Abstract
Introduction. A new approach to the formation of the methodological basis of system analysis in the application to the problems on mechanical oscillatory structure dynamics is considered. The study objective is to develop a method forevaluating properties of the mechanical oscillatory systems with account for viscous friction forces based on frequency functions and damping functions that depend on the so-called coefficient of connection forms, which is the ratio of characteristics of generalized coordinates. Materials and Methods. The graphoanalytical methods used for evaluating the dynamic properties of mechanical oscillatory two-degree-of-freedom systems are based on determining the extreme values of the frequency functions and the damping function, which are determined from the relations between the kinetic, potential energy and the values of the energy dissipation function. Mathematical models are based on Lagrange formalism, matrix methods, and elements of the theory of functions of a complex variable. Results. A method is proposed for constructing frequency functions and damping functions for a class of mechanical oscillatory two-degree-of-freedom systems based on the analytical expressions that reflect features of the ratio of the potential and kinetic energy of the system considering viscous friction forces represented by the dissipative function. General analytical expressions for the frequency function and the damping function are derived. Graphoanalytical analysis of extreme properties of the corresponding frequency functions and damping functions is performed for mechanical vibrational systems with elastic-damping elements with symmetry properties. The results of numerical experiments are presented. A criterion for classifying frequency functions and damping functions based on the topological features of the graphs of the corresponding functions is proposed. Discussion and Conclusions. The developed method for constructing frequency functions and damping functions can be used to display the dynamic features of mechanical oscillatory systems. The proposed matrix method for constructing a frequency-damping function for a two-degree-of-freedom system can be extended to the mechanical vibrational systems considered in different coordinate systems.
Highlights
A new approach to the formation of the methodological basis of system analysis in the application to the 360 problems on mechanical oscillatory structure dynamics is considered
Частотная функция и функция демпфирования в оценке динамических процессов evaluating properties of the mechanical oscillatory systems with account for viscous friction forces based on frequency functions and damping functions that depend on the so-called coefficient of connection forms, which is the ratio of characteristics of generalized coordinates
The graphoanalytical methods used for evaluating the dynamic properties of mechanical oscillatory two-degree-of-freedom systems are based on determining the extreme values of the frequency functions and the damping function, which are determined from the relations between the kinetic, potential energy and the values of the energy dissipation function
Summary
Целью исследования является разработка метода оценки свойств механических колебательных систем с учетом сил вязкого трения на основе частотных функций и функции демпфирования, зависящих от так называемого коэффициента форм связности, представляющего собой отношение характеристик обобщенных координат. Используемые графоаналитические методы оценки динамических свойств механических колебательных систем с двумя степенями свободы основаны на определении экстремальных значений частотных функций и функции демпфирования, определяемых из соотношений, связывающих кинетическую, потенциальную энергию и значения функции рассеяния энергии. Предложен метод построения частотных функций и функций демпфирования для класса механических колебательных систем с двумя степенями свободы на основе аналитических выражений, отражающих особенности соотношения потенциальной и кинетической энергии системы с учетом сил вязкого трения, представленных диссипативной функцией. Разработанный метод построения частотных функций и функций демпфирования может быть использован для отображения динамических особенностей механических колебательных систем.
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