Stochastic resonance (SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise.Using the linear response theory (LRT),the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained.The effects of damping coefficient,noise intensity,signal amplitude,and frequency on spectral amplifications are explored.Meanwhile,the power spectral density (PSD) and signal-to-noise ratio (SNR) are calculated to quantify SR and verify the theoretical results.The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity.That is,both of the noise-induced suppression and resonance can be observed by choosing proper system parameters.Especially,when the ratio of the second harmonic amplitude to the fundamental one takes a large value,the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.