MEM423Sp10_11.2.sDOF

MEM423Sp10_11.2.sDOF - MEM423 Mechanics of Vibrations...

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

View Full Document Right Arrow Icon
MEM423 Mechanics of Vibrations (1.10, 2.1-2.3, 2.6) Dr. Ajmal Yousuff Dept. Mech. Engg. & Mechanics Drexel University
Background image of page 1

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

View Full DocumentRight Arrow Icon
Vibrations (1-DOF) Degrees of Freedom: The (minimum # of) variables needed to describe the dynamics of the system. need not be unique. Yousuff MEM423 Vibrations 2 mass support spring support (fixed) Elastic rod M 1 2 support (pinned) rigid rod x K
Background image of page 2
Spring Consider an ideal spring: Mass-less Linear No damping Yousuff MEM423 Vibrations 3 F x reference F kx Slope = k k:force/unit distance
Background image of page 3

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

View Full DocumentRight Arrow Icon
Illustration (static) Yousuff MEM423 Vibrations 4 s reference m Free Body Diagram F = ks W = mg mg ks  If m (or, W = mg) is known, and s is measured, If k and s are known, / k mg s W
Background image of page 4
Dynamics Yousuff MEM423 Vibrations 5 s unstrectched m f(t) X (>0) equilibrium Newton’s 2 nd Law : (mass)(acceleration) = (sum of external forces)
Background image of page 5

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

View Full DocumentRight Arrow Icon
Equation of Motion Yousuff MEM423 Vibrations 6 2 2 ( ) ( ) dx m mg k x s f t dt But mg = ks (static equilibrium)
Background image of page 6
Solution Rewrite: Complementary solution: aux. eqn.: 2 (with ( ) 0, and ) k ft m
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

MEM423Sp10_11.2.sDOF - MEM423 Mechanics of Vibrations...

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

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