a) Consider the system shown in Figure Q3a, consisting of a spring connected tothe free end of a clamped bar. Estimate the first two natural frequencies usinga finite element approach. The element matrices are given by[M]= PAL[k].=[216 1 2EA 1-11andk-k[K] spring-k kE, pFigure Q3ab) Describe the convergence and validation studies that are carried out during afinite element based modal analysis. Explain why it is that use of a coarserfinite element mesh is likely to result in increased estimated resonancevalues.

Step 1: Step 2: Step 3: Step 4:

Answered: a) Consider the system shown in Figure…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Question 3 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 finite element approach. The element matrices are given by [M]=P\[1 PA2 1] 1 2 and [K] spring k E, P Figure Q3a. b) Describe the convergence studies that are carried out during a finite element based modal analysis. c) Describe mode shape orthogonality. Use mode shape vector, mass and stiffness matrices in the discussion.
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