Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Abstract

The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

“…There exist two types of instability behaviors for lightweight structures in mechanics fields [1,2].…”

“…These complicated instability behaviors can occur in many engineering structures (brake squealing [4], panel flutter [5,6], wing/control surface flutter [7,8], conveying pipeline flutter and others [9,10,11]), and have been attracted much attentions till now. However, the above structures posing buckling or flutter instabilities can be treated as various variants of the simple Ziegler double pendulum model [1,2]. This model refers to a linked double pendulum with specific discrete mass, stiffness and damping, and under the follower type circular loading on its end, thus constitutes a nonlinear damped circular non-conservative system.…”