Зависимость собственных частот и собственных форм колебаний от инерционно-жесткостных характеристик систем с конечным числом степеней свободы

Abstract

В работе предложен новый подход к исследованию чувствительности собственных частот и форм колебаний к варьированию параметров динамической системы. Собственные формы колебаний определяются из условий достижения экстремумов функции Рэлея. Предложен подход к линейной аппроксимации динамических характеристик систем с несколькими степенями свободы на изменение их инерционно-жесткостных параметров. Проведен анализ влияния инерционно-жесткостных характеристик на спектр собственных частот и формы колебаний.The paper presents a new approach to the linear approximation of the dynamic characteristics of the study and the sensitivity of the natural frequencies and mode shapes to variations in inertial stiffness parameters of the dynamic system. Natural modes are determined by the conditions for maximization or minimization of the Rayleigh function. The influence of the inertial stiffness characteristics on the spectrum of natural frequencies and their own forms of vibrations. The applicability of this approach based on the use of exact solutions for a finite variation of inertial stiffness parameters (so-called "benchmark" decisions), to predict changes in natural frequencies and natural modes. It is shown that the linearization gives acceptable accuracy over a wide range varying discrete dynamic system parameters. Accordingly, it can be linearized and reverse dependencies. Thus, these approximations are applicable for solving the parametric sensitivity of the synthesis. Subsequently, data approximation can be used to design problems, since thus the response function in a neighborhood of the nominal parameter set is linearised. In the presence of linear (or linearized) restrictions (for example, by weight or stiffness) the problem of linear programming to replace the original nonlinear programming problem.