چكيده به لاتين
Nanobeams are one of the most important nanostructures used in nano-devices such as oscillators and sensor devices. The behavior of viscoelastic nanotubes, have attracted a great deal of attentions in scientific community. One of the most important fields in dynamic researches is evaluating the behavior of nanotubes under a moving load, nanoparticle or nano-cars.
Nowdays numerical and analytic methods have been proposed to investigate the dynamic behavior of nanotubes under the influence of nanoparticles. But until now, the dynamic behavior of viscoelastic nanotubes under the influence of nano-particle with constant and harmonic force in the presence of a magnetic field has not been studied.
On the basis of nonlocal viscoelasticity theory, the current paper deals with the forced vibration analysis of simply supported viscoelastic carbon nanotube under moving nano-particle in the presence of the longitudinal magnetic field. For the modeling of carbon nanotubes, we cannot use the classical continuum theory. Eringen's non-local theory is a good theory to add the small scale effects in nanoscale beams. Due to Kelvin-Voigt and Maxwell model does not describe the actual behavior of a viscoelastic object, nanotube is modeled by the three parameters standard viscoelastic model. On the basis of the Boltzmann superposition principle, the integral constitutive equation for linear visco-elastic Euler-Bernoulli beam is written and then nonlocal viscoelastic Euler-Bernoulli beam theory and Newton's second law by considering Lorentz magnetic force which has been formulated via Maxwell relations, are employed to achieve the equation of motion. Galerkin method has been used to discretize the equation of motion and Laplace transform method has been utilized to solve equation of motion in the time domain. Numerical studies are carried out to illustrate the influences of nonlocal parameter, relaxation time, aspect ratio, magnetic field, nano-particle velocity and the excitation frequency on the maximum non-dimensional dynamic deflection and time history of the midspan displacements.
The simulation results show that increase in the magnitude of longitudinal magnetic field leads to a decrease in the non-dimensional dynamic deflections because of carbon nano tube becomes stiffer. It is discerned that except for the resonance case, the non-dimensional dynamic displacements generally improve until a certain value of the velocity parameter, and after this value, increase in the velocity parameter leads to a decrease in the non-dimensional dynamic deflections. It also should be noted that the non-dimensional dynamic deflection decreases with increase in the values of relaxation time.
