Mathematical Modeling of Torsional and Longitudinal Oscillations in a Mine Winding Plant as a Multimass System

The purpose of the study is to determine the dynamic loads in the mechanical system of a mine winding plant. A 6-mass equivalent dynamic design model is constructed by reducing the number of discrete masses in the original 12-mass system by a special method. Spectra of natural oscillation frequencies of the initial and design systems are obtained. Differential equations that describe oscillations in the shaft line and ropes are drafted. Oscillation curves of the moments in the elastic coupling of the design system are obtained using numerical integration of the equations. The dynamic response factors are calculated. It was confirmed that the conversion of a 12-mass system into a 6-mass system almost does not affect the accuracy of determining the dynamic loads in the transmission line of the hoist in a given frequency range. The proposed methodology for constructing a mathematical model can be used not only for mine hoists, but also for other machines with multiple moving masses.

ON REGULAR AND IRREGULAR NONLINEAR VIBRATIONS IN TORSIONAL DISCRETE-CONTINUOUS SYSTEMS

The paper deals with regular and irregular nonlinear vibrations of discrete-continuous systems torsionally deformed. The systems consist of an arbitrary number of shafts connected by rigid bodies. In the systems, a local nonlinearity having a soft type characteristic is introduced. This nonlinearity is described by the polynomial of the third degree. General governing equations using the wave approach are derived for a multimass system. Detailed numerical considerations are presented for a two-mass system and a three-mass system. The possibility of occurrence of irregular vibrations is discussed on the basis of the Poincaré maps and bifurcation diagrams.

The Norms of Multimass States in Relativistic Quantum Field Theory

We examined the problem of the appearance of negative norm states in multimass models. It is shown explicitly how the bound state with the same quantum numbers as the elementary meson, can acquire the positive norm. It is inferred from our argument that the multimass system of dynamical origin can be quantized without the negative norm, contrary to the multimass system of kinematical origin.

Hydrodynamic Mass Matrix for a Multibodied System

A matrix technique is developed herein for generating the hydrodynamic mass matrix associated with a multimass system immersed in a liquid environment. The technique assumes that the liquid environment may be represented by a series of flow-channels and nodes. Flow-channels are introduced in the region between surfaces of neighboring solids, and nodes are used to connect two or more flow channels. It is assumed that the solid bodies undergo unidirectional motion and that potential flow theory is applicable. Equations for fluid flow in a variable area flow-channel are obtained by first developing the governing equations for fluid flow in a channel bounded by two parallel surfaces which may move in translation both perpendicular and parallel to the direction of flow. The continuity equation is then developed for an arbitrary node, and the general matrix equation for computing hydrodynamic mass obtained by applying the developed equations to a particular problem.