A study on Lamb Wave Propogation in Elastic Continua

Abstract

The objective of the thesis is to study the propagation of Lamb waves that travel in elastic plate with free boundaries and also when it is loaded with inviscid liquid. Frequency equations are obtained for the propagation of Lamb waves. The properties of Lamb waves are defined by dispersion curves which are plotted between phase velocities and wave number. Lamb waves are formed by the interference of multiple reflections at the free surfaces of the plate. In Lamb waves, the particle displacement occurs in both directions that is in direction of wave propagation and perpendicular to the plane of plate. These waves are commonly used in providing information in ultrasonic non destructive testing. Chapter1 includes the introduction of classical theory of elasticity. The mechanics of continuous elastic bodies is presented in this chapter. The generalised Hooke’s Law is discussed with brief explanation of stress-strain curve. The theory of elastic waves and discussion on types of elastic waves like surface and Lamb waves is presented in this chapter. It also contains the basic governing equations of elasticity and expression for the speeds of primary and secondary waves. These expressions are derived using Helmoholtz decomposition. Various applications of Lamb waves are also discussed. Chapter2 deals with the propagation of Lamb waves in stress free boundaries of elastic plate. In this chapter, the mathematical modeling of problem is done and frequency equations are obtained from the basic governing equation of elasticity in absence of body forces. Dispersion curves are obtained for symmetrical and antisymmetrical modes. The study carried out in chapter2 is extended to the study of Lamb wave propagation in layered structure in chapter3. Here the plate is sandwiched between the finite layers of inviscid liquid loading. In this chapter frequency equations are derived. The effect of liquid loading are shown graphically. In the absence of the liquid loading the dispersion equations reduced to the equations obtained in the chapter2. The study carried out in this thesis is the particular case of the article[1] in the absence of couple stress effects.