An automobile is modeled as a simple four-degree-of-freedom system as shown in the accompanying figure. The...

Transcribed Image Text:

An automobile is modeled as a simple four-degree-of-freedom system as shown in the accompanying figure. The parameters of the model are as follows: 3 k k mi === equivalent damping coefficient for two shock absorbers (both front and back) equivalent stiffness of two springs (both front and back) === equivalent stiffness of two tires (both front and back) = combined mass of automobile body and motor I. = mass moment of inertia of combined mass of body and motor about its mass center G m2 = equivalent mass of two wheels (both front and back) Assuming small amplitudes of oscillation for the system, verify that the stiffness matrix K and damping matrix C are, respectively, and -k -k -k [441] 2k1 k(2) - k(2-4) k(l} + 1}) K = -k -k 2c C- c(2) - -kl (k + k) 0 C c(12 4) -C c(1} + 1) ch -ch [11] -c -c ch -cl 0 (k + k) k1 m, T m2 k2 93 91 888 G 12 k1 92 m2 94 k2 An automobile is modeled as a simple four-degree-of-freedom system as shown in the accompanying figure. The parameters of the model are as follows: 3 k k mi === equivalent damping coefficient for two shock absorbers (both front and back) equivalent stiffness of two springs (both front and back) === equivalent stiffness of two tires (both front and back) = combined mass of automobile body and motor I. = mass moment of inertia of combined mass of body and motor about its mass center G m2 = equivalent mass of two wheels (both front and back) Assuming small amplitudes of oscillation for the system, verify that the stiffness matrix K and damping matrix C are, respectively, and -k -k -k [441] 2k1 k(2) - k(2-4) k(l} + 1}) K = -k -k 2c C- c(2) - -kl (k + k) 0 C c(12 4) -C c(1} + 1) ch -ch [11] -c -c ch -cl 0 (k + k) k1 m, T m2 k2 93 91 888 G 12 k1 92 m2 94 k2