# Vibration Analysis

• Dec 15th 2008, 02:56 AM
samer_guirguis_2000
Vibration Analysis
Would someone help me understand what does this mean, knowing that I am not aquanted with topology, functional analysis or operator theory.
• Dec 15th 2008, 04:48 AM
Mush
Each linear operator (A) on a Hilbert Space has a corresponding adjoint operator (A*). This linear operator is self-adjoint if A =A*.
• Dec 15th 2008, 07:01 AM
samer_guirguis_2000
Thank you for you reply, but how can I relate this to a vibrating system?
• Dec 15th 2008, 10:43 AM
Opalg
Quote:

Originally Posted by samer_guirguis_2000
Thank you for you reply, but how can I relate this to a vibrating system?

Vibration analysis will probably be concerned with linear differential operators acting on some space of functions. These functions will probably be defined on some interval [a,b], and they will have an inner product $\langle f,g\rangle$, defined by $\langle f,g\rangle = \int_a^bf(t)g(t)\,dt$. A linear differential operator L acting on these functions will have an adjoint L*, defined by $\langle L^*f,g\rangle = \langle f,Lg\rangle$ for all f,g. Unsurprisingly, L is called selfadjoint if L*=L.

That is the mathematical setting for selfadjoint differential operators. If you want something more specific to vibration analysis, you'll have to give us a more concrete example of the sort of differential operators you're meeting in this theory.