Several nonlinear ultrasonic detection techniques have so far been developed, such as the nonlinear resonant ultrasound spectroscopy [6], nonlinear elastic wave spectroscopy [7,8], and higher harmonic generations [9,10]. Among all these techniques, the second harmonic Lamb waves in a plate before the initiation of cracks are of particular interest. The second harmonic generation can be induced by various nonlinear sources in a typical NL-SHM system, either distributed or localized in nature. The distributed one is typically the material nonlinearity of the plate (MNP), a damage-related nonlinear source which has been extensively investigated in previous studies [11–17]. Relevant to the material degradations, the MNP-induced second harmonic Lamb waves exhibit the so-called cumulative effect when the synchronism conditions are satisfied, i.e., the match of the phase velocities between the first and the second harmonics and the nonzero power flux among them, resulting in a limited number of mode pairs that can be used for SHM [15]. Recently, the cumulative effect of the MNP-induced second harmonic *S*_{0} mode Lamb waves has been shown to exist in the low-frequency range when the phase velocities approximately match [16]. Compared with the commonly used high-frequency mode pairs, the use of the *S*_{0} mode Lamb waves in the low-frequency range is attractive for the structural health monitoring (SHM) applications in terms of the flexibility it offers in choosing the excitation frequencies and the lower demand for the measuring equipment. Localized nonlinear sources, such as the instrumental nonlinearity, adhesive nonlinearity (AN) [18] and so on, are often considered as typical non-damage-related nonlinear sources. Generally speaking, the second harmonic Lamb waves induced by these localized nonlinear sources propagate independently in the plate, thus exhibiting the noncumulative effect. Specifically, the influence of AN was shown to be inevitable and non-negligible in a typical piezoelectric wafer-actuated SHM system [18], which may exceed that of the instrumental nonlinearity. Therefore, AN is chosen as a typical example of the localized nonlinear sources, to be investigated in this paper.