MA1 K A1  ω2 If system has two frequencies and MA1 K  ω12 A1 (13) MA2 K  ω22 A2 (14) AT AT Multiply Eqn.(13) by and Eqn.(14) by 2 1 AT  MA AT (15) ω2 1 2 1 2 1 AT MA AT KA  (16) ω2 1 1 2 1 2 Eqn.(15)-(16) MA AT 0  1 2 Above equation is a condition for mass orthogonality. KA2 A1T 0  Above equation is a condition for stiffness orthogonality. By knowing the first modal vector one can easily obtain the second modal vector based on either mass or stiffness orthogonality. This principle is used in the matrix iteration method to obtain the second modal vector and second natural frequency. This technique is referred as Sweeping technique
ω2 MA1  K A1 If system has two frequencies and ω12 MA1  K A1 (13) ω22 MA2  K A2 (14) Multiply Eqn.(13) by AT and Eqn.(14) by AT 2 1 ω2 AT MA  AT (15) 1 2 1 2 1 ω2 AT MA  AT KA (16) 1 1 2 1 2 Eqn.(15)-(16) AT MA  0 1 2 Above equation is a condition for mass orthogonality. A1T KA2  0 Above equation is a condition for stiffness orthogonality. By knowing the first modal vector one can easily obtain the second modal vector based on either mass or stiffness orthogonality. This principle is used in the matrix iteration method to obtain the second modal vector and second natural frequency. This technique is referred as Sweeping technique
Unit-7_Lect-4.docx