Research Areas in Vibrations

Computational Structural dynamics

Sample plots of the frequency dependent shape function

The study of complex dynamical systems requires numerical modeling, often, in terms of finite elements (FE). An FE discretization scheme involving frequency dependent shape functions have been developed, which bypasses the need for fine meshing. The shape of these functions adapt according to the frequency of the excitations.

Nonlinear dynamics

Poincare map of a chaotic system & Phase plot of a nonlinear system

Dynamical systems exhibiting geometric nonlinearities exhibit interesting phenomenological behavior. A qualitative and quantitative analysis of these systems enables an understanding of the stability and behavior of the nonlinear system. Studies are currently being carried out for stability analysis of complex dynamical fluid-structure interaction problems.

Random vibrations

Schematic diagram & Typical probability density function of response

Analysis of structural systems subjected to random dynamic loads, such as earthquakes, wind turbulence or ocean waves require an understanding of how the randomness in the loads propagates through the structural system. These studies require extensive use of theories of probability and statistics in conjunction with principles of structural dynamics.