Nadarajah, "Scattering of the fundamental anti-symmetric
lamb wave by a mid-plane edge delamination in a fiber-composite laminate," Procedia Engineering, vol.
Because of the anti-symmetric
nature of this shape, the two hemispheres are unequal in all measures.
where [beta]t is a propagation constant along the z-axis, [[omega].sub.0]([beta]) corresponds to the frequency of the fundamental symmetric [[omega].sub.S]([beta]) or antisymmetric [[omega].sub.A]([beta]) (super-) modes of the coupled PCWs, [phi](x, z) denotes the (super-) mode's transverse field distribution supporting following symmetric [[phi].sub.S](-x, z) = [[phi].sub.S](x, z) and anti-symmetric
[[phi].sub.A](-x, z) = -[[PHI].sub.A](x, z) properties with respect to the x-axis and having a periodicity in z with a period 2[pi]/h [29,30].
8 gives the real and imaginary part which is associated with the symmetric and anti-symmetric
components of the signal.
[[[M.sub.si]].sub.x] is the anti-symmetric
matrix about [M.sub.si], [v.sub.c] is 3-D camera velocities.
The conversion of the anhydride groups ([X.sub.Anh]) is calculated from the absorbance of the anti-symmetric
carbonyl stretching (C=O) vibration band at 1781 [cm.sup.-1] of the anhydride groups before (t = 0) and after (f = t) reaction with ATA using the absorbance of the band at 1470 [cm.sup.-1], which originates from the overlapping anti-symmetric
C[H.sub.3] bending and C[H.sub.2] scissoring vibrations of the IIR backbone as an internal reference.
The next common bifurcated band in all of the spectra is at 2850-2935 cm-1 due to symmetric and anti-symmetric
stretching modes of sp3 C-H of methylene groups of soft segment.
where J is anti-symmetric
matrix, R is symmetric positive definite matrix, P is a mapping of the state x with corresponding dimensions, then system (6) is called a pseudo-generalized Hamiltonian system , hence we have the following theorem.
Cheng, "Identification of corrosion damage in submerged structures using fundamental anti-symmetric
Lamb waves," Smart Materials and Structures, vol.
In order to derive its two port ABCD parameters, symmetric and anti-symmetric
excitations of the ports are considered.
A brief analysis of each filter case (even/odd order filters that are symmetric, anti-symmetric
and non symmetric) for both the analysis and synthesis banks was performed to determine the best manner for implementing the desired FIR filters in hardware.