αV2 V1   V2  βV3 V3 0 V α β 1 1 0V2 0  0 0 1V3 SV1  S V1 where is referred as Sweeping matrix and is the trial  vector. New dynamics matrix is: D   DS s 1 A  1 2 ω2 2 The above Eqn. Converges to second natural frequency and second modal vector. This method of obtaining frequency and modal vectors between first and the last one is referred as sweeping technique. Examples: 2 For the Example problem 1, Find second natural frequency and modal vector of the system shown in the Fig.10 using matrix iteration method and Sweeping technique. Use flexibility influence co-efficients. For this example already the first frequency and modal vectors are obtained by matrix iteration method in Example 1. In this stage only how to obtain second frequency is demonstrated. First Modal vector obtained in Example 1 is: A1 1 2.61 A1 A  3 A 3.23 2 0 0 M 0  2 the mass matrix 0 0 1 Find sweeping matrix 0 α β S  1 0 0 0 0 1
V1 αV2  V2  V3 βV3  0 α β V 1 1  0 0V2 0 0 1V3  SV1 where  S is referred as Sweeping matrix and V1 is the trial vector. New dynamics matrix is:   DS D  1 A ω2 s 1 2 2 The above Eqn. Converges to second natural frequency and second modal vector. This method of obtaining frequency and modal vectors between first and the last one is referred as sweeping technique. Examples: 2 For the Example problem 1, Find second natural frequency and modal vector of the system shown in the Fig.10 using matrix iteration method and Sweeping technique. Use flexibility influence co-efficients. For this example already the first frequency and modal vectors are obtained by matrix iteration method in Example 1. In this stage only how to obtain second frequency is demonstrated. First Modal vector obtained in Example 1 is: A1 1 A1  A 2.61 A 3 3.23 2 0 0 M  0 2 the mass matrix 0 0 1 Find sweeping matrix 0 α β S  0 1 0 0 0 1
Unit-7_Lect-5.docx