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Nanocomposites and magnetic field effects on nanostructures have received great attention in recent years. A large amount of research work was focused on developing the proper theoretical framework for describing many physical effects appearing in structures on nanoscale level. Great step in this direction was successful application of nonlocal continuum field theory of Eringen. In the present paper, the free transverse vibration analysis is carried out for the system composed of multiple single walled carbon nanotubes (MSWCNT) embedded in a polymer matrix and under the influence of an axial magnetic field. Equivalent nonlocal model of MSWCNT is adopted as viscoelastically coupled multi-nanobeam system (MNBS) under the influence of longitudinal magnetic field. Governing equations of motion are derived using the Newton second low and nonlocal Rayleigh beam theory, which take into account small-scale effects, the effect of nanobeam angular acceleration, internal damping and Maxwell relation. Explicit expressions for complex natural frequency are derived based on the method of separation of variables and trigonometric method for the "Clamped-Chain" system. In addition, an analytical method is proposed in order to obtain asymptotic damped natural frequency and the critical damping ratio, which are independent of boundary conditions and a number of nanobeams in MNBS. The validity of obtained results is confirmed by comparing the results obtained for complex frequencies via trigonometric method with the results obtained by using numerical methods. The influence of the longitudinal magnetic field on the free vibration response of viscoelastically coupled MNBS is discussed in detail. In addition, numerical results are presented to point out the effects of the nonlocal parameter, internal damping, and parameters of viscoelastic medium on complex natural frequencies of the system. The results demonstrate the efficiency of the suggested methodology to find the closed form solutions for the free vibration response of multiple nanostructure systems under the influence of magnetic field. [ABSTRACT FROM AUTHOR]

In this communication, we propose a nonlocal fractional viscoelastic model of a nanobeam resting on the fractional viscoelastic foundation and under the influence of the longitudinal magnetic field and arbitrary number of attached nanoparticles. Size effects are taken into account using the differential form of the nonlocal constitutive relation together with the fractional Kelvin-Voigt model. The governing equation for the free vibration of a nanobeam is derived, where Maxwell’s equations are used in order to represent the effect of the longitudinal magnetic field. We propose an analytical solution of the problem based on the Laplace transform, Mellin-Fourier transforms, and residue theory. From the validation study, it is shown that the obtained complex roots of the characteristic equation, where the imaginary part is the damped frequency and the real part is the damping ratio, are approximated eigenvalues of the system. In the parametric study, several numerical examples are given to investigate the influence of different parameters on complex roots as well as different masses and numbers of nanoparticles on the damped vibration behavior of a nanobeam system. [ABSTRACT FROM AUTHOR]

The recent development in nanotechnology resulted in growing of various nanoplate like structures. High attention was devoted to graphene sheet nanostructure, which enforced the scientist to start developing various theoretical models to investigate its physical properties. Magnetic field effects on nanoplates, especially graphene sheets, have also attracted a considerable attention of the scientific community. Here, by using the nonlocal theory, we examine the influence of in-plane magnetic field on the viscoelastic orthotropic multi-nanoplate system (VOMNPS) embedded in a viscoelastic medium. We derive the system of m partial differential equations describing the free transverse vibration of VOMNPS under the uniaxial in-plane magnetic field using the Eringen's nonlocal elasticity and Kirchhoff's plate theory considering the viscoelastic and orthotropic material properties of nanoplates. Closed form solutions for complex natural frequencies are derived by applying the Navier's and trigonometric method for the case of simply supported nanoplates. The results obtained with analytical method are validated with the results obtained by using the numerical method. In addition, numerical examples are given to show the effects of nonlocal parameter, internal damping, damping and stiffness of viscoelastic medium, rotary inertia and uniaxial in-plane magnetic force on the real and the imaginary parts of complex natural frequencies of VOMNPS. This study can be useful as a starting point for the research and design of nanoelectromechanical devices based on graphene sheets. [ABSTRACT FROM AUTHOR]

Nano-materials such as graphene sheets have a great opportunity to be applied in development of a new generation of nanomechanical sensors and devices due to their unique physical properties. Based on the nonlocal continuum theory and vibration analysis, the single-layered graphene sheet with attached nanoparticles affected by in-plane magnetic field is proposed as a new type of the mass-nanosensor. The nonlocal Kirchhoff-Love plate theory is adopted to describe mechanical behavior of single-layered graphene sheet as an orthotropic nanoplate. The equation of motion of a simply supported orthotropic nanoplate is derived, where the influence of Lorentz magnetic force is introduced through classical Maxwell׳s equations. Complex natural frequencies, damped frequency shifts and relative shift of damping ratio for nanoplate with attached nanoparticles are obtained in the explicit form. The influences of the nonlocal and magnetic field parameter, different mass weights and positions of attached nanoparticles and damping coefficients on the relative damped frequency shift and relative shift of damping ratio are examined. The presented results can be useful in the analysis and design of nanosensors applied in the presence of strong magnetic field. Our results show that magnetic field could be successfully used to improve sensibility performances of nanomechanical sensors. [ABSTRACT FROM AUTHOR]