Singular value analysis is used to develop eigenvalue and eigenvector trends for beams supported by periodically-spaced, elastic elements. These trends are illustrated for both straight and bent beams as a function of the number of spans in the system, the boundary conditions, and the ratio of support to beam stiffness. As might be speculated, the effect of boundary conditions decreases as the number of spans increases. Also the effect of a bend becomes more pronounced as the bend is moved nearer the center of the beam. Simplified models are presented which provide excellent approximations of the first natural frequency for certain values of the ratio of support to beam stiffness.

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