Final Exam: Beam Vibration Modes

Indivual effort only

Problem Statement
Set up the global Finite Element stiffness and mass matrices for a beam composed of frame elements with the above mass and stiffness matrices.
for the following beams of rectangular cross=section:
a. cantilever (clamped-free) end boundary conditions)
b. pinned beam (pinned-pinned) end boundary conditions)
Report on 2 cases:
1. beam composed of 2 elements
2. beam composed of 3 elements
The beam properties are as follows:
length =10 inches
width = 1 inch
thickness = .25 inch
E= 30.0 E6 psi
weight density = 490 lb/cu ft


Determine the displacement mode shapes and frequencies for the above conditions

Submit only

  1. source codes (with comments, etc)
  2. input files
  3. 4 plots of the solutions, 2 for each of parts 2a and 2b.
    4. Do only fundamental (lowest frequency) +2 harmonics
  4. table of frequencies; associate one with each mode shape
Due:  Apr 29,   11:00 AM