Resonance is often discussed in the context of damped mechanical systems subjected to external, periodic forcing, wherein the system is stable, but exhibits a peak in the response at a critical resonant frequency. Instead, we consider systems that are subjected to _internal forcing_ via periodic variations in a parameter, thereby giving rise to very

different solution behaviour.

In particular, we examine the stability of fluid flows containing immersed, elastic boundaries, where the flow is driven by periodic variations in the elastic properties of a solid material. Such a system is a prototype for active biological tissues such as heart muscle fibres immersed in blood. Using Floquet theory, we derive an eigenvalue problem which can be solved numerically to determine values of the forcing frequency and fluid viscosity for which the system becomes unstable. We also describe direct numerical simulations of the fluid-structure interaction that are being performed to verify the existence of these parametric resonances.

This is joint work with R. Cortez (Tulane), C. Peskin (NYU) and D. Varela (CalTech).