Mathematical modeling of the self vibration frequencies of mechanical frames of controls rigs

Abstract

Cross vibrations in cylindrical thin – border tubes and in rectangular frames which are made from these tubes and calculating method of their frequency are analyzed in the article. The theory of instantaneous cylindrical tubes and main equations of theory of elasticity can be used to develop the mathematical model. Vibrations of one and two layers thin – border tubes are considered, differential equations with partial derivatives are created to discribe vibrations. Determination of approximate solution method of differential equations are simple and practical which can be used to calculate self vibration frequencies. Digital values of self vibration frequencies in one and two layers thin – border tubes and in rectangular frames which are made from these tubes are compared.