Lecture 8 Modal Analysis

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1 Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal ANSYS, Inc. February 27, 2015

2 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal wll be covered. Chapter Contents: A. Bascs of Free Vbraton B. Theory and Assumpton C. Geometry D. Contact E. Soluton Setup F. Modal Results G. Vbraton Wth Prestress H. Workshop 8.1, Free Vbraton Machne Frame 2

3 A. Bascs of Free Vbraton The free vbraton analyss procedure s very smlar to performng a lnear statc analyss, so not all steps wll be covered n detal. The schematc setup for modal (free vbraton) s shown here. Later a prestressed modal setup wll be covered. 3

4 B. Theory and Assumptons The lnear equaton of moton for free, un-damped vbraton s Assume harmonc moton: M u K u 0 u sn t 2 u sn t Substtutng {u} and {u} In the governng equaton gves an egenvalue equaton: 2 K M 0 4

5 Theory and Assumptons As shown on prevous slde, for vbraton analyss, the natural crcular frequences and mode shapes are calculated from: Assumptons for modal analyss: [K] and [M] are constant: Lnear elastc materal behavor s assumed K 2 M 0 Small deflecton theory s used, and no nonlneartes ncluded [C] s not present, so dampng s not ncluded {F} s not present, so no exctaton of the structure s assumed The structure can be constraned or unconstraned Mode shapes { } are relatve values, not absolute 5

6 C. Geometry Modal analyss can employ any type of geometry: Sold bodes, surface bodes and lne bodes. The Pont Mass feature can be used: A pont mass adds mass wthout addtonal flexblty to the structure thus reducng the natural frequency (K/M)^0.5. Materal propertes: Young s Modulus, Posson s Rato, and Densty are requred. Structural and thermal loads are not avalable n free vbraton: If no supports (or partal) are present, rgd-body modes wll occur at or near 0 Hz. The choce of boundary condtons wll affect the mode shapes and frequences of the part. Carefully consder how the model s constraned. 6

7 D. Contact Contact regons are avalable n free vbraton analyses however contact behavor wll dffer for the nonlnear contact types: Contact Type Modal Analyss Intally Touchng Insde Pnball Regon Outsde Pnball Regon Bonded Bonded Bonded Free No Separaton No Separaton No Separaton Free Rough Bonded Free Free Frctonless No Separaton Free Free Frctonal Bonded Free Free All contact wll behave as bonded or no separaton n a modal analyss: If a gap s present: Nonlnear contacts wll be free (no contact). Bonded and no separaton contact wll depend on the pnball sze. 7

8 E. Soluton Setup Wthn Mechancal Analyss Settngs: Specfy the number of modes to fnd (default s 6). Optonally specfy a frequency search range (defaults from 0Hz to 1e+08Hz). Note: damped modal analyss s covered n the dynamcs course. Request addtonal result output f desred. 8

9 Soluton Setup When a soluton s complete, the soluton branch wll dsplay a bar chart and table lstng frequences and mode numbers. RMB to request the modes to be dsplayed (or select all). Indvdual mode shapes can be anmated. 9

10 F. Modal Results Modal Results: Because there s no exctaton appled to the structure the mode shapes are relatve values not actual ones. Mode shape results are mass normalzed. The same s true for other results (stress, stran, etc.). Because a modal result s based on the model s propertes and not a partcular nput, we can nterpret where the maxmum or mnmum results wll occur for a partcular mode shape but not the actual value. 10

11 G. Vbraton wth Pre-Stress Whle many prestressed modal examples appear n muscal nstruments (gutar strngs, drum heads, etc.), there are numerous engneerng applcatons where the ncluson of prestress effects are crtcal. Note: whle prestressng n tenson wll cause frequences to ncrease, compressve states can decrease natural frequences. 11

12 ... Vbraton wth Pre-Stress Setup a pre-stressed modal analyss n the schematc by lnkng a statc structural system to a modal system at the soluton level. Notce n the modal branch, the structural analyss result becomes an ntal condton. 12

13 ... Vbraton wth Pre-Stress The stress state of a structure under nfluences the modal soluton by modfyng the stffness of the structure. K x F o A lnear statc analyss s performed S o A stress stffness matrx s calculated from the structural analyss K S 2 M 0 The orgnal free vbraton equaton s modfed to nclude the [S] term 13

14 H. Workshop 8.1 Free Vbraton Workshop 8.1 Free Vbraton Analyss Goal: Investgate the vbraton characterstcs of the machne frame shown here by testng 2 sets of constrants. 14

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