Oscillatory instabilities in active mechanical networks

Active mechanical networks represent systems across domains and length scales, from actin meshes in cells to limbs in animals and robots. The stability of these networks is governed by an interplay between actuation, constraints, external forces, and viscoelastic properties of the network. Unlike passive systems, active systems under constraints are subject to loads that arise from internal actuation. If the combination of forces due to the external loads, constraints, and viscoelasticity fails to restore the original configuration after a perturbation, the system is unstable. Using a structural stability analysis of a general active mechanical network subject to Pfaffian constraints, we show that a network with circulation-free stiffness, damping, and feedback can only destabilize by static buckling when subject to holonomic constraints. In contrast, the same mechanical network with non-holonomic constraints can exhibit either static buckling or flutter instability. We provide bounds on the system's viscoelasticity and show how feedback can stabilize active networks under different types of constraints.