TY - JOUR
TI - Stable methods to solve the impedance matrix for radially inhomogeneous cylindrically anisotropic structures
DO - https://doi.org/doi:10.7282/T31G0NZN
AU - Norris, Andrew N.
AU - Nagy, Adam J.
AU - Amirkulova, Feruza A.
PY - 2013
T2 - Journal of Sound and Vibration
VL - 332
IS - 10
SP - 2520
EP - 2531
AB - A stable approach for integrating the impedance matrix in cylindrical, radial inhomogeneous structures is developed and studied. A Stroh-like system using the time-harmonic displacement-traction state vector is used to derive the Riccati matrix differential equation involving the impedance matrix. It is found that the resulting equation is stiff and leads to exponential instabilities. A stable scheme for integration is found in which a local expansion is performed by combining the matricant and impedance matrices. This method offers a stable solution for fully anisotropic materials, which was previously unavailable in the literature. Several approximation schemes for integrating the Riccati equation in cylindrical coordinates are considered: exponential, Magnus, Taylor series, Lagrange polynomials, with numerical examples indicating that the exponential scheme performs best. The impedance matrix is compared with solutions involving Buchwald potentials in which the material is limited to piecewise constant transverse isotropy. Lastly a scattering example is considered and compared with the literature.
KW - Anisotropic structure
KW - Cylindrical coordinates
KW - Exponential instability
KW - Inhomogeneous structure
KW - Lagrange polynomials
KW - Piece-wise constants
KW - Radially inhomogeneous
KW - Riccati matrix differential equations
KW - Riccati equations
LA - English
ER -