有限元模态分析--ANSYS.ppt
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1、Modal Analysis,Module 2,July 22, 2004 Inventory #002110 2-2,Module 2 Modal Analysis,A. Define modal analysis and its purpose. B. Discuss associated concepts, terminology, and mode extraction methods. C. Learn how to do a modal analysis in ANSYS. D. Work on one or two modal analysis exercises.,July 2
2、2, 2004 Inventory #002110 2-3,Modal Analysis A. Definition & Purpose,What is modal analysis? A technique used to determine a structures vibration characteristics: Natural frequencies Mode shapes Mode participation factors (how much a given mode participates in a given direction) Most fundamental of
3、all the dynamic analysis types.,July 22, 2004 Inventory #002110 2-4,Modal Analysis Definition & Purpose,Benefits of modal analysis Allows the design to avoid resonant vibrations or to vibrate at a specified frequency (speakers, for example). Gives engineers an idea of how the design will respond to
4、different types of dynamic loads. Helps in calculating solution controls (time steps, etc.) for other dynamic analyses. Recommendation: Because a structures vibration characteristics determine how it responds to any type of dynamic load, always perform a modal analysis first before trying any other
5、dynamic analysis.,July 22, 2004 Inventory #002110 2-5,General equation of motion: Assume free vibrations and ignore damping: Assume harmonic motion ( i.e. ) The roots of this equation are i2, the eigenvalues, where i ranges from 1 to number of DOF. Corresponding vectors are ui, the eigenvectors.,Mod
6、al Analysis B. Terminology & Concepts,July 22, 2004 Inventory #002110 2-6,Modal Analysis Terminology & Concepts,The square roots of the eigenvalues are wi , the structures natural circular frequencies (radians/sec). Natural frequencies fi are then calculated as fi = wi /2p (cycles/sec). It is the na
7、tural frequencies fi that are input by the user and output by ANSYS. The eigenvectors ui represent the mode shapes - the shape assumed by the structure when vibrating at frequency fi.,July 22, 2004 Inventory #002110 2-7,Modal Analysis Terminology & Concepts (cont.),Mode Extraction is the term used t
8、o describe the calculation of eigenvalues and eigenvectors. Mode Expansion has a dual meaning. For the reduced method, mode expansion means calculating the full mode shapes from the reduced mode shapes. For all other methods, mode expansion simply means writing mode shapes to the results file.,July
9、22, 2004 Inventory #002110 2-8,Modal Analysis - Terminology & Concepts Mode Extraction Methods,Several mode extraction methods are available in ANSYS: Block Lanczos (default) Subspace PowerDynamics Reduced Unsymmetric Damped (full) QR Damped Which method you choose depends primarily on the model siz
10、e (relative to your computer resources) and the particular application.,July 22, 2004 Inventory #002110 2-9,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Block Lanczos,The Block Lanczos method is recommended for most applications. Efficient extraction of large number of modes (40
11、+) in most models Typically used in complex models with mixture of solids/shells/beams etc. Efficient extraction of modes in a frequency range Handles rigid-body modes well,July 22, 2004 Inventory #002110 2-10,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Subspace,When extracting
12、 a small number of modes (40) in similar size models, the subspace method can be more suitable. Requires relatively less memory but large diskspace May have convergence problems when rigid body modes are present. Not recommended when constraint equations are present. Generally superseded by Block La
13、nczos,July 22, 2004 Inventory #002110 2-11,Modal Analysis - Terminology & Concepts Mode Extraction Methods - PowerDynamics,For large (100K+ DOF) models and a small number of modes ( 20), use the PowerDynamics method. It can be significantly faster than Block Lanczos or Subspace, but: Requires large
14、amount of memory. May not converge with poorly shaped elements or an ill-conditioned matrix. May miss modes (No Sturm sequence check) Recommended only as a last resort for large models.,July 22, 2004 Inventory #002110 2-12,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Reduced,For
15、 models in which lumping mass does not create a local oscillation, typically beams and spars, use the Reduced method. Memory and disk requirements are low. In general fastest eigen solver Employs matrix reduction, a technique to reduce the size of K and M by selecting a subset of DOF called master D
16、OF. Reduction of K is exact but M loses some accuracy Accuracy of M depends on number and location of master DOF. Generally not recommended due to Expertise required in picking master DOF Efficient alternatives such as Block Lanczos reduced cost of hardware,July 22, 2004 Inventory #002110 2-13,Modal
17、 Analysis - Terminology & Concepts Mode Extraction Methods - Unsymmetric,The unsymmetric method is used for acoustics (with structural coupling) and other such applications with unsymmetric K and M. Calculates complex eigenvalues and eigenvectors: Real part is the natural frequency. Imaginary part i
18、ndicates stability - negative means stable, positive means unstable.,July 22, 2004 Inventory #002110 2-14,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Damped,Damping is normally ignored in a modal analysis, but if its effects are significant, the Damped method is used. Typical a
19、pplication is rotor dynamics, where gyroscopic damping effects are important. Two ANSYS elements, BEAM4 and PIPE16, allow gyroscopic effects to be specified in the form of real constant SPIN (rotational speed, radians/time). Calculates complex eigenvalues and eigenvectors: Imaginary part is the natu
20、ral frequency. Real part indicates stability - negative means stable, positive means unstable.,July 22, 2004 Inventory #002110 2-15,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Q-R damped,A second mode extraction method that considers damping effects is the Q-R Damped method. Fa
21、ster and more stable than the existing Damped Solver Works with poorly conditioned models All forms of damping allowed including damper elements Combines the best features of the real eigensolution method (Block Lanczos) and the Complex Hessenberg method (QR Algorithm) Outputs complex eigenvalues (
22、frequency and stability) and damping ratio of each mode Supports the use of a material dependent damping ratio MP,DMPR in a subsequent mode superposition harmonic analysis,July 22, 2004 Inventory #002110 2-16,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Q-R damped,MODOPT,QRDAMP,
23、NMODE,July 22, 2004 Inventory #002110 2-17,Modal Analysis - Terminology & Concepts Mode Extraction Methods - Q-R damped,Comparison Demonstrating the Superior Solution Performance of the QR Damped Mode Extraction Method,July 22, 2004 Inventory #002110 2-18,Modal Analysis - Terminology & Concepts Summ
24、ary for symmetric, undamped solvers,July 22, 2004 Inventory #002110 2-19,Modal Analysis C. Procedure,Four main steps in a modal analysis: Build the model Choose analysis type and options Apply boundary conditions and solve Review results,July 22, 2004 Inventory #002110 2-20,Modal Analysis Procedure
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