Homework 23 Solution

Homework 23 Solution - Lecture 23 MEEN 357 Homework...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 23 MEEN 357 Homework Solution 1 Lecture-23-Homework-Solution.doc RMB 1 u 1 m 1 k 2 m 2 k 2 u 3 k 3 u 3 m 5 k 4 m 4 k 4 u 1. Consider the four degree of freedom vibrating system shown in the following figure. The equations of motion of this system are () ( ) 2 1 11 1 2 2 1 2 2 2 22 2 1 3 3 2 2 2 3 33 3 2 4 4 3 2 2 4 44 4 3 5 4 2 du mk u k u u dt u u k u u dt u u k u u dt u u k u dt =− + + + (23.1) a. Derive the normal form of the system (23.1). Solution Define
Background image of page 1

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

View Full DocumentRight Arrow Icon
Lecture 23 MEEN 357 Homework Solution 2 Lecture-23-Homework-Solution.doc RMB 1 2 1 1 2 1 1 2 2 2 2 3 2 2 2 4 5 3 3 6 3 2 3 7 2 4 8 4 4 2 4 2 du dt u du du dt x du dt x u dt x du x d dt dt x du u dt dt x du dt x u dt x du du dt dt dt ⎡⎤ ⎢⎥ == = ⎣⎦ x x (23.2) Next, use the differential equations (23.1) to write (23.2) 2 as () 1 2 12 1 11 13 1 2 4 3 3 22 21 32 31 53 3 6 3 5 3 4 3 43 33 4 5 4 4 44 du dt x kk uu u mm xx x du x dt k k x x d du x dt dt k k k m du dt k k u −+ −− +− x 4 37 5 3 8 5 4 75 7 k x x m x k k x
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/28/2010 for the course MEEN 357 taught by Professor Anamalai during the Fall '07 term at Texas A&M.

Page1 / 6

Homework 23 Solution - Lecture 23 MEEN 357 Homework...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online