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: 1 CE573 – Structural Dynamics Homework #10 1. 2 3 4 5 There is another approach to illustrate the forces acting on this system. In this second approach  called the D’Alembert’s approach—t he inertial forces (tangential and centrifugal) are shown on the figure. They are shown as acting in the direction opposite to associated accelerations. and the rest follows just as done above. 6 2. Using the interstory drifts as the coordinates, say 1 ∆ and 2 ∆ , the equations of motion for free vibration can be written as (remember the freebody diagrams and force balances we did in class): 1 1 2 2 2 story story k M M M M k ∆ ∆ + = ∆ ∆ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ ɺɺ Casting the problem of finding modal frequencies and modeshapes as an eigenvalue problem, the modal frequencies 1 ϖ and 2 ϖ will be those unique frequencies that will satisfy the characteristic equation, i.e. will be those unique frequencies that will satisfy the characteristic equation, i....
View
Full Document
 Spring '11
 various
 Linear Algebra, modal frequencies

Click to edit the document details