چكيده به لاتين
The main aim of the current thesis has been the investigation of the viscoelasticity on the application of graphene sheets as nanoscale mas sensors.
Reviewing the previous researchs related to the energy dissipation at the nanosclaes reveals that the Kelvin-Voigt model has been used to represent the size-dependent viscoelastic behavior of nanoplates. The main reason for doing that has been due to the lack of comprehensive mathematical formulations (or constitutive equations) by which one can use any desired viscoelastic model in the modeling of viscoelastic behavior of a structure (micro/nano). Using some assumptions, definitions and also the superposition principle, an interrelation between the integral and differential forms of viscoelasticity has been obtained. A new mathematical framework was derived and termed as the generalized Hooke’s law for viscoelastic materials (GHLVMs).
Using GHLVMs, in this thesis, the viscoelastic Zener models have been employed to represent the internal damping of nanoscale mass sensors. Doing so, three distinct nanoscale mass sensors have been considered. In first one, GHLVMs has been combined with the nonlocal elasticity theory of Eringen and by employing the Kirchhoff hypotheses, the governing equation of motion of the sensor has been obtained (Zener-Kirchhoff nanoplates). In the second one, a system consists of two coupled Zener-Kirchhoff nanoplates have been used as a nanoscale mass sensor and the third one use has been made of two coupled Zener-Mindlin nanoplates. In the last one, the GHLVMs has been combined with the nonlocal strain gradient elasticity theory to obtain the equations of motion of a nanoscale mass sensor.
In this thesis, using the Lennerd-Jones potentional model, a dynamical system consisting of a nanoplate and a nanoparticle has been derived. In other words, a theoretical model has been derived to account for the van der Waals interactions between a nanoparticle and a nanoplate. To do so, the nanoparticle and the nanoplate have been modeled, respectively, as a concentrated mass and a continuous media. Finally, a model has been derived in which the van der Waals interactions have been incorporated into the equation of motion of the sensor via a spring. A closed-form relation has been derived for the spring constant of the van der Waals interactions.
A comparison study between the Zener and Kelvin models reveals that the Kelvin model is not a suitable model for representing the viscoelastic behavior. It is worth mentioning that the viscoelatic characteristics of graphene have not been extracted yet. Accordingly, in this thesis, two sets of physical constants have been used in the theoretical calculations. It has been shown that the Kelvin model is not capable of being interpolated if the viscoelastic characteristics of graphene are available. On the other hand, in theoretical points of view, the mathematical formulations presented in this thesis are capable of being used to represent the viscoelastic behavior of graphene by a suitable viscoelastic model.
