Energy in elastic fiber embedded in elastic matrix containing incident SH wave

A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials

Vorticity Dynamics and Sound Generation in Two-Dimensional Fluid Flow

An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vorticity equation. The resulting rotation frequency includes the effects of finite vortex core size and viscosity and reduces, in the appropriate limit, to the rotation frequency of the Kirchhoff point vortex theory. The expansion is then used in the low Mach number Lighthill equation to derive the far-field acoustic pressure generated by the Gaussian vortex pair. This pressure amplitude is compared with that of a previous fully numerical simulation in which the Reynolds number is large and the vortex core size is significant compared to the vortex separation. The present analytic result for the far-field acoustic pressure is shown to be substantially more accurate than previous theoretical predictions. The given example suggests that the vorticity expansion is a useful tool for the prediction of sound generated by a general distributed vorticity field

The theory of the top

The Theory of the Top. Volume IV. Technical Applications of the Theory of the Top is the fourth and final volume in a series of self-contained English translations of the classic and definitive treatment of rigid body motion. Key features: * Complete and unabridged presentation with recent advances and additional notes; * Annotations by the translators provide insights into the nature of science and mathematics in the late 19th century; * Each volume interweaves theory and applications. The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Göttingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld.  Graduate students and researchers interested in theoretical and applied mechanics will find this series of books a thorough and insightful account.  Other volumes in the series include Introduction to the Kinematics and Kinetics of the Top, Development of the Theory in the Case of the Heavy Symmetric Top, and Perturbations.  Astronomical and Geophysical Applications