• Advances in nano research
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• 제16권3호
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• pp.273-288
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• 2024

The geometrical nonlinear vibrations of the gold nanoscale rod are investigated for the first time by considering the internal modals interactions using different nonlinear beam theories. This phenomenon is usually one of the important features of nonlinear vibration systems. For a more detailed analysis, the von-Karman effects, preserving all the nonlinear terms in the strain-displacement relationships of gold nanoscale rods in three displacement directions, are considered to analyze the nonlinear axial vibrations of gold nanoscale rods. It uses highly accurate analytical-numerical solutions for the clamped-clamped and clamped-free boundary conditions of nanoscale gold rods. Also, with the help of Hamilton's principle, the governing equation and boundary conditions are derived based on Eringen's theory. The influence of nonlinear and nonlocal factors on axial vibrations was investigated separately for all three theories: Simple (ST), Rayleigh (RT) and Bishop (BT). Using different theories, the effects of inertia and shear on the internal resonances of gold nanorods were studied and compared in terms of twoto-one and three-to-one internal resonances. As the nonlocal parameter of the gold nanorod increases, the maximum nonlinear amplitude occurs. So, by adding nonlocal effects in a gold nanorod, the internal modal interactions resulting from the unique structure can be enhanced. It is worth noting that shear and inertial analysis have a significant effect on internal modal interactions in gold nanorods.

• Advances in nano research
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• 제16권2호
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• pp.111-125
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• 2024

Recently, a lot of research has been done on the analysis of axial vibrations of homogeneous and FG nanotubes (nanorods) with various aspects of vibrations that have been fully mentioned in history. However, there is a lack of investigation of the dynamic internal resonances of FG nanotubes (nanorods) between them. This is one of the essential or substantial characteristics of nonlinear vibration systems that have many applications in various fields of engineering (making actuators, sensors, etc.) and medicine (improving the course of diseases such as cancers, etc.). For this reason, in this study, for the first time, the dynamic internal resonances of FG nanorods in the simultaneous presence of large-amplitude size dependent behaviour, inertial and shear effects are investigated for general state in detail. Such theoretical patterns permit as to carry out various numerical experiments, which is the key point in the expansion of advanced nano-devices in different sciences. This research presents an AFG novel nano resonator model based on the axial vibration of the elastic nanorod system in terms of derivation from large-amplitude size dependent internal modals interactions. The Hamilton's Principle is applied to achieve the basic equations in movement and boundary conditions, and a harmonic deferential quadrature method, and a multiple scale solution technique are employed to determine a semi-analytical solution. The interest of the current solution is seen in its specific procedure that useful for deriving general relationships of internal resonances of FG nanorods. The numerical results predicted by the presented formulation are compared with results already published in the literature to indicate the precision and efficiency of the used theory and method. The influences of gradient index, aspect ratio of FG nanorod, mode number, nonlinear effects, and nonlocal effects variations on the mechanical behavior of FG nanorods are examined and discussed in detail. Also, the inertial and shear traces on the formations of internal resonances of FG nanorods are studied, simultaneously. The obtained valid results of this research can be useful and practical as input data of experimental works and construction of devices related to axial vibrations of FG nanorods.