Abstract:
The study deals with dynamic analysis of non-prestressed Rayleigh beam carrying an added mass and traversed by uniform partially distributed moving loads. The governing partial differential equations were analysed to determine the dynamical behaviour of the system under consideration. It is shown that the amplitude deflection decreases as the length of the load (E) increases for a fixed value of the moving load (ML) when a non-prestressed moving force problem WF (x, t) is considered. Also we observed that for the moving mass problem, the amplitude deflection WML (x, t) decreases as the length of the load (E) increases for various time t and a particular value of the moving load.

Abstract:
An analytical-numerical method is presented that can be used to determine the dynamic behavior of pre-stressed Rayleigh been carrying an added mass and traversed by uniform partially distributed moving loads.This study demonstrates the transformation of a familiar governing equation into a new solvable coupled partial differential equations, been solved using Finite Difference Method. Furthermore, the paper show that the response of structures due to moving mass which has often been neglected in the past, must be properly taken into account because it often differs significantly form the moving force model.

Abstract:
This study examines the effects of moving loads on viscously damped axial force Rayleigh beam. The authors especially tried to find the effect of the moving mass and moving force in connection with the length of the span of a Rayleigh beam. The authors also examined the effect of the lengths of the beam and of the load. It was observed that as mass of the moving load increases the deflection along the length of the beam also increases. It was further observed that the deflection of the moving mass is greater than that of the moving force.

Abstract:
The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.

Abstract:
An investigation into the dynamical behaviour of axial force Rayleigh beam traversed by uniform partially distributed moving loads is carried out. The beam is assumed to be Prismatic while the shear deformation, rotatory inertia and damping are taking into consideration. The resulting coupled partial differential equation is solved using finite difference method. Graphs were prepared for the results obtained. It was found that the response amplitude for the moving mass problem is greater than the response amplitude of the moving force problem.

Abstract:
This study is concerned with dynamical behavior of Euler Bernoulli beam traversed by uniform partially distributed moving masses. The governing partial differential equation was systematically analyzed and the analytical numerical solution for classical boundary condition obtained. The deflection of the Euler- Bernoulli beam is calculated under various specified conditions and the results displayed graphically. It is found that moving force solution is not an upper bound for an accurate solution of the moving mass problem.

Abstract:
We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.

Abstract:
We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use a stretching transformation of the time coordinate. We find that to 1st order, one-armed spiral structures, and to 2nd order additionally two-armed spiral features may appear. Furthermore, we identify a dispersion relation determining the instability of the ring. The theoretical results are confirmed in several simulations, using two different numerical methods. These computations prove independently the existence of a secular spiral instability driven by viscosity, which evolves into persisting leading and trailing spiral waves. Our results settle the question whether the spiral structures found in earlier simulations of the spreading ring are numerical artifacts or genuine instabilities.

Abstract:
Transverse oscillations of solar filament and prominence threads have been frequently reported. These oscillations have the common features of being of short period (2-10 min) and being damped after a few periods. Kink magnetohydrodynamic (MHD) wave modes have been proposed as responsible for the observed oscillations, whereas resonant absorption in the Alfven continuum and ion-neutral collisions are the best candidates to be the damping mechanisms. Here, we study both analytically and numerically the time damping of kink MHD waves in a cylindrical, partially ionized filament thread embedded in a coronal environment. The thread model is composed of a straight and thin, homogeneous filament plasma, with a transverse inhomogeneous transitional layer where the plasma physical properties vary continuously from filament to coronal conditions. The magnetic field is homogeneous and parallel to the thread axis. We find that the kink mode is efficiently damped by resonant absorption for typical wavelengths of filament oscillations, the damping times being compatible with the observations. Partial ionization does not affect the process of resonant absorption, and the filament plasma ionization degree is only important for the damping for wavelengths much shorter than those observed. To our knowledge, this is the first time that the phenomenon of resonant absorption is studied in a partially ionized plasma.

Abstract:
We study Rayleigh-Taylor instability (RTI) at the coronal-prominence boundary by means of 2.5D numerical simulations in a single-fluid MHD approach including a generalized Ohm's law. The initial configuration includes a homogeneous magnetic field forming an angle with the direction in which the plasma is perturbed. For each field inclination we compare two simulations, one for the pure MHD case, and one including the ambipolar diffusion in the Ohm's law, otherwise identical. We find that the configuration containing neutral atoms is always unstable. The growth rate of the small-scale modes in the non-linear regime is larger than in the purely MHD case.