Research Projects

Beams are ubiquitous structures in civil and mechanical engineering, and frequently encountered in applied physics, micro- and nano-systems. Due to its wide applicability, we consider the study of dynamics and acoustics of Rayleigh beam. The presence of a defect in structures affect its local characteristics (stiffness, damping…) and in turn results in a change in their global behaviour. In this study we consider a mode-1 crack and its effect on the dynamics and acoustics of the Rayleigh beam. The Rayleigh beam is modelled as a piecewise linear (PWL) structure with disparate interface stiffness depending on the curvature at the location of the crack. The interface also incorporates the Bouc-Wen hysteretic damping model. The first part of the study dwells on the free and forced dynamics of the Rayleigh beam. The analytical study involves application of action-angle variables, non-smooth basis functions, method of averaging and Galerkin method. It is expected that the responses are chaotic in addition to regular periodic regimes. The second part of the study would dwell on the wave scattering at the PWL interface. An analytical estimation of the scattered waves is essential in many engineering applications like structural health monitoring, non-destructive evaluation and diagnostics. To this end, we invoke method of multiple scales, modulation theory, inverse scattering transform and Weiner-Hopf technique in this study.