{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MEM423Sp10_11.2.sDOF

# MEM423Sp10_11.2.sDOF - MEM423 Mechanics of Vibrations(1.10...

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

MEM423 Mechanics of Vibrations (1.10, 2.1-2.3, 2.6) Dr. Ajmal Yousuff Dept. Mech. Engg. & Mechanics Drexel University

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

View Full Document
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 M 2 support (pinned) rigid rod x 1 support M 1 K 1 M 2 K 2 x 1 x 2
Spring Consider an ideal spring: Mass-less Linear No damping Yousuff MEM423 Vibrations 3 F x reference F kx F x Slope = k k: force/unit distance

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

View Full Document
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 ks
Dynamics Yousuff MEM423 Vibrations 5 s unstrectched m f(t) X (>0) equilibrium Newton’s 2 nd Law : (mass)(acceleration) = (sum of external forces)

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

View Full Document
Equation of Motion Yousuff MEM423 Vibrations 6 2 2 ( ) ( ) d x m mg k x s f t dt But mg = ks (static equilibrium)
Solution Rewrite:

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.

{[ snackBarMessage ]}