有限元分析——谐响应

Harmonic Analysis - Terminology & Concepts
Equation of Motion
• General equation of motion:
Training Manual
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
Harmonic Analysis
A. Definition & Purpose
What is harmonic analysis? •
Training Manual
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
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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July 22, 2004 Inventory #002110 3-5
B. Terminology & Concepts
Training Manual
Nature of harmonic loads
Complex displacements
Equation of motion
Harmonic Analysis
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ψ
Real
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Harmonic Analysis - Terminology & Concepts
Complex Displacements
• Calculated displacements will be complex if:
Sinusoidally varying, at known frequencies. Phase angle ψ allows multiple, out-of-phase loads to be applied. Defaults to zero. All applied loads are assumed to be harmonic, including temperatures and gravity.
Topics covered:
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Solution methods
Ju来自百度文库y 22, 2004 Inventory #002110 3-6
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
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Output:
– Harmonic displacements at each DOF, usually out of phase with the applied loads. – Other derived quantities, such as stresses and strains.
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Harmonic Analysis
… Definition & Purpose
Why should you do a harmonic analysis? •
Training Manual
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
Nature of Harmonic Loads
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Imaginary
Training Manual
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
– Damping is specified. – Applied load is complex (i.e, imaginary part is non-zero).
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.
A. Define harmonic analysis and its purpose.
D. Work on a harmonic analysis exercise.
Harmonic Analysis
Module 3
July 22, 2004 Inventory #002110 3-2
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
& [M]{&&}+[C]{u}+[K]{u} = {F} u
• [F] and {u} are harmonic, with frequency ω:
{F} = {Fmax eiψ}eiωt = ({F}+ i{F2})eiωt 1 {u} = {umax eiφ}eiωt = ({u1}+ i{u2})eiωt
• Equation of motion for harmonic analysis:
(−ω2[M] + iω[C] + [K])({u1}+ i{u2}) = ({F}+ i{F }) 1 2
July 22, 2004 Inventory #002110 3-7
Harmonic Analysis - Terminology & Concepts
Harmonic Analysis
… Definition & Purpose
Harmonic analysis is used in the design of: •
Training Manual
DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1 DYNAMICS 8.1
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).
Module 3
Harmonic Analysis
Training Manual
B. Learn basic terminology and concepts underlying harmonic analysis.
C. Learn how to do a harmonic analysis in ANSYS.