The asymptotic estimation of the vibration spectrum for a system of two identical Euler–Bernoulli beams coupled via each of the four standard types of linear dissipative joint has been solved for the case when one beam is clamped and the other beam is free at the outer ends. Here, we generalize those results and solve the problem for all 40 combinations of energy-conserving end conditions. We provide both asymptotic and numerical results, and we compare the various systems with an eye toward determining which configurations lead to asymptotically equivalent vibration spectra.
Abriola, Chris; Coleman, Matt; Darakchieva, Aglika; and Wales, Tyler, "The Vibration Spectrum of Two Euler–Bernoulli Beams Coupled Via a Dissipative Joint" (2017). Mathematics Faculty Publications. 50.
Abriola, C., Coleman, M. P., Darakchieva, A., & Wales, T. (2017). The vibration spectrum of two Euler–Bernoulli beams coupled via a dissipative joint. Involve, 10(3), 443-463. doi: 10.2140/involve.2017.10.443.