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Therefore, a root exists in the interval where a sign change occurs. Assume that this occurs between velocities (c p ) n and (c p ) n+1 or (cg ) n and (c g ) n+1 ; (vi) use some sort of iterative root-finding algorithm such as Newton-Raphson and bisection, to locate precisely the velocity in the interval (c p ) n < (c p ) < (c p ) n+1 or (c g ) n < (cg ) < (c g ) n+1 ; (vii) after finding the root, continue searching at the current (ω ⋅ h) or ( f ⋅ h) for other roots according to steps (ii) through (vi); and (viii) choose another (ω ⋅ h) or ( f ⋅ h) and repeats steps (ii) through (vii).
3b) p2 = ω2 cL − k 2 , q2 = 2 ω2 cT 2 − k2 , k = 2π λwave . 3c) A1 , A2 , B1 and B2 are four constants determined by the boundary conditions. k , ω and λwave are the wavenumber, circular frequency and wavelength of the wave, respectively. 4) where E denotes the Young’s modulus of the medium ( E = 2µ (1 + ν ) ). It can be seen that Lamb waves are actually the superposition of longitudinal and transverse/shear modes. An infinite number of modes exist simultaneously, superimposing on each other between the upper and lower surfaces of the plate, finally leading to well-behaved guided waves.
For example, it has been observed that 52% of the total energy dissipates when Lamb waves pass through a damage area of 7 mm in diameter in a composite laminate (100 mm × 100 mm) . 7; the latter refers to changes in propagation velocity and signal bandwidth subject to wave frequency. 3 enumerates the experimentally measured attenuation coefficients of Lamb waves (defined as loss of power per unit distance) in some typical composite materials, including carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP).