Nanomechanical Resonators (NRs) not only process the motion characteristics of macroscopic mechanical resonators, while also exhibiting an ultra-small small scale and exceptionally high vibration frequency. By coupling NRs with other microstructures such as quantum dots and photonic crystals, many fascinating quantum optical effects will appear in such hybrid nanomechanical systems. The hybrid NR systems are exceptionally sensitive to small forces and can be driven by electric field, light fields, and other modalities, which attract significant research interest. In such hybrid systems, by changing the coupling between the nanomechanical resonator and other micro-structures, the frequencies of the NRs, and the strength of the driving field, the linear optical properties and nonlinear optical properties often change significantly. In this paper, the hybrid nanomechanical resonator system has been proposed. The system consists of two suspended NRs, one of which is embedded with a quantum dot. The NR systems coupled with quantum dots have received extensive attention, but there are few studies on the nonlinear optical properties of such systems. Our work mainly focuses on investigating the nonlinear optical properties of the hybrid system. Deriving the Hamiltonian for each component of the system, and use the Heisenberg equation to obtain the Langevin equation. Through the solution of above equations using semi-classical theory, the dimensionless linear susceptibility and nonlinear optical susceptibility of the system are calculated. The linear and nonlinear absorption and Kerr coefficient of the system under resonance and red detuning are studied by drawing a spectrum diagram based on the relationship between dimensionless linear susceptibility and nonlinear optical susceptibility and detuning. Finally, the optical characteristics of the system are discussed by adjusting the coupling strength, NRs frequency and Rabi frequencies.We studied the dimensionless linear susceptibility, and observed that two peaks appear at the abscissa Δs/ωm1=±1. The frequency of the nanomechanical corresponds exactly to the location two peaks separate. Within a small range along the abscissa, the dispersion and absorption in the spectrum exhibit significant variations. The dimensionless linear susceptibility reveals that the system has phonon-induced transparency and double-Fano resonances phenomenon. Upon activating coupling strength β between quantum dot and NR₁, a peak appears in the spectrum, and the amplitude of the peak increases with the increase of the coupling strength β. The vertical vibrations of quantum dot embedded in NR₁ interact with the NR₁, resulting the appearance of peaks in the spectrum. Next, we study the nonlinear absorption and Kerr coefficient. After the coupling strength λ between NR₁ and NR₂ is activated, there is a splitting in the spectrum, and the splitting distance increases with the coupling strength of the peak. To further analyze the coupling parameters, after taking points, drawing and fitting, the results show that a functional relationship exists, which is related to the two coupling parameters and the lateral distance and longitudinal height difference of the splitting peak respectively. On this basis, we propose a method to estimate the unknown coupling strength according to the splitting transverse distance and longitudinal height in the spectral line. In the case of red detuning, we analyzed the Kerr coefficient. With the increase of the frequency of the NR₂, the two peaks will move to the right and affect the distance between them, and the horizontal coordinate at the peak of the absorption peak remains unchanged. Increasing Rabi frequencies and detuning does not affect the position and distance between the two peaks, while which can cause the horizontal coordinate of the peak of the absorption peak to move to the right. Finally, we plot the dimensionless linear susceptibility, nonlinear absorption and Kerr coefficient on a graph, and analyzed these results collectively. At Δs/ωm1=-1.1 and Δs/ωm1=-0.9, the linear absorption is negative, and the nonlinear absorption and Kerr coefficient are smaller positive values, which means that phonon-induced transparency occurs here. When the Rabi frequencies or coupling strength β get to zero, the Kerr coefficient will change to zero. By adjusting the Rabi frequencies, it is observed that the peak value of the Kerr coefficient is inversely proportional to the Rabi frequencies.