The research on dynamic stability in non-conservative mechanics gained momentum over the last few decades. It was found that systems subjected to non-conservative loads can become dynamically unstable (Flutter), or statically unstable (Divergence). Thus, to identify the buckling loads irrespective of the nature of loads a dynamic instability analysis is always necessary. Flutter leads to a self-sustaining oscillation which absorbs energy from a steady source, whereas divergence leads to a blowing-up motion. Flutter happens in structural systems when follower forces (or torques) are present. For such structures, a static buckling analysis yields absurd results. Nonconservative systems display unusual and counter-intuitive dynamics and stability properties. The occurrence of flutter and divergence instabilities is usually analyzed to be avoided in mechanical structures, although sometimes these become desirable, for instance, to harvest energy. However, the determination of these instabilities is a challenging mechanical problem. This is due to the non-self adjoint (non-Hermitian) character of the governing equations that depend on multiple parameters.
The current study focuses on two types of systems, (i) Systems with a non-self adjoint governing differential equation with respect to boundary conditions, (ii) Systems with a non-self adjoint governing differential equation with respect to the equation itself. For the stability analysis of these systems, exact analysis methods are tedious and hence approximate methods become necessary. This talk explains the conservative and non-conservative nature of loads, and introduces the flutter and divergence instabilities encountered in systems. The seminar focuses on the approximate analyses used for dynamic stability analysis, their applications, and limitations.