A new method for determining natural modes and their frequencies with the concept of node in vibrations of M-DOFs

Document Type : Research Article


Lecturer at Engineering Department of Golestan University


This paper evaluates the vibration of M-DOF systems by calculating the natural frequencies and mode shapes. The introduced method is established on the base of the node concept, which is the point of a mode shape with zero displacement. In this method, a system with two or more degrees of freedom is transformed into two or more isolated systems with one- DOF. Those systems are isolated in node places and vibrate with the same frequencies in every mode. Each spring located between two adjacent lumped masses will be converted to series combination of two separated springs. The stiffness of the first spring is equal to the effective stiffness of the two series separated springs. The proposed method provides a good physical understanding about the concept of vibration modes. Besides, this method is accurate and sometimes is simpler and quicker than the common method.


Main Subjects

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