoparticle surface and the inner surface of the SWCNT are incorporated in the formulation of the problem. The equivalent continuum structure associated with the SWCNT is considered and modeled using nonlocal Rayleigh beam theory under simply supported boundary conditions. The governing equations are then established both in the strong and weak forms. The set of linear equations are solved in the time domain using generalized Newmark- β method. The effects of mass weight of the moving nanoparticle, its velocity, and small scale effect parameter on the dynamic amplitude factors of longitudinal and transverse displacements as well as those of axial force and bending moment are studied in some detail. Additionally, the possibility of moving nanoparticle separation from the inner surface of the SWCNT is investigated. The role of influential parameters on the possibility of this phenomenon is also addressed and discussed.