Nomenclature
A/B/C	third order elastic constants	k	wave number
A 1	amplitude of primary wave	N	fatigue cycles
A 2	amplitude of second harmonic wave	R	stress ratio
$a_n(z)$	magnitude of nth double frequency Lamb wave	U 0	excitation displacement amplitude
A(t)	temporal waveform	w	angular velocity
B(Y)	thickness profile	v	Poisson’s ratio
c	group velocity	z	propagation distance
cl	longitudinal wave velocity	zn	half the oscillation spatial period
$c_p^{\omega }$	phase velocity of primary wave	α	scale factor
$c_p^{2\omega }$	phase velocity of second harmonic wave	β	absolute nonlinearity parameter
ct	transverse wave velocity	ρ	density
Δd	element size	σmax	maximum stress
E	elasticity modulus	σ 0.2	yield stress
Abbreviations
SHG	second harmonic generation	FE	finite element
DFLW	double frequency Lamb wave	STFT	short time Fourier transform