259355946-2009-CT-4140-Book-of-Slides.38

# 259355946-2009-CT-4140-Book-of-Slides.38 - 38 Forced...

• Notes
• 1

This preview shows page 1. Sign up to view the full content.

145 CT 4140 Structural Mechanics Faculty of Civil Engineering and Geosciences 2009 Delft, The Netherlands Forced Vibrations of a Fixed-Fixed String under General Forcing Multiplying the above equation by sin( β m x) and integrating from 0 to L, we obtain: ( ) ( ) ( ) 2 2 1 2 0 2 , sin L n n n n n d q x t x dx Q t dt AL ω β ρ Ψ + Ψ = = The general solution to the above equation reads: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 1 1 0 cos sin sin t n n n n n n n n n d t t t Q t d dt ω ω τ ω τ τ ω ω Ψ Ψ = Ψ + + Thus, we found the following expression that satisfies the equation of motion and the boundary conditions: ( ) ( ) ( ) ( ) 1 , sin with defined above n n n n w t x t x t β = = Ψ Ψ To find the unknown constants, we will use the initial conditions. Lecture 11 Forced Vibrations of a Fixed-Fixed String: General Forcing 146 CT 4140 Structural Mechanics Faculty of Civil Engineering and Geosciences 2009 Delft, The Netherlands Forced Vibrations of a Fixed-Fixed String under General Forcing Substituting the above solution into the initial conditions, we obtain: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 0 0 1 0, 0,
This is the end of the preview. Sign up to access the rest of the document.
• Fall '09
• Andrei V. Metrikine
• Structural Engineering, Dynamics Of Structures, SDOF, MDOF, Vibration, Trigraph, Boundary value problem, Civil Engineering and Geosciences, Fixed-Fixed String

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern