Study on Wave Propagation Phenomena in Layered Media

Abstract

The wave propagation includes the situation where waves originate and propagate in the medium with different material properties and geometry. Studying the sur face wave propagation in the layered structure has been of interest to researchers due to their extensive applications in the fields of geophysics, composite materials, acoustics as well as in nondestructive evaluation. The interactions among these layers depend on many factors such as mechanical properties, loading conditions, interfacial conditions, etc. Traditionally, the layered model involves a substrate based on the classical elastic model but this theory ignore the microstructure-related scale effects. To capture the size effects, two size-dependent models, i.e., ‘Micropolar elastic model’ and ‘Couple stress elastic model’ have been considered along with other different ma terial layers such as smart material (piezoelectric material), viscoelastic material, orthotropic material, self-fiber reinforced material. The whole work of the thesis is structured into six chapters which are summarized as follow: Chapter-1 This chapter involves the basic overview on continuum mechanics, classical theory of elasticity with brief summary on generalized Hooke’s law. This chapter also in volves the emergence of different microcontinuum theories, i.e., ‘Micropolar theory’ and ‘Couple stress theory’ of elasticity, basic governing equations together with consti tutive equations are summarized. This also includes the brief overview on anisotropic materials like piezoelectric materials (also called ‘Smart Materials’) and viscoelastic materials. Chapter-2 In this chapter, the propagation of Love wave have been investigated in a piezoelectric xi xii ceramic bonded over a couple stress elastic half-space. The substrate is considered to have properties of a microstructure like granular macromorphic rock (Dionysos Mar ble). This study has been carried out by using two sets of piezoelectric medium, i.e., P ZT −5H and BaT iO3. Closed-form expressions of the resulting dispersion relations are obtained analytically by applying feasible boundary conditions for both the cases of electrically open and electrically short conditions. The significant effects of the underlying microstructure of substrate, the thickness of piezoelectric layer along with the effects of piezoelectric constants and dielectric constants have been examined and demonstrated graphically on the phase velocity profiles of Love wave. Chapter-3 In this chapter, Love-type surface waves have been explored in the size-dependent micropolar substrate with a finite layer of piezoelectric material. An analytical ex pression for the dispersion equations has been obtained for electrically open and short conditions and the results are shown graphically. For studying the impacts of under lying microstructure of the substrate, the layer thickness of piezoelectric material, piezoelectric and dielectric parameters, the dispersion curves have been plotted for non-dimensional phase velocity against non-dimensional wave number. The main objectives of Chapter 2 and Chapter 3 is to identify a size-dependent models for studying Love-wave propagation in layered structure. It was observed that the couple stress model and micropolar elastic model may be used as substrate to overcome the shortcomings of classical theory of elasticity. Chapter-4 This chapter is an extension of chapter 2 and chapter 3 in which study is extended to the double-layered model by considering another layer between the finite layer of piezoelectric material and the size-dependent substrate. The consideration of verti cally heterogeneous viscoelastic material layer is more beneficial in the design process to achieve an explicit objective. In this context, this chapter contains two problems on the propagation of Love-type waves in two-layered structure comprising a piezoelec tric material layer, viscoelastic layer along with the size-dependent substrate. Two materials of piezoelectric medium, i.e., P ZT −5H and BaT iO3 materials are used to xiii carry out this study. In first problem of this chapter, the couple stress elastic theory have been considered for analyzing the microstructural characteristics on Love wave propagation in double layered structure. The dispersion equations are calculated for the real and damping case in closed form expression for open and short circuits. Numerical calculations have been done to examine the impact of different parameters by taking two distinct piezoelectric materials, i.e., P ZT − 5H and BaT iO3. The relevant particular cases are derived to validate the present study. In second problem of this chapter, the micropolar model is considered for investi gating the effects of micropolarity and their related parameters on the propagation of Love-type surface wave in double-layered structure. An analytical expression for the real and damping dispersion equations have been obtained in the compact-form under electrically open and electrically short conditions. The real and damping phase velocity profiles are affected significantly with the variation in associated parameter involved in the study. The influence of characteristic length and coupling number associated with substrate, the influence of heterogeneity and the internal friction pa rameter related to viscoelastic material along with the effects of piezoelectric materials have been demonstrated graphically. Particular cases are also deduced using relevant conditions. Chapter-5 In this chapter, the propagation of Love-type wave have been studied considering the imperfect bonding between the substrate and the material layer. The strength of many engineering layered models rely on the bonding between the structural compo nents. In chapter-2, 3 and 4, the problems are solved considering the perfect bonding between the material layer and substrate. But in reality, this condition is difficult to fulfil. Keeping this aspect in mind, Love-type surface wave have been studied in functionally graded orthotropic medium under initial stress bonded imperfectly over the size-dependent micropolar medium. The main focus of the study is to show the impact of imperfect bonding at the common interface of material layer and substrate. The compact-form of dispersion relations is accomplished to study Love-type wave xiv characteristics in a composite layered system. Numerical computations are performed and results are manifested through graphs to study the effect of various factors in volved in the study. Chapter-6 The purpose of this chapter is to explore the characteristics of Rayleigh-type surface wave propagation in a size-dependent couple stress substrate with a finite thickness self-fiber reinforced layer. The compact form of the secular equation is achieved by employing suitable boundary conditions for the model proposed. The phase velocity profiles of Rayleigh wave propagation in the size-dependent composite structures are illustrated which are extensively useful. The characteristic curves are plotted to man ifest the effects of different affected parameters on the phase velocity of Rayleigh-type waves, namely the varying reinforced medium thickness, the parameter of material length representing the microstructural behavior of the substrate. The findings of the above study may be utilized for the development of Love wave based devices, in non-destructive evaluation, geophysics, civil engineering, rock me chanics, and can be an inspiration for engineering developments.