Research

Mathematical Sciences

Title :

Mathematical Modelling of Edge Wave Propagation

Area of research :

Mathematical Sciences

Principal Investigator :

Dr. Santanu Manna, Indian Institute Of Technology (IIT) Indore, Madhya Pradesh

Timeline Start Year :

2023

Timeline End Year :

2026

Contact info :

Details

Executive Summary :

Nowadays, composite plates are widely used in various fields of Civil and Mechanical Engineering due to their lightweight, high stiffness and strength. Therefore, it is essential to analyze the different types of plates, so that, one can improve the reliability of the plate structure. In a fabrication process, the mathematical study of composite plates provides the bridge between modelling results and real field applications. Edge waves propagation in a composite plate gathers an increased amount of attention to the researchers because of its huge applications in non-destructive testing technology and also in crack detection in the manufacturing industries. Flexural waves exist at the stress-free edge of a thin elastic and travel along the edge of that structure, are known as edge waves. There are two different types of edge waves: (a) flexural (bending) and (b) extensional. The flexural edge waves are dispersive waves, whereas augmentation of edge waves are non-dispersive. These waves decay exponentially as it moves away from the edge. The idea of edge wave propagation was first developed in 1960 by Konenkov. Later on, Thurston and McKenna (1974) rediscovered the flexural acoustic waves along the edge of a plate. Recently, Kaplunov and his teams (2016, 2017) studied the effect of elastic foundations on edge wave propagation in the framework of classical plate theory. In the class of acoustic surface wave fields, the properties of the edge wave behave like a general Rayleigh wave motion on the surface boundary of the semi-infinite plate. The edge waves have a localized phenomenon compared to the body waves. Some powerful applications of the edge wave can be found in the non-destructive testing (NDT) of thin structures, like aircraft wings, rotor blades, submarine hulls, imperfections, and cracks within the bofy etc., Also, the edge wave theory is useful to study the dynamic behavior of ice sheets and large artificial floating structures such as floating airports and platforms. The existence of this kind of wave is restricted not only to the isotropic plates but can also exist in anisotropic, circular and laminated plates. Also, the importance to consider the nonlocal elasticity is that the stress fields in a nonlocal elasticity theory at a particular element depend not only on the strain at that particular element but also on the strain at every other element in that domain (cf. Karličić et al., 2016). From the previous development on the edge wave, it is understood that the analysis has been made within the framework of the local elasticity theory. In this project, our main objective is to work on the composition of the plates, which can be used in the fabrication process of the material. These kinds of materials are usually used in-flight body structure, blades of air-mill, the body structure of ships, etc. Also, the bending edge wave theory will be formulated for nonlocal plates using refined plate theory.

Total Budget (INR):

6,60,000

Organizations involved