We study the hydrodynamic interaction between two closely-spaced wavingelastic cylinders immersed within a viscous liquid, at the creeping flowregime. The cylinders are actuated by a forced oscillation of the slope attheir clamped end and are free at the opposite end. We obtain an expression forthe interaction force and apply an asymptotic expansion based on a smallparameter representing the ratio between the elastic deflections and thedistance between the cylinders. The leading-order solution is an asymmetricoscillation pattern at the two frequencies ($omega_1,omega_2$) in which thecylinders are actuated. Higher orders oscillate at frequencies which arecombinations of the actuation frequencies, where the first-order includes the$2omega_1,2omega_2,omega_1+omega_2$, and $omega_1-omega_2$ harmonics. Forin-phase actuation with $omega_1= omega_2$, the deflection dynamics areidentical to an isolated cylinder with a modified Sperm number. Forconfigurations with $omega_1pprox omega_2$, the $omega_1-omega_2$ moderepresents the dominant first-order interaction effect due to significantlysmaller effective Sperm number. Experiments are conducted to verify andillustrate the theoretical predictions.
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