Fall 2000, METBD451 - FEA Dynamic Applications

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Sample Problems for Exam 2

 

A beam on two supports carries an unbalanced motor in the middle.

Assume that the beam is very stiff against any horizontal displacement, but it is not so stiff against vertical inputs.  Use a 2D beam element (BEAM3).

Constraints: left end is pinned, right end has only vertical support

The beam is steel: Beam cross-section:
  • Young's Modulus = 29x106 psi
  • Poisson's ratio = 0.3
  • Density = 0.283 lbm/in3
  • Length, L = 48 in.
  • Hollow Rectangular
  • Area, A = 5.4 in2
  • Moment of Inertia, I = 12.6 in4
  • Height = 3 in.

The motor is treated as a lumped mass (MASS21) without rotary inertia.  The mass is 100 lbm.

The frequency range is 0 to 180 Hz and the vertical force produced by the unbalanced motor has an amplitude of 5 lbf.

Damping of 3.5% of critical acts on this system.

List the first 4 natural frequencies, classified as to the type of motion (bending or axial)

***** FREQUENCIES FROM SUBSPACE ITERATION *****
MODE FREQUENCY (HZ) TYPE
1 106.79 bending
2 647.43 axial
3 812.83 bending
4 1361.70 bending

What is the maximum UY deflection of the motor (mid-point of the beam) over the frequency sweep ?

4.5e-04 in.

at what frequency does the max. UY deflection occur ?

106 Hz

What is the maximum FY force of the left end of the beam over the frequency sweep ?

38 lbf

at what frequency does the max. UY deflection occur ?

106 Hz