System Views on the Features of the Dynamics of Elements of Oscillatory Structures

Abstract

AbstractAn approach to the formation of a methodological basis for the system analysis of the dynamics of mechanical oscillatory structures based on frequency functions and damping functions is being developed. The argument of the functions is the coefficient of connectivity of the forms of motion of mass-inertia elements. The connectivity coefficient reflects the lever relationship of the parameters of the generalized coordinates. Mechanical oscillatory systems that are not connected to the support surfaces are considered. Mechanical oscillatory systems are formed by two mass-inertia elements, a spring and a damper. The aim of the study is to develop a method for constructing frequency functions and damping functions. The method is based on the use of an energy ratio that relates the kinetic, potential energy and the values of the energy dissipation function. The Lagrange formalism is used for composing differential equations. To determine the forms of frequency functions and damping functions, the so-called parametrizing function is used. Frequency functions and damping functions for mechanical oscillatory systems performing free movements are constructed. The graph-analytic evaluation of the extreme properties of frequency functions and damping functions is carried out. The possibility of the existence of four extreme values for frequency functions is shown. A topological criterion for classifying the forms of graphs of frequency functions and damping functions is proposed. The developed method can be used to display the dynamic features of mechanical oscillatory systems that include devices for converting movements.KeywordsMechanical systemDynamicsFrequency functionDamping functionConnectivity of movementExtreme propertiesOscillationViscous friction