23_trussbwa_04

23_trussbwa_04 - Truss Structures - Natural Frequency...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Frequency Manipulation via SDP Brian W. Anthony Robert M. Freund Truss Structures - Natural 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
7
Background image of page 2
8 Background : Mechanical Systems
Background image of page 3

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

View Full DocumentRight Arrow Icon
Simple Mechanical System m 1 u 1 k 1 9
Background image of page 4
10
Background image of page 5

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

View Full DocumentRight Arrow Icon
System wants to vibrate when forced. 0 2 4 6 8 10 12 14 16 18 20 0 0.5 1 1.5 2 2.5 3 Frequency (Hz or Cycles/Sec) Amplitude 1 DOF System (k/m) .5 Natural Frequencies – How a Mechanical Examples • Ball on a string • Beam(s) • For a simple mechanical systems it is relatively easy to systematically effect a change in the natural frequency. 11
Background image of page 6
Beam Vibration Narrow Beam How would we change the frequency of vibration? Beam Vibration Narrow Beam Narrow Beam - Natural Frequency = 5.6 Hz Narrow and Short Beam - Natural Frequency = 11.7 Hz Wide Beam - Natural Frequency = 7.8 Hz 12
Background image of page 7

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

View Full DocumentRight Arrow Icon
Another Mechanical System F(t) m 2 m 3 m 1 u 1 k 1 k 2 k 3 u 2 u 3 Write Newton’s Law for Each Mass F = ma Another Mechanical System F(t) m 2 m 3 m 1 u 1 k 1 k 2 k 3 u 2 u 3 m 1 (d 2 u 1 /dt 2 ) + k 1 u 1 + k 2 (u 1 2 ) = 0 m 2 (d 2 u 2 /dt 2 ) + k 2 (u 2 1 ) + k 3 (u 2 3 ) = 0 m 3 (d 2 u 3 /dt 2 ) + k 3 (u 3 2 ) = F(t) M (d 2 U /dt 2 ) + KU = F (t) The Dynamics Model (The Equations of motion). In Matrix Form -u -u -u -u 13
Background image of page 8
Equations of Motion M K are the natural frequencies of vibration (squared). • The Eigenvectors of M K are the mode shapes (the relative displacement of each degree of freedom) M(d 2 U /dt 2 ) + KU = F(t) The Equations of motion
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/04/2011 for the course ESD 15.094 taught by Professor Jiesun during the Spring '04 term at MIT.

Page1 / 35

23_trussbwa_04 - Truss Structures - Natural Frequency...

This preview shows document pages 1 - 10. Sign up to view the full document.

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