1. Problem Parameters Steel beam
1 m long
0.1 m diameter
E = 2.3 E11 N / m^2
Rho = kg/m^3
Euler-Bernoulli beam model (neglect shear deformation and rotary inertia)
Boundary conditions as stated at top of slide

2. Free/Free

3. Clamped/Clamped

4. Pinned/Pinned, Support stiffness at each bearing is 1E10 N/m

5. Pinned/Pinned, Support stiffness at each bearing is 1E9 N/m

6. Pinned/Pinned, Support stiffness at each beairng is 1E8 N/m

7. Pinned/Pinned, Support stiffness at each bveaering is 1E7 N/m

8. Pinned/Pinned, Support stiffness at each bearing is 1E6 N/m
Pinned/Pinned, Support stiffness at each bearing is 1E6 N/m. Note that the shape and frequency of the 3rd mode shown here match very closely to the first non-zero mode of the free/free