摘要： Cavity optomechanical system has made rapid advances in the past decades, which is mainly used to study the macroscopic quantum effects of the micromechanical resonators, such as the ground-state cooling of the mechanical resonator, mechanical squeezing, entanglement, macroscopic quantum superposition, etc. Owing to the unique advantages of optomechanical systems, numerous potential applications have been proposed, e.g., the ultrahigh precision metrology, exploring the quantum-classical boundary, and studying the weak signal transducer. The progress of the gravitational-wave detection is a great example for the application of optomechanics. In recent years, the periodically modulated optomechanical systems have attracted significant attention, which have been used to study various macroscopic quantum effects. However, in those modulation proposals, most of them focus on modulating the driven laser field, which results in the first-order moments of the system operators and the effective optomechanical coupling changing periodically to achieve and study some quantum effects. On the other hand, the frequency modulated quantum systems also exhibit a rich behavior and display nonequilibrium properties that are absent in their static counterparts, such as the phenomena of motional averaging and narrowing, Landau–Zener–Stückelberg–Majorana interference, and the formation of dressed states with the appearance of sidebands in the spectrum. However, in cavity optomechanical systems, the study of the influence coming from the frequency modulation is relatively rare to date. In this paper, we study an usual cavity optomechanical system where the frequency of the optical mode is shaken periodically. As we all know, the stability of optomechanical systems is closely related to the effective optomechanical coupling strength. For an excessively large coupling strength, the optomechanical systems are unstable and the studying is also meaningless. However, we find that the shaking optical mode can reduce the effective optomechanical coupling strength arbitrarily when the shaking frequency is much larger than the mechanical resonator frequency, and the deeply physical mechanism can be explained through the Raman-scattering and frequency domain pictures. The result indicates that it will be possible to study the steady quantum effects of optomechanical system even with strong coupling where the standard optomechanical systems without frequency modulation are always unstable. In order to verify the above analyses, we study the ground-state cooling of the mechanical resonator and the entanglement between the optical and mechanical modes in the conventional unstable region, and the results indicate that the final mean phonon number and entanglement not only can be achieved but also can be modulated by the optical shaking parameters. Our proposal provides a method to study the macroscopic quantum effects even in conventional unstable region.