The following boundary conditions and loads are applied to the ultrasonic transducer model:
The outside diameter of the holder is fixed (constrained in all structural degrees of freedom). A static analysis is performed to calculate the prestress due to the tightening of the bolt to the driver assembly. A preload force of 50 N is applied to the bolt face.
The static analysis is performed only to create the stress-stiffening matrix that influences the overall stiffness matrix. Since the effect of the bolt preload to the stiffness of the driver is considered in the linear perturbation analysis, the actual adjustment is not required in the dynamic analysis.
Between each piezoelectric ring is an electric terminal. The rings are polarized in opposite directions, so the positive and negative terminals alternate.
Because the terminal is equipotential, all the voltage degrees of freedom for each terminal are coupled, leaving two independent voltage degrees of freedom at the terminal locations. One voltage is specified as ground (voltage of 0).
In the coupled field modal analysis, the positive terminal is left unconstrained. In the harmonic response analysis, a voltage of 5V constant with respect to frequency is applied to the positive terminal.
