Modes of wave propagation and dispersion relations in anisotropic shells and plates

• Main Authors: Yu-Cheng Liu, 劉育成
• Other Authors: Jin-Huang Huang
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/87507738291496836729

博士 === 逢甲大學 === 機械與航空工程研究所博士班 === 96 === The investigations of the dispersion relations and associated mode patterns of a cylindrical shell and composite plate are investigated. For cylindrical shell, a complete set of analytical solutions, based on Flügge’s theory, for all orders of circular harmonics, n=0, 1, 2, …, ∞, is presented. The traditional numerical root search process, which requires considerable computational effort, is no longer needed. Solutions of the modal patterns for all propagating and non-propagating modes are particularly emphasized, because a complete set of properly normalized eigenvectors are crucial for solving the vibration problem of a finite shell under various admissible boundary conditions. The dispersion relations and the associated eigenvectors are also the means by which to construct transfer matrices used to analyze the vibroacoustic transmission in cylindrical shell structures or pipe-hose systems. The eigenvectors obtained from the conventional method in shell analysis are not as conveniently normalized as those commonly used in mathematical physics. The present research proposes a new alternative method to find eigenvectors that are normalized such that their norms equal unity. A parallel display of the dispersion curves and the associated modal patterns has been used in the discussion and shown to provide a more insightful understanding of the wave phenomena in a cylindrical shell. For the composite plate, the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thicknesses on the dispersion relations and modes of wave propagation in inclusion-reinforced composite plates is discussed. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Mori-Tanaka mean-field theory is used to predict the effective elastic moduli of the composite plate explicitly. The effective elastic moduli are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior. The resulting moduli are then used to determine the dispersion relations and the modal patterns of Lamb waves using the dynamic stiffness matrix method. The wave types and orders are identified by analyzing the dispersion curves and inspecting the calculated modal patterns. Results indicate that the Lamb waves in an orthotropic composite plate can also be classified as either symmetric or antisymmetric waves. It is also found that the inclusion contents, aspect ratios and plate thicknesses affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns. Propagation speed is generally increased with the aspect ratio, e.g., using longer fibers generally results in a higher propagation speed.