Overview

Test Case

Consider a pendulum consisting of a mass B attached to the free end of a pinned bar L. The system moves in a vertical plane, and the only forces acting on the mass are the gravitational attraction of the earth and the force applied to the bar. The bar is subjected to a known moment M_bar. Determine the minimum and maximum relative rotation of the bar.

Figure 142: Problem Sketch

Analysis Assumptions and Modeling Notes

Refer to Figure 143: Workbench Model below. The pendulum has a frictionless pinned end and a point mass on the free end. The bar is assumed to be massless so the bar's density is set to 1e-10 kg which is insignificant compared to the point mass of 0.2 kg. The stiffness behavior is set to rigid. Rotational movement is assumed to be in the vertical plane about the Y Axis, so a revolute joint restricts the movement to the XZ plane. The initial angular velocity of the bar is 2 rad/s. A gravity load of -9.81 m/s² is applied to the model.

For Analysis Settings, the number of steps is set to two, and the end time step is set to two seconds. The first time-step is 1e-5 seconds. This step will establish the initial angular velocity condition.

An acceleration load of -9.81 m/s² is defined in the X direction to model the gravity force. A Joint Load is applied to the Revolute - Ground to Massless Bar. The Type is set to Rotational Velocity. The initial step condition is set to 2 rad/s. The load is deactivated for the rest of the simulation.

For Solution Settings, a Joint Probe is scoped to the boundary condition Revolute - Ground to Massless Bar. The Relative Rotation Result is selected in the Z axis.

Figure 143: Workbench Model

Results Comparison

The expected maximum relative rotation value (with a null applied moment) according to the formulation is 28.6 degrees. The minimum relative rotation is -28.6 degrees.