ANSYS Tutorial. Modal Analysis

Transcription

1 ANSYS Tutorial Slides to accompany lectures in Vibro-Acoustic Desin in Mechanical Systems 2012 by D. W. Herrin Department of Mechanical Enineerin Lexinton, KY Tel: Modal Analysis Modal/Harmonic Analysis Usin ANSYS Used to determine the natural frequencies and mode shapes of a continuous structure Dept. of Mechanical Enineerin 2 Acoustic Desin 1

2 Review of Multi DOF Systems Modal/Harmonic Analysis Usin ANSYS x 1 x 2 K 1 K 2 F 1 F 2 M 1 M 2 K 3 C 1 C 2 C 3 Expressed in matrix form as [ M ]{ u } + [ C]{ u } + [ K]{ u} = { F} Dept. of Mechanical Enineerin 3 Acoustic Desin Review of Multi DOF Systems Modal/Harmonic Analysis Usin ANSYS [ M ]{ u } + [ C]{ u } + [ K]{ u} = { F} The mass, dampin and stiffness matrices are constant with time The unknown nodal displacements vary with time Dept. of Mechanical Enineerin 4 Acoustic Desin 2

3 Modal Analysis Modal/Harmonic Analysis Usin ANSYS A continuous structure has an infinite number of derees of freedom The finite element method approximates the real structure with a finite number of DOFs N mode shapes can be found for a FEM havin N DOFs Modal Analysis ü Process for determinin the N natural frequencies and mode shapes Dept. of Mechanical Enineerin 5 Acoustic Desin Modal Analysis Modal/Harmonic Analysis Usin ANSYS Given suitable initial conditions, the structure will vibrate ü at one of its natural frequencies ü the shape of the vibration will be a scalar multiple of a mode shape Given arbitrary initial conditions, the resultin vibration will be a ü Superposition of mode shapes Dept. of Mechanical Enineerin 6 Acoustic Desin 3

4 Modal Analysis Modal/Harmonic Analysis Usin ANSYS Determines the vibration characteristics (natural frequencies and mode shapes) of a structural components Natural frequencies and mode shapes are a startin point for a transient or harmonic analysis ü If usin the mode superposition method Dept. of Mechanical Enineerin 7 Acoustic Desin Mode Shape of a Thin Plate (240 Hz) Modal/Harmonic Analysis Usin ANSYS Dept. of Mechanical Enineerin 8 Acoustic Desin 4

5 Mode Extraction Methods Modal/Harmonic Analysis Usin ANSYS Subspace Block Lanczos PowerDynamics Reduced Unsymmetric Damped and QR damped (Include dampin) Dept. of Mechanical Enineerin 9 Acoustic Desin Steps in Modal Analysis Build the model Modal/Harmonic Analysis Usin ANSYS ü Same as for static analysis ü Use top-down or bottom-up techniques Apply loads and obtain solution ü Only valid loads are zero-value displacement constraints ü Other loads can be specified but are inored Expand the modes and review results Dept. of Mechanical Enineerin 10 Acoustic Desin 5

6 Modal/Harmonic Analysis Usin ANSYS b = 43 in h = 5 in In-Class Exercise E = 30E6 psi 2 lb s 3 ρ= 8.031E 4 in in 360 inches Dept. of Mechanical Enineerin 11 Acoustic Desin In-Class Exercise Modal/Harmonic Analysis Usin ANSYS Set element type to BEAM188 Set the appropriate material constants and section properties Create Keypoints at the start and end of the beam and a Line between them Dept. of Mechanical Enineerin 12 Acoustic Desin 6

7 Create Three Keypoints Modal/Harmonic Analysis Usin ANSYS Preprocessor > Modelin - Create > Keypoints > In Active CS Enter the followin values for keypoint 1 NPT=1, x=0, y=0 z=0 <Apply> Enter the followin values for keypoint 2 NPT=2, x= 180, y=0 z=0 <Apply> Enter the followin values for keypoint 3 NPT=3, x= 360, y=0 z=0 <Apply> <Okay> Dept. of Mechanical Enineerin Acoustic Desin Create Lines Between Keypoints Modal/Harmonic Analysis Usin ANSYS Preprocessor > Modelin - Create > Lines > Straiht Line Select KP 1 and 2 in raphics window Select KP 2 and 3 in raphics window <Okay> Dept. of Mechanical Enineerin Acoustic Desin 7

8 Mesh the Lines to Create Elements Modal/Harmonic Analysis Usin ANSYS Preprocessor > Meshin - Size Controls > Lines - All Lines > Size = 5 <Okay> Preprocessor > Meshin - Mesh Lines > Pick All <Okay> Dept. of Mechanical Enineerin Acoustic Desin Mesh the Line and Apply B.C.s Modal/Harmonic Analysis Usin ANSYS Fix the Keypoint at the riht end of the beam Dept. of Mechanical Enineerin 16 Acoustic Desin 8

9 Set Solution Options Modal/Harmonic Analysis Usin ANSYS Chane the analysis type to Modal ü Solution > Analysis Type > New Analysis ü <Modal> Set the analysis options ü Solution > Analysis Options ü Extract 10 mode <OK> ü Enter <1500> for the endin frequency Dept. of Mechanical Enineerin 17 Acoustic Desin Set Solution Options Modal/Harmonic Analysis Usin ANSYS At this point, you have told ANSYS to find a particular quantity of modes and to look within a particular frequency rane. If ANSYS finds that quantity before it finishes the frequency rane, it will stop the search. If ANSYS does not find that quantity before finishin the frequency rane, then it will stop the search. Dept. of Mechanical Enineerin 18 Acoustic Desin 9

10 Set Solution Options Modal/Harmonic Analysis Usin ANSYS Solve the load set ANSYS enerates a substep result for each natural frequency and mode shape Dept. of Mechanical Enineerin 19 Acoustic Desin Postprocessin Modal/Harmonic Analysis Usin ANSYS List results summary ü General Postproc > List Results > Results Summary Read results for a substep ü General Postproc > Read Results > First Set ü Plot deformed eometry ü General Postproc > Read Results > Next Set ü Plot deformed eometry Dept. of Mechanical Enineerin 20 Acoustic Desin 10

11 Harmonic Response Analysis Modal/Harmonic Analysis Usin ANSYS Solves the time-dependent equations of motion for linear structures underoin steady-state vibration All loads and displacements vary sinusoidally at the same frequency F = Fsin( ω t+φ ) i F = Fsin( ω t+φ ) j 1 2 Dept. of Mechanical Enineerin 21 Acoustic Desin Harmonic Response Analysis Modal/Harmonic Analysis Usin ANSYS Analyses can enerate plots of displacement amplitudes at iven points in the structure as a function of forcin frequency Dept. of Mechanical Enineerin 22 Acoustic Desin 11

12 Forced Response Modal/Harmonic Analysis Usin ANSYS Apply a 1.0 N load at the left end of the beam New Analysis > Harmonic Set the Analysis Options ü Set the solution method to Mode Superposition ü Set the DOF printout format to Amplitude and phase <OK> ü Set the number of modes to 10 <OK> Dept. of Mechanical Enineerin 23 Acoustic Desin Forced Response Modal/Harmonic Analysis Usin ANSYS Set the frequency substeps ü Solution > Load Step Opts Time Frequency > Freq and Substeps ü Set the Harmonic Frequency Rane to between 0 and 50 Hz ü Set the number of substeps to 100 ü Set to Stepped Dept. of Mechanical Enineerin 24 Acoustic Desin 12

13 Forced Response Modal/Harmonic Analysis Usin ANSYS Set the dampin ü Solution > Load Step Opts Time Frequency > Dampin ü Set the Constant Dampin Ratio to 0.01 Solve the model Dept. of Mechanical Enineerin 25 Acoustic Desin Expansion Pass Modal/Harmonic Analysis Usin ANSYS Finish Solution > Analysis Type > Expansion Pass Dept. of Mechanical Enineerin 26 Acoustic Desin 13

14 Expansion Pass Setup Modal/Harmonic Analysis Usin ANSYS Solution > Load Step Opts > Expansion Pass > Sinle Expand > Rane of Solu s 100 Important if yes the files are hue 50 Solution > Solve > Current LS Dept. of Mechanical Enineerin 27 Acoustic Desin Forced Response Modal/Harmonic Analysis Usin ANSYS Enter time history postprocessor > Define Variables Define New Variables Graph Variables List Variables and print out to file Dept. of Mechanical Enineerin 28 Acoustic Desin 14

15 Create Nodes Modal/Harmonic Analysis Usin ANSYS Preprocessor > Modelin - Create > Nodes > In Active CS Enter the followin values for Node 1 NPT=1, x=180, y=-10 z=0 <Apply> Dept. of Mechanical Enineerin Acoustic Desin Add Vertical Truss Member Modal/Harmonic Analysis Usin ANSYS Preprocessor > Element type > Add/Edit/Delete <Add> <Okay> Select Link 180 <Close> Preprocessor > Real Constants > Add/Edit/Delete <Add> <Okay> to select type 1 Enter the values A= 10 in 2 <Okay> Dept. of Mechanical Enineerin 30 Acoustic Desin 15

16 Set Element Attributes Modal/Harmonic Analysis Usin ANSYS Modelin > Create > Elements > Elem Attributes Select appropriate material properties and real constant table Preprocessor > Modelin - Create > Elements > Auto-Numbered-Thru Nodes Select appropriate nodes and apply Dept. of Mechanical Enineerin 31 Acoustic Desin 16