STRUCTURAL AND MECHANICAL VIBRATIONS QUESTION A multi DOF vibratory system shown in Figure 4 is composed of several mass

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STRUCTURAL AND MECHANICAL VIBRATIONS QUESTION

Structural And Mechanical Vibrations Question A Multi Dof Vibratory System Shown In Figure 4 Is Composed Of Several Mass 1 (155.01 KiB) Viewed 31 times

A multi DOF vibratory system shown in Figure 4 is composed of several mass, spring and damping elements.
(System parameters: 𝑘1 = ⋯ = 𝑘7 = 26519.2 𝑁/𝑚, 𝑚1 = ⋯ = 𝑚4 = 450 𝑘𝑔, 𝑐1 = … = 𝑐7 = 1000 𝑁𝑠/𝑚m)
a. Derive the equation of motion of the system by applying Lagrange equations.
b. Calculate the natural frequencies by applying “modal analysis”.
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.
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