39.5. Boundary Conditions and Loading

Both structural and electric boundary conditions are applied:

39.5.1. Structural Boundary Condition

The outside diameter of the holder is 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 pretension node. For the subsequent dynamic analyses, the adjustment is changed to 0.0.

Although the actual pretension adjustment (change in grip length) is non-zero, the static analysis is performed only to create the stress-stiffening matrix that influences the overall stiffness matrix. In a harmonic response analysis, all loads are applied sinusoidally, so imposing a preload force or non-zero adjustment creates a harmonically-varying bolt load, which is incorrect. The effect of the bolt preload to the stiffness of the driver is considered in the linear perturbation analysis, so the actual adjustment is not required to be applied in the dynamic analysis.

39.5.2. Voltage Coupling and Boundary Condition

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 of 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 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.