模态有效质量的学习

1、17*32 Description of AnalysisThis analysis type (accessed with ANTYPE:MODAL) is used for natural frequency and mode shape detainination. Th已 equation of motion for an undamped system, expressed in matrix notation using the 日bov已 assumptions is:Mu + Ku = 0(17-37)Note that K: th已 structur已 stifi&i已铝 m

2、atrix, may include pr已stress effects (PSTRES;ON). For a discussion of the damped eigensolver CMO D OPT;DA1P or MODOPT; QRDAMP) see Ei或nvahi巳 and EiEEtivectcir Extr 日 cticin-For a linear systenk free vibrations wiD be harmonic of the form:u= 州匚时呷(17-38)where:qj = eigen* 已 ctor representing the mode s

3、hape of the ith natural frequency吨=ith natural circular :&已quency (radians per unit time) t = timeThus: Equaticin 17-37 becomes:(-叫勺 M + K)虬= (1739)This equality is satisfied if either (q. = 0 or if the determinant of (EC-异 ZJ) is zero. The first option is the trivial one an. to the mass matrix is s

4、elected (AIODOPT,: OFF):仲仲 j=1(17-42)If normalization of each eigenvector (cp) to 1.0 is selected (AIODOPT;: ON): (q)i is normalized such that its largest component is 1.0 (unity)-17.7*5* Participation Factors and Mode CoefficientsThe participation factors for the given excitation direction are defi

5、ned as:?i = 巾iM口forthe base excitation option(17-110)= ,?for the force excitation option(17-111)where:Yj = participation factor for the ith mode甲 i = eigenvector normalized using Equaticiti ”-42 (Nrmkey on the MO DO PT command has no effect)(D = vector describing the excitaiion dtrection (see Equati

6、ciii 17-112)(F = input force vectorTh已 vector describing th已 excitation dir已ction has th已 form:D = Te(17-112)where:口=国口疤.T10000-查)-(Y-Yof0100(X-Xo)T =001(Y-Yo)-(X-Xo)0000100000010_000001_DJ=excitation at DOF j in dire ction a; a maybe either X, Y, Z ,or rotations about one of these axesX: Y: Z = glo

7、bal Cart已sian coordinates of a point on th已 geometrjrXq： Yq： = global Cartesian coordinates of point about which rotations are done (reference point) (e = six possible unit vectorsTV巳 can calculate the statically 已equivalent actions at j 血已 to rigid-body displacements of th已 isEerenc 已 point using the concept of translation of ax 已 s |T (AV 已 aver and Johnston(29).17.78 Effective MassThe effective mass (output as EFFECTIVE MASS) for the F” mode (which is a. Junction of excitation direction) is (Clough and Penzien(SO):?i呢= 神 Mli巾 iNote from Equatioiithat巾?网巾 i=i(17-135)(17-136)2 _(17-135)(17-