This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ME 563 Mechanical Vibrations Lecture #13 Multiple Degree of Freedom Modal Coordinate Transformation What Did We Learn? 1 By making the assumption, {x(t)}={A}e st , we observed that the free response was actually a sum of the modes of vibration: If we write this differently, we reveal the most important thing about this course: Coordinate Transformation 2 The solution for the free response is actually a coordinate transformation in disguise: If this is the form of the solution, why not use it to begin with? Generalized coordinates (Physical DOFs) Principal coordinates (Modal DOFs) Modal transformation matrix (Modal vectors) Modal Solution Method 3 Consider the case again with no damping: The equations of motion have been converted to modal equations of motion. Are these equations easier to solve? Orthogonality of the Modes 4 The equations are easier to solve provided the modal vectors are orthogonal with respect to the system matrices: This final equation indicates that two different modes...
View
Full
Document
This document was uploaded on 12/23/2011.
 Fall '09

Click to edit the document details