Dynamics of a Ring-Type Macro Gyroscope Under Electromagnetic External Actuation Forces

This paper investigates the dynamic behaviour of a rotating ring that forms an essential element in ring-based vibratory gyroscopes that utilize oscillatory electromagnetic forces. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electromagnetic force that acts on the ring structure is formulated. In order to predict the dynamic behaviour of a ring system subjected to external excitation and body rotation, discretized equations obtained via Galerkin’s procedure is employed to investigate the time as well as frequency response behavior. Dynamic response in the driving and the sensing directions are examined via time responses, phase diagram, Poincare’ map and bifurcation plots when the input angular motion and the nonlinear electromagnetic force are considered simultaneously. The analysis is envisaged to aid ongoing experimental research as well as for providing design improvements in Ring-based Gyroscopes.

An active electromagnetic stabilization of the Leipholz column

An active electromagnetic stabilization of the Leipholz column We study the application of electromagnetic actuators for the active stabilization of the Leipholz column. The cases of the compressive and tensional load of the column placed in air and in water are considered. The partial differential equation of the column is discretized by Galerkin's procedure, and the stability of the obtained control system is evaluated by the eigenvalues of its linearization. Four different methods of active stabilization are investigated. They incorporate control systems based on feedback proportional to the transverse displacement of the column, its velocity and the current in the electromagnets. Conditions in which these strategies are effective in securing safe operation of the column are discussed in detail.

Nonlinear Vibrations of a Beam With a Tip Mass Attached to a Rotating Hub

A model of a light beam mounted to a rigid hub and forced by an external torque has been analysed in the paper. An additional loading caused by a small mass attached to the end of the beam and the influence of mass moment of inertia of the hub have been also taken into account. The motion of a flexible light beam is a composition of slewing motion and undesired vibrations, which can be crucial if the stiffness of the structure is not high, comparing to the external dynamical load. The nonlinear model of the beam proposed in [2], [3] have been applied to explain behaviour of the system. That model has taken into account bending, tension and a non-linear curvature, which differs the system from the classical approach [4] or the approach presented in [5] for large displacement of a beam model. The influence of the mass moment of inertia of the hub and the tip-mass is investigated in the paper. Differential equation of motion and dynamical boundary conditions are derived by applying the Hamilton’s principle whilst the reduced model have been obtained by virtue of the Galerkin’s procedure.

One-to-One Internal Resonance of Symmetric Crossply Laminated Shallow Shells

This paper presents the response of symmetric crossply laminated shallow shells with an internal resonance ω2≈ω3, where ω2 and ω3 are the linear natural frequencies of the asymmetric vibration modes (2,1) and (1,2), respectively. Galerkin’s procedure is applied to the nonlinear governing equations for the shells based on the von Ka´rma´n-type geometric nonlinear theory and the first-order shear deformation theory, and the shooting method is used to obtain the steady-state response when a driving frequency Ω is near ω2. In order to take into account the influence of quadratic nonlinearities, the displacement functions of the shells are approximated by the eigenfunctions for the linear vibration mode (1,1) in addition to the ones for the modes (2,1) and (1,2). This approximation overcomes the shortcomings in Galerkin’s procedure. In the numerical examples, the effect of the (1,1) mode on the primary resonance of the (2,1) mode is examined in detail, which allows us to conclude that the consideration of the (1,1) mode is indispensable for analyzing nonlinear vibrations of asymmetric vibration modes of shells.

Flow Between Eccentric Rotating Cylinders

In this numerical study of flow between eccentric cylinders, the size of the separation eddy and the position of the points of separation and reattachment are found to be Reynolds number dependent. The separation point moves in the direction of rotation upon increasing the Reynolds number, in contradiction to the first-order inertial perturbation theory of Ballal and Rivlin [1]. The numerical methods employed in this study include Galerkin’s procedure with B-spline test functions.