Abstract
Radially polarized open-cylindrical piezoelectric transducers are widely used in the field of acoustic logging while drilling (LWD). Unlike the wireline logging transducer, the structure of the acoustic LWD transducer is an open structure; in this case, its radial vibration is accompanied by apparent circumferential vibration. In this paper, based on the two-dimensional wave equations and electrostatic charge equation, according to the free boundary conditions of the transducer, the resonance frequency equation of radial-circumferential coupled vibration for the acoustic LWD transducer is obtained. The vibration modal and resonance frequency for transducers of several typical sizes are simulated using COMSOL software. The results show that when the geometrical size of the transducer satisfies certain conditions, the theoretical calculation and the numerical analysis are in good agreement and the relative error is controlled below 3%. Meanwhile, the horizontal directivity of the LWD transducer after actual installation is discussed, and it is found that adding appropriate coupling materials can improve the monopole sound field radiation. So, it is expected that this work can serve as a reference for the acoustic LWD transducer design and install.
Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes
