a) Consider the system shown in Figure Q3a, consisting of a spring connected to the free end of a clamped bar. Estimate the first two natural frequencies using a finite element approach. The element matrices are given by [M]= PAL [k]. = [21 6 1 2 EA 1 -1 1 and k-k [K] spring -k k E, p Figure Q3a b) Describe the convergence and validation studies that are carried out during a finite element based modal analysis. Explain why it is that use of a coarser finite element mesh is likely to result in increased estimated resonance values.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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a) Consider the system shown in Figure Q3a, consisting of a spring connected to
the free end of a clamped bar. Estimate the first two natural frequencies using
a finite element approach. The element matrices are given by
[M]= PAL
[k].
=
[21
6 1 2
EA 1
-1
1
and
k-k
[K] spring
-k k
E, p
Figure Q3a
b) Describe the convergence and validation studies that are carried out during a
finite element based modal analysis. Explain why it is that use of a coarser
finite element mesh is likely to result in increased estimated resonance
values.
Transcribed Image Text:a) Consider the system shown in Figure Q3a, consisting of a spring connected to the free end of a clamped bar. Estimate the first two natural frequencies using a finite element approach. The element matrices are given by [M]= PAL [k]. = [21 6 1 2 EA 1 -1 1 and k-k [K] spring -k k E, p Figure Q3a b) Describe the convergence and validation studies that are carried out during a finite element based modal analysis. Explain why it is that use of a coarser finite element mesh is likely to result in increased estimated resonance values.
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