Theory of Oscillations by Sergey Viktorovich Eliseev & Andrey Vladimirovich Eliseev

Author:Sergey Viktorovich Eliseev & Andrey Vladimirovich Eliseev
Language: eng
Format: epub
ISBN: 9783030312954
Publisher: Springer International Publishing

5.1.2 Joints in a Beam System with Two Degrees of Freedom

Consider a beam system with two degrees of freedom, paying attention to the possibility of introducing joints at certain points by means of their “displacement”. In the computational scheme shown in Fig. 5.5, this possibility is represented for the cases of the coincidence of the points A1 and A2, B1 and B2, when the system loses one degree of freedom, but the joint in the form of a kinematic pair of class V or a rotational hinge enables the solid body to perform oscillating and reciprocating motions, A and B. In the future, the possibilities of joints not only in the system of coordinates y1 and y2, but also in other coordinate systems will be considered. We note that, in addition to the joints at the points A and B, it is also possible to consider the constraints of motion with respect to the coordinates of pp. A2 and B2 at the same time, which can be determined by the condition y2 − y1 = 0. In this case, the system (see Fig. 5.5) with one degree of freedom and performs vertical translational motion on an elastic element with stiffness k1 + k2.

Fig. 5.5The computational scheme of a system having two elastic supports and moving in the system of coordinates y1, y2

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