Transverse Beams (Beams)

For Euler-Bernoulli beams with only axial displacement, homogeneous material, constant cross-section and free vibration, the EOM is

where

The eigenfunction will be in the general form of

where the natural frequencies can then be calculated using

Analytically Finding the Natural Frequencies of a Fixed-Free Beam in Transverse Vibration

Analytically Finding the Natural Frequencies of a Fixed-Pinned Beam in Transverse Vibration

Common Boundary Conditions

Limitations

• Constant

  • Cross-section (Area and MOI)

  • Material (Density and Young’s Modulus)

• Autonomous/Free Vibration

• Homogeneous boundary conditions

• Euler-Bernoulli (“slender”) beam

• Linear-Elastic Deformation

Code