VM179

VM179
Dynamic Double Rotation of a Jointed Beam

Overview

Reference:

Any basic mechanics text

Analysis Type(s):

Full Transient Dynamic Analysis (ANTYPE = 4 w/HHT)

Element Type(s):

Multipoint Constraint Revolute Joint Elements (MPC184)

Structural Mass Elements (MASS21)

3D 2 Node Beam (BEAM188)

Input Listing:

vm179.dat

Test Case

A torque M₁ is applied at the pinned end of an aluminum beam to cause a 90° rotation. A second torque M₂ is then applied at a revolute joint in the beam to create an out-of-plane rotation. The joint has a rotational stiffness k, inertial mass J, frictional torque T_f, and locks when a 5° rotation occurs. Structural mass elements with rotational mass are added at the joint notes. Determine the position of the beam at the end of each rotation.

Figure 270: Jointed Beam Problem Sketch

Material Properties

Geometric Properties

E = 70 x 10⁹ N-m

ρ = 1 x 10^-6 kg/m³

υ = 0.35

Lock at = 5° = 0.08727 rad

= 1 m

M₁ = 0.7854 N-m

M₂ = 0.5 N-m

Analysis Assumptions and Modeling Notes

Since step changes in acceleration occur due to the applied step loads, load steps with small time periods are used to "ramp" the accelerations to peak values while maintaining essentially no movement in the beams. The applied moments allow the beam to come to rest in the vertical position. A restart is included to demonstrate and test this program feature.

Results Comparison

	Target	Mechanical APDL	Ratio
Deflection_x , in (t = 1.0)	-0.5858	-0.58707	1.002
Deflection_y , in (t = 1.0)	1.4142	1.41550	1.001
Angle_z , rad (t = 1.0)	0.7854	0.78631	1.001
Deflection_x , in (t = 2.0)	-2.000	-2.01701	1.008
Deflection_y , in (t = 2.0)	2.000	1.99993	1.000
Angle_z , rad (t = 2.0)	1.5708	1.57930	1.005
Deflection_x , in (t = 3.0)	-2.000	-2.03534	1.018
Deflection_y , in (t = 3.0)	1.9962	1.99588	1.000
Deflection_z , in (t = 3.0)	0.08716	0.08716	1.000
Angle_x , rad (t = 3.0)	0.08727	0.08727	1.000
Angle_z , rad (t = 3.0)	1.5708	1.58850	1.011