STRUCTURAL AND MECHANICAL VIBRATIONS QUESTION A multi DOF vibratory system shown in Figure 4 is composed of several mass
Posted: Tue Jun 07, 2022 1:39 pm
STRUCTURAL AND MECHANICAL VIBRATIONS QUESTION
A multi DOF vibratory system shown in Figure 4 is composed of several mass, spring and damping elements.
(System parameters: π1 = β― = π7 = 26519.2 π/π, π1 = β― = π4 = 450 ππ, π1 = β¦ = π7 = 1000 ππ /πm)
a. Derive the equation of motion of the system by applying Lagrange equations.
b. Calculate the natural frequencies by applying βmodal analysisβ.
c. Define and draw the mode shapes of free, undamped motion.
d. Using the concept of Generalized Mass, examine the orthogonality of the modal vectors.
x2(t) k6 wwwwww k2 ΡΠ± 5 www k7 mβ www S kl F2(t) www c5 k4 Fl(t) mβ my www- m4 보 c4 k3 cl c7 wwwww c3 x3(t) x4(t) xl(t)
- Structural And Mechanical Vibrations Question A Multi Dof Vibratory System Shown In Figure 4 Is Composed Of Several Mass 1 (155.01 KiB) Viewed 32 times
(System parameters: π1 = β― = π7 = 26519.2 π/π, π1 = β― = π4 = 450 ππ, π1 = β¦ = π7 = 1000 ππ /πm)
a. Derive the equation of motion of the system by applying Lagrange equations.
b. Calculate the natural frequencies by applying βmodal analysisβ.
c. Define and draw the mode shapes of free, undamped motion.
d. Using the concept of Generalized Mass, examine the orthogonality of the modal vectors.
x2(t) k6 wwwwww k2 ΡΠ± 5 www k7 mβ www S kl F2(t) www c5 k4 Fl(t) mβ my www- m4 보 c4 k3 cl c7 wwwww c3 x3(t) x4(t) xl(t)