2K α23 α33 5  2K α12 α13 α11 α  α32 α21 α22 α32 α31 α33 1 1 1 1 α 1 3 3   2K 1 3 5 First natural frequency and modal vector 1 MA A  r r ω2 r DA 1 A  r r ω2 r D K  Obtain Dynamic M matrix 1 1 1 2 0 0 2 2 1 D m m  1 3 3 0 2 0  2 6 3 2K 2K 1 3 5 0 0 1 2 6 5 Use basic Eqn to obtain first frequency DA 1 A  1 1 ω2 r Assume trial vector and substitute in the above Eqn. 1  u 1  1 Assumed vector is: 1 First Iteration 2 2 1 1 1 m 5m 2  6 3 1  2.2 2K 2K 2 5 1 6 2.6
α23 2K α33  5 2K α11 α12 α13 α  α21 α22 α32 α32 α31 α33 1 1 1 α   1 1 3 3 2K 1 3 5 First natural frequency and modal vector MA  1 A ω2 r r r DA  1 A ω2 r r r Obtain Dynamic matrix D  K M 1 1 1 2 0 0 2 2 1 D  m 1 3 3 0 2 0  m 2 6 3 2K 2K 1 3 5 0 0 1 2 6 5 Use basic Eqn to obtain first frequency DA  1 A ω2 1 1 r Assume trial vector and substitute in the above Eqn. 1  Assumed vector is: u 1  1 1 First Iteration 2 2 1 1 1  m 2 6 3 1  5m 2.2 2K 2K 6 2 5 1 2.6
Unit-7_Lect-4.docx