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Abstract

The repeated natural frequency (RNF) is an important concept in vibration, and also fundamental to numerical computation and modal identification. Still, descriptions of physically simple systems, and especially mass–spring systems, are scarce in current textbooks. Here the authors investigate the conditions needed to establish a system with two degrees of freedom (DOF) possessing an RNF. The criterion is met if and only if entries of the mass matrix are proportional to the corresponding entries of the stiffness matrix. A two-DOF mass–spring system possessing an RNF is two independent systems in nature. Then, two three-DOF examples, all possessing an RNF, are constructed and discussed. One example is configured by identical masses connected by identical springs along a circumference. This model can be easily extended to higher-order systems. The article includes the general formula for the natural frequencies.

Keywords

mass–spring system modal analysis eigenvalue repeated natural frequency

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Systems with Few Degrees of Freedom and Repeated Natural Frequencies

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