modal mass is needed in all applications where the frequencyresponsefunction(FRF)(ortheimpulsere-sponsefunction(IRF))hastobeconstructedfromthe modal parameters, such as structural modification, health-monitoring applications, and damage detection [1–4,10]. Amodeshapeissaidtobemass-normalizedwhenthe modalmassisdimensionless,i.e., m 1.Onthecontrary,a
  • %develop modal matrix for i=1:ms . for j=1:ms ph(i,j)=p1(i,j)/sqrt(L(j,j)); end end . disp(‘ Natural frequencies in rad/sec’) disp(omega) disp(‘ normalized modal vector’) disp(ph) ph’*m*ph %give alpha and beta alpha=0.6978; beta=9.4e-4; disp(‘ damping matrix’) cd=alpha*m+beta*k; cd . for i=1:ms zeta(i)=0.5*(alpha/omega(i)+beta*omega(i)); end

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    into a matrix Φ allows the matrices M and K to be diagonalized. Specifically, the eigenvectors are mass-normalized such that: ΦT MΦ = I and ΦT KΦ = Ω2 (3) The matrix Φ can be intuitively described as a matrix which trans-forms between object space and mode space: each column of Φ contains the shape of a normal mode, while ΦT f ...

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    Figure 4.8.1 Normalized steady-state energy versus change in modes' frequencies 41 ... M Structural mass matrix ... Diagonal matrix of modal frequencies . TT .

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    damped modal analyses as well as substructure generation. In its most general form, the damping matrix is composed of the following components. E ij 1 1 1 11 2 2 1 [M] ( g)[K] [M ] [( g g )[K ]] [C ] 1 [C [C]] [G ] ma m e v g N N N mm i j j j k i j k N ml ml D E D E : : : : ¦ ¦ ¦ ¦¦ (1) where: [C] = structure damping matrix, α = mass matrix

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