6.22 Lagrange’s Equation
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6.2 Using Dunkerley’s method, determine the fundamental frequency of a
uniformly loaded cantilever beam with a concentrated mass M at the end,
equal to the mass of the uniform beam having flexural rigidity EI. The
frequency of the beam due to uniform load is
p 1 = 3.515
2
E I
M L 3
6.3 Determine the fundamental frequency of the lumped mass simply supported
on an uniform beam shown in the figure by Dunkerley’s method.
6.4 For the cantilever uniform beam having lumped masses as shown, write
the equations of motion and apply matrix iteration technique to obtain the
frequency and the mode shape for the fundamental mode.
6.5 For the spring–mass system shown in the figure, determine all the natural
frequencies and mode shapes by Stodola’s method.
6.6 Treat the 3-degree spring–mass system shown in the figure as a periodic
structure. Solve for frequencies and modes of vibration.
253
6.2 Using Dunkerley’s method, determine the fundamental frequency of a
uniformly loaded cantilever beam with a concentrated mass M at the end,
equal to the mass of the uniform beam having flexural rigidity EI. The
frequency of the beam due to uniform load is
p 1 = 3.515
2
E I
M L 3
6.3 Determine the fundamental frequency of the lumped mass simply supported
on an uniform beam shown in the figure by Dunkerley’s method.
6.4 For the cantilever uniform beam having lumped masses as shown, write
the equations of motion and apply matrix iteration technique to obtain the
frequency and the mode shape for the fundamental mode.
6.5 For the spring–mass system shown in the figure, determine all the natural
frequencies and mode shapes by Stodola’s method.
6.6 Treat the 3-degree spring–mass system shown in the figure as a periodic
structure. Solve for frequencies and modes of vibration.