Влияние варьируемых инерционно-жесткостных параметров на характеристики динамических многомассовых систем

Abstract

В статье исследуются собственные частоты и соответствующие им собственные формы многомассовой системы. В качестве расчетной была выбрана система с 3мя степенями свободы. Исследования выполняются на основе функции Рэлея. В то же время результаты расчета сравниваются с решением, полученным методом Даламбера. В процессе расчета была выполнена оценка влияния жесткости всех упругих и массовых элементов. Построены зависимости решений от изменения входных параметров, выполнен анализ результатов.

The article investigates the natural frequencies and the corresponding mode shapes multimass own system. The review, which shows the current situation in the field of study of free oscillations using Rayleigh method. In the above operation was calculated as the chosen system with 3 degrees of freedom. A mathematical apparatus for the study of the dynamic characteristics of dynamic multibody systems. Research carried out in an analytical form based on the Rayleigh function with the Maple. At the same time, the calculation results are compared with the solution obtained by d'Alembert. The results are presented in the form of a surface in three-dimensional space, which describes the function of the Rayleigh solutions to such figure are orthogonal to each other. It also provides cross-section of the figure in the sections, in which the minimum of the function (1st natural frequency), a saddle point (2nd natural frequency) and a maximum function (third natural frequency) in the polar coordinate system. By varying the stiffness characteristics of the inertial-changing spectrum of natural frequencies and natural modes. This represents the interests of the development of methods of operational analysis of the reaction spectrum of the natural vibration frequencies and their own forms of vibrations to such variation. This was shown in the presented article. They were built according to decisions on the change of the input parameters. The analysis of the results. The paper also set goals for further research.