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

Diverse methods of dynamic analysis of structures are associated with natural modes concept which are equal to characteristic vectors in math. The common approach for determining of natural mode shapes is a characteristic values problem. In this approach a characteristic matrix is made by having stiffness and mass matrices. An equation will be obtained when the determinant of the characteristic matrix is equal to zero. That equation roots are natural frequencies. Finally, modal vectors will be obtained for every frequency. This paper method is established on the base of 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 to two or more isolated systems with one- DOF. Those systems are isolated in node places and vibrate with same frequencies in every mode. Each spring which located between two adjacent lumped mass will be converted to series combination of two separated springs. 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 common method.