Dynamic Responses - Mechanics of Structures: Variational and Computational Methods - page 645

FIGURE P10.16

10.18 Use the lumped mass matrix of Problem 10.2 to find the natural frequencies of the
frame of Fig. P10.1.

Answer: ω = 546 , ω = 1479 , ω = 5801 , ω = 8606 , ω = 20 047 , ω = 34 536 .

1 2 3 4 5 6

10.19 Use the condensed stiffness and mass matrices of Problem 10.3 to find the natural
frequencies of the frame of Fig. P10.1.

Answer:

Consistent mass matrix Lumped mass matrix

ω 1 = 663 , ω 2 = 1825 , ω 1 = 559 , ω 2 = 1499

ω = 24 150 , ω = 52 574 , ω = 19 663 , ω = 34 045

3 4 3 4