Real Part Of Frequency Research Articles

On the vibrations of a high-speed rotating multi-hybrid nanocomposite reinforced cantilevered microdisk

In this study, the vibrational characteristics of a rotating multi-hybrid nanocomposite reinforced (MHCR) cantilevered disk (MHCRCD) are presented. The centrifugal and Coriolis effects due to the rotation are considered. The strains and stresses can be determined via the high-order shear deformable theory (HSDT). For access to various mass densities, as well as the Poisson ratio, the rule of the mixture is applied, although a modified Halpin-Tsai theory is used for obtaining the module of elasticity. The boundary conditions and governing equations are obtained using Hamilton’s principle and finally are solved via generalized differential quadrature method (GDQM). Vibration characteristics of the rotating MHCRCD with various boundary conditions are described according to the curves drawn by Matlab software. Also, the simply supported conditions are applied to edges and also, cantilever (clamped–free) boundary conditions are investigated in R = Ri , and R0 , respectively. Apart from the numerical solution, a 3-D finite element model using ABAQUS software was presented using the finite element package to simulate the response of the rotating MHCRCD. The results created from a finite element simulation illustrates a close agreement with the semi-numerical method results. The outcomes show that the fibers' angel, angular velocity speed, and various patterns of carbon nanotube (CNT) have a considerable impact on the amplitude, and vibration behavior of a rotating MHCRCD. As an applicable result in related industries, the rotating speed effect on the real part of frequency is more effective in the higher values of the radius ratio.

The Definition of Linear Frequencies of Bending Vibrations of Magnetoelastic Cylindrical Shell by Exact Space Treatment

The free bending vibrations of magnetoelastic cylindrical shell in axial magnetic field are considered. The solution is carried out by developed for elastic plates by V. Novatsky exact space method which is applied by ourselves to solution of magnetoelasticity equations without any hypothesis. Obtained by means of exact solution dispersion relation between frequency and wave number of vibration of shell is investigated numerically and obtained tables for real part of frequency with respect to wave, number and field are compared with those obtained by averaged treatment based on Kirkhoff hypothesis. The results are quite different which shows that in contrast to the elastic bending vibrations for magnetoelastic plates and shells mentioned hypothesis are not applicable.

Numerical analysis of quasinormal modes in nearly extremal Schwarzschild–de Sitter spacetimes

We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild-de Sitter spacetimes. Our results show that for low-order quasinormal modes, the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is a quite good approximation for the quasinormal frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where $r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which corresponds quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating ${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where $\omega$ denotes the quasinormal frequency. This means that for gravitational perturbations, the real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of frequency seems to go to zero in the limit.

Particle Simulation of Drift-Cyclotron Instability

The drift-cyclotron instability may occur in a collisionless Maxwellian magnetized plasma, driven by the free energy associated with a spatial density gradient normal to the magnetic field. Electrostatic particle simulations are used to study this instability with both species magnetized and treated fully nonlinearly. During the linear stage simulations show exponential growth in time over a few ion cyclotron periods, with the growth rates in fair agreement with a linear nonlocal theory, while the real parts of frequencies are not well resolved in the short growth period. The total electrostatic field energy reaches a peak of a few percent of the initial ion kinetic energy for most runs, with ωpi2/ωci2 and mass ratios ranging from 25 to 200. These simulation saturation levels are somewhat above those predicted by existing nonlinear theories. At the time of saturation, the phase space pictures of electrons and ions show bunching and density profile modification occurs.