26 Dynamics_Harmonic

26 Dynamics_Harmonic - Harmonic Analysis Module 3 Harmonic...

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Harmonic Analysis 3-2 Module 3 Harmonic Analysis A. Define harmonic analysis and its purpose. B. Learn basic terminology and concepts underlying harmonic analysis. C. Learn how to do a harmonic analysis in ANSYS.
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3-3 Harmonic Analysis A. What is harmonic analysis? A technique to determine the steady state response of a structure to sinusoidal ( harmonic ) loads of known frequency. Input: Harmonic loads (forces, pressures, and imposed displacements) of known magnitude and frequency. May be multiple loads all at the same frequency. Forces and displacements can be in-phase or out-of phase. Surface and body loads can only be specified with a phase angle of zero. Output: Harmonic displacements at each DOF, usually out of phase with the applied loads. Other derived quantities, such as stresses and strains. 3-4 Harmonic Analysis Harmonic analysis is used in the design of: Supports, fixtures, and components of rotating equipment such as compressors, engines, pumps, and turbomachinery. Structures subjected to vortex shedding (swirling motion of fluids) such as turbine blades, airplane wings, bridges, and towers.
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3-5 Harmonic Analysis Why should you do a harmonic analysis? To make sure that a given design can withstand sinusoidal loads at different frequencies (e.g, an engine running at different speeds). To detect resonant response and avoid it if necessary (by using dampers, for example). 3-6 Harmonic Analysis B. Topics covered: Equation of motion Nature of harmonic loads Complex displacements Solution methods
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3-7 General equation of motion: [F] and {u} are harmonic, with frequency ω : Equation of motion for harmonic analysis: Equation of Motion [] {}[] { } [] {} { } F u K u C u M = + + } { { } } {} { } { {} } {} { t i 2 1 t i i max t i 2 1 t i i max e ) u i u ( e e u u e ) F i F ( e e F F ω ω φ ω ω ψ + = = + = = [] [ ][] } {} {{ } { } ) F i F ( ) u i u )( K C i M ( 2 1 2 1 2 + = + + ω + ω 3-8
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26 Dynamics_Harmonic - Harmonic Analysis Module 3 Harmonic...

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