Lecture19-Prof.Ju

# Lecture19-Prof.Ju - CEE M237A MAE M269A Lecture 19 The Ritz...

This preview shows pages 1–8. Sign up to view the full content.

CEE M237A / MAE M269A Lecture 19: The Ritz Method II Professor J. Woody Ju

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 3–Use of More Coordinate Functions in Example 1 y Consider a series of sinusoidal coordinate functions: 2 () ( ) 1 ,s i n The case for 2 is Example 1. Consider now a series of problems beginning with 3 and incrementing each time by one until 7. By this process, it is possible to observe the step- N n n nx wxt a t L N NN N = = = = = π by-step improvement in the accuracy of the Rayleigh-Ritz analysis. For each value of , an is generated and solved to give all the modal data. algebraic eigenvalue problem N
Example 3–Use of More Coordinate Functions in Example 1 (Cont’d) y y The above eqn. is obtained first by means of Hamilton’s principle (or Lagrange’s eqn.) and then by invoking simple harmonic motion in time as in Example 1 3 As an example, the algebraic eigenvalue problem for 7 is N = 3 where 2 γ σ =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 3–Use of More Coordinate Functions in Example 1 (Cont’d) y y 4 For this particular example, observe that for 7, the algebraic eigenvalue problem can be obtained by truncation N < Moreover, it is possible by mathematical induction to state the form of the algebraic eigenvalue problem for 7 if further studies are needed or if the higher modes are of interest. N >
Example 3–Use of More Coordinate Functions in Example 1 (Cont’d) 5 2 N = 3 N =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example 3–Use of More Coordinate Functions in Example 1 (Cont’d) 6 4 N = 5 N =
Example 3–Use of More Coordinate Functions in Example 1 (Cont’d) 7 6 N = 7 N =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/18/2011 for the course MAE 269A taught by Professor Ju during the Spring '11 term at UCLA.

### Page1 / 27

Lecture19-Prof.Ju - CEE M237A MAE M269A Lecture 19 The Ritz...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online