This paper deals with the transverse free vibrations of a system in which two beams are coupled with a spring-mass device. The dynamics of this system are coupled through the motion of the mass. The entire system is modeled as two two-span beams and each span of the continuous beams is assumed to obey the Euler-Bernoulli beam theory. Considering the compatibility requirements across each spring connection position, the eigensolutions (natural frequencies and mode shapes) of this system can be obtained for different boundary conditions. Some numerical results and experimental validations are presented to demonstrate the method proposed in this article.
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