No abstract

The rotational dynamics of a disc-shaped permanent magnet rotor levitated over a high temperature superconductor was studied experimentally and theoretically. The interaction between the rotor magnet and the superconductor was modelled by assuming the magnet to be a magnetic dipole and the superconductor a diamagnet. In the magnetomechanical analysis of the superconductor part, the frozen image concept was combined with the diamagnetic image, and the damping in the system was neglected. The interaction potential of the system is the combination of magnetic and gravitational potentials. From the dynamical analysis the equations of motion of the permanent magnet were stated as a function of lateral, vertical, tilt, precision and rotating angles. The vibration behaviour and correlation of the vibration of one direction with that of another were determined with a numerical calculation based on the Runge-Kutta method. The various vibrational frequencies identified were vertical, radial, tilt, precession and rotation. The tests performed for experimental verifications were translational and rotational. The permanent magnet was 'spun up' under vacuum conditions to analyse the dynamics of the free 'spin down' behaviour of the permanent magnet.

No abstract

No abstract

No abstract

This paper deals with different approaches to describing the relationship between the bending moment and curvature of a Euler—Bernoulli beam undergoing a large deformation, from a tutorial point of view. First, the concepts of the mathematical and physical curvature are presented in detail. Then, in the case of a cantilevered beam subjected to a single moment at its free end, the difference between the linear theory and the nonlinear theory based on both the mathematical curvature and the physical curvature is shown. It is emphasized that a careless use of the nonlinear mathematical curvature and moment relationship given in most standard textbooks may lead to erroneous results. Furthermore, a numerical example is given for the reader to make a quantitative assessment.

In this study, some physical properties of a laminated composite beam were estimated by using the inverse vibration problem method. Laminated composite plate was modeled and simulated to obtain vibration responses for different length-to-thickness ratios in ANSYS. A numerical model of the laminated composite beam with unknown parameters was also developed using a two-dimensional finite element model by utilizing the Euler-Bernoulli beam theory. Then, these two models were embedded into the optimization program to form the objective function to be minimized using genetic algorithms. After minimizing the squared difference of the natural frequencies from these two models, the unknown parameters of the laminated composite beam were found. It is observed in this study that the Euler-Bernoulli beam theory suppositions approximated the real results with a rate of %0.026 error as the thickness of the beam got thinner. The estimated values were finally compared with the expected values and a very good correspondence was observed.

No abstract