Connectivity of disturbances, vibration frequencies and nodal points in evaluation of dynamic interactions of elements of mechanical oscillatory systems

Аuthors

Eliseev A. V.

Irkutsk State Transport University (IrGUPS), 15, Chernyshevsky str., Irkutsk, 664074, Russia

e-mail: eavsh@ya.ru

Abstract

The methodological base for assessment, correction and formation of dynamic states of technical objects of transport and technological purpose, which are under conditions of external loads of kinematic and power nature, is developing. The methodology finds application in the development of mathematical models of means and methods for evaluating the dynamic states of vibration technological machines used to test and strengthen long parts of aviation equipment. The purpose of the study is to develop a methodology for the formation of structural and dynamic properties of technical objects under conditions of vibration loads of a power or kinematic nature. Mechanical oscillatory systems with finite number of degrees of freedom formed by solid bodies on elastic supports under conditions of external power disturbances of harmonic form are used as design diagrams of technical objects. The objective is to develop mathematical models for estimating dynamic states of technical objects based on establishing a connection between the structure of external disturbances, represented by the connectivity coefficient, frequent oscillations of the system and the position of characteristic points of the system, in particular, the oscillation node. Methods of theoretical mechanics, Laplace integral transformations, vibration theory, structural mathematical modeling are used. The structural approach of mathematical modeling used is based on the comparison of mechanical oscillatory systems used as calculation schemes of technical objects, structural schemes of dynamically equivalent automatic control systems, for which the input signal is an external disturbance, and the output signal is the reaction of the system, in the form of the amplitude of the oscillation of the generalized coordinate of the object, the dynamic state of which is estimated. Within the framework of the structural approach, transfer functions of the system or interpartial connections are used to assess dynamic states, interpreting elastic and lever interactions between the elements of the system in a physical sense. Within the framework of the structural approach, transfer functions of the system or interpartial connections are used to assess dynamic states, interpreting elastic and lever interactions between the elements of the system in a physical sense. A model of plane movements of a rigid body on elastic supports performing small forced steady oscillations caused by an external kinematic disturbance is used as a basic calculation scheme. It is assumed that the kinematic disturbances are determined by the steady oscillation of a massive solid. The essence of the method lies in the possibility of establishing a relationship between the dynamic characteristics of the solid themes of the system. In the development of structural mathematical modeling, an approach has been developed to assess the dynamic states of a technical object based on the relationships between three characteristics: the oscillation frequency, the structure of external disturbances and the characteristic points of a technical object, in particular, the oscillation node. It has been shown that a third characteristic can be estimated from two known characteristics, for example, obtained on the basis of measurements. Based on the developed methodology, a device is proposed that allows determining the frequency of external disturbance. Such a device can be used to develop measuring means for vibration parameters of technical objects. By analogy with oscillation nodes, the method used can be generalized to the tasks of establishing relationships between the axes and centers of stiffness of two or more solids under conditions of vibration disturbances, taking into account the frequency and structure of external disturbances.

Keywords:

mechanical oscillatory system, structural mathematical modeling, transfer functions, connectivity of external disturbances, vibration nodes, frequencies of external disturbances, evaluation of dynamic state

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