Bubble dynamic behavior and frequency response of encapsulated microbubbles in nonlinear acoustic field is significant in applications such as tumor therapy, thrombolysis, tissue destruction, and ultrasonic lithotripsy. The acoustic cavitation effect includes stable cavitation and transient cavitation. The transformation from stable cavitation to transient cavitation requires a certain threshold, which is also called the transient cavitation threshold. Phospholipid-coated microbubbles are commonly used to enhance acoustic cavitation. However, the acoustic effects of different coating materials are not very clear, especially when considering the nonlinear effects caused by diffraction, scattering, and reflection during ultrasonic propagation. In this paper, the bubble dynamic behaviors and frequency responses of microbubbles under different frequencies, acoustic pressures, and viscoelastic properties of different shell materials are analyzed by coupling the Gilmore-Akulichev-Zener model with the nonlinear model of a lipid envelope and using the KZK equation to simulate the nonlinear acoustic field. At the same time, the influence of the coated material and nonlinear acoustic effects are considered. The bubble dynamic behavior and frequency response under the actually measured sound field are compared with those simulated by the KZK equation. The results show that the nonlinearity will lead the velocity of the microbubble wall to decrease, and when the pressure of ultrasound increases, the main frequency component of the microbubble oscillation increases, making the radial motion of the microbubble more violent. When the frequency changes, the closer the oscillation frequency of the microbubble is to the resonant frequency, the stronger the radial motion of the microbubble is. The coating material can change the harmonic component in the oscillation frequency. When the harmonic is close to the resonance frequency, the radial motion of the microbubble is enhanced. The elasticity of the coated material has almost no effect on the microbubble's frequency response, and the initial viscosity and surface tension of encapsulated microbubble will change the oscillation frequency distribution of encapsulated microbubble. When the initial viscosity of the coated microbubble is smaller, the subharmonic component of the microbubble oscillation increases. When the frequency of the subharmonic is closer to the resonance frequency than the main frequency, the acoustic cavitation effect is significantly enhanced. On the other hand, when the initial surface tension of the encapsulated microbubble increases, the main frequency and subharmonic component of the microbubble oscillation are enhanced, so that the acoustic cavitation effect is also enhanced. Therefore, this study can further elucidate the bubble dynamics of encapsulated microbubbles, stimulated by nonlinear ultrasound, benefiting the frequency response analysis of coated microbubbles under nonlinear acoustic fields.