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Math Help - Vibration Analysis

  1. #1
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    Vibration Analysis

    In vibration analysis I found the terms: "self-adjoint and non-self-adjoint systems".
    Would someone help me understand what does this mean, knowing that I am not aquanted with topology, functional analysis or operator theory.
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    Each linear operator (A) on a Hilbert Space has a corresponding adjoint operator (A*). This linear operator is self-adjoint if A =A*.
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  3. #3
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    Thank you for you reply, but how can I relate this to a vibrating system?
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  4. #4
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    Quote Originally Posted by samer_guirguis_2000 View Post
    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.
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