Wave Propagation in Layered Anisotropic Media
with Application to CompositesBy
- A.H. Nayfeh, University of Cincinnati, OH, USA
Recent advances in the study of the dynamic behavior of layered materials in general, and laminated fibrous composites in particular, are presented in this book. The need to understand the microstructural behavior of such classes of materials has brought a new challenge to existing analytical tools. This book explores the fundamental question of how mechanical waves propagate and interact with layered anisotropic media. The chapters are organized in a logical sequence depending upon the complexity of the physical model and its mathematical treatment.
North-Holland Series in Applied Mathematics and Mechanics
Published: September 1995
- Introduction. Historical background. Field Equations and Tensor Analysis. The stiffness tensor. Material symmetry. Matrix forms of stiffness. Engineering constants. Transformed equations. Expanded field equations. Planes of symmetry. Bulk Waves. An overview. The Christoffel equation. Material symmetry. Computer aided analysis. Group velocity. Energy flux. Generalized Snell's Law and Interfaces. Boundary conditions. Characterization of incident waves. Critical angles. Two fluid media. Two isotropic media. Formal Solutions. Common form of solutions. Triclinic layer. The monoclinic case. Higher symmetry materials. Formal solutions in fluid media. The &agr; - c relation and the Christoffel equation. Scattered Wave Amplitudes. Notation. Reflection from a free surface. Scattering from fluid-solid interfaces. Scattering from solid-solid interface.Interface Waves. Surface waves. Pseudo-surface waves. Scholte waves. Free Wave in Plates. Free waves in triclinic plates. Free waves in monoclinic plates. Higher symmetry material plates. Numerical computation strategy. General Layered Media. Geometric description of unit cell. Analysis. Properties of the transfer matrix. Free waves on the layered cell. Waves in a periodic medium. Bottom bounding solid substrate. Propagation Along Axes of Symmetry. Geometry. SH waves. Motion in the sagittal plane. Free waves on the layered cell. Waves in a periodic medium. Bottom bounding solid substrate. Fluid-Loaded Solids. Reflection from a substrate. Plates completely immersed in fluids. Higher symmetry cases. Leaky waves. Experimental technique. Piezoelectric Effects. Basic relations of piezoelectric materials. Simplified field equations. Analysis. Formal solutions. Higher symmetric materials. Remarks on the monoclinic-m case. Reflection and transmission coefficients. Sample illustrations. Remarks on layered piezoelectric media. Transient Waves. Theoretical development. Source characterization. Integral transforms of formal solutions. Isotropic media. Anisotropic media. Cagniard-de Hoop transformation. Semi-space media. Scattering from Layered Cylinders. Field equations. Formal solutions in isotropic cylinders. Characterization of incident waves. Formal solutions for a layer. Scattering amplitudes. Elastic Properties of Composites. General description of fibrous composites. The model. The layered model. The square fibrous case. Anisotropic fiber and matrix. Strain energy approach. Undulated fiber. Appendix. References. Additional References. Subject Index. Author Index.