Instability of a Quasi-Dynamic System Subjected to a Circulatory Force.

摘要

The state of stability of a double pendulum consisting of two viscoelastically hinged weightless, rigid bars carrying only a single concentrated mass and subjected to a circulatory and some conservative forces is examined. In the absence of damping in its hinges, this system, which is an example of a quasi-dynamic system, possesses multiple regions of stability and instability and can become unstable through divergence only. It is shown that the state of divergence may be attained whenever the natural frequency of the system either vanishes or becomes infinite. When damping is present in its hinges, the system becomes unstable through either divergence characterized by a vanishing frequency or by flutter. For very slight damping, the value of the critical flutter load is less than that of the critical load of divergence whose onset is characterized by an infinite frequency in the associated non-dissipative system.