Dynamics of Machines - Part II - IFS.pdf

1.3 Data of the Mechanical System
ρ material density of the beam 7, 800 Kg/m 3
E elasticity modulus 2 × 10 11 N/m 2
L total length of the beam 0.600 m
b width of the beam 0.030 m
h thickness 0.0012 m
mi concentrated mass (i = 1, ...,6) 0.191 Kg
Table 1: Data of the mass-spring system ”A”.
ρ material density of the beam 7, 800 Kg/m 3
E elasticity modulus 2 × 10 11 N/m 2
L total length of the beam 0.300 m
b width of the beam 0.025 m
h thickness 0.0010 m
ρ material density (steel) 7, 800 Kg/m 3
mi concentrated mass (i = 1, ...,6) 0.191 Kg
Table 2: Data of the mass-spring system ”B”.
1.4 Calculating Equivalent Stiffness Coefficients – Beam Theory
(a) (b)
Figure 3: (a) Flexible beam – clamped-free boundary condition case with force applied to the end
L; (b) clamped-free boundary condition case with force applied to a general position L ∗ ;
By applying a vertical force F at the end of the beam as shown in figure 3(a) and using Beam
Theory, one can write:
EI d4y(x) = 0 (1)
dx4 Integrating in X once, one has:
EI d3 y(x)
dx 3 = F(x) = C1 (2)
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