TY - JOUR
T1 - On the theory of wave propagation in anisotropic plates
JF - Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
SP - 2197
LP - 2222
M3 - 10.1098/rspa.2000.0609
VL - 456
IS - 2001
AU - Shuvalov, A. L.
Y1 - 2000/09/08
UR - http://rspa.royalsocietypublishing.org/content/456/2001/2197.abstract
N2 - A theoretical framework is developed which describes wave propagation in infinite homogeneous elastic plates of unrestricted anisotropy. The approach exploits the propagator matrix which is the exponential of the fundamental elasticity matrix underlying Stroh's formalism of anisotropic elastodynamics. The matrices of plate impedance and admittance are introduced, and their analytical properties are established, which appear fruitful for computing and analysing the plate wave spectra. On this basis, the dispersion equation can be cast into the form of a real equation involving the monotonic function, whose zeros and poles are the wave velocities in a given plate subjected to different boundary conditions (traction–free or clamped faces). It is proved that three fundamental wave branches exist for any orientation of wave propagation in an anisotropic plate with traction–free faces, and that those branches are missing if one or both faces are clamped. The intrinsic symmetry of the wave motion in an arbitrary plate is revealed. The general formalism is applied to elaborate the long–wavelength low–frequency approximation for a (thin) free plate of unrestricted anisotropy. The frequency–dispersive wave velocities, displacements and tractions at the onset of the fundamental wave branches are derived explicitly. The conditions for the extreme velocity values and some other useful universal connections are determined for an arbitrary thin plate, and exemplified for specific anisotropy cases.
ER -