(Solved): STRUCTURAL AND MECHANICAL VIBRATIONS   A multi DOF vibratory system shown in Figure 4 is co ...

STRUCTURAL AND MECHANICAL VIBRATIONS

 

A multi DOF vibratory system shown in Figure 4 is composed of severak mass, spring and damping elements. k7 F2(1) x3(1) x2(1) k6 wwwwwww c6 k2 5 www www m? c5 U 3 k4 x4(1) xl(t) kl Figure 4 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. MATLAB Coding: Write a code to e. Apply modal analysis to the mass and stiffness matrices. Do NOT use the built in function "eigen values or eigen vectors". f. Using the modal vectors that you calculated in (c), write a code to check the orthogonality of the modes. System parameters: k? = = ky = 26519.2 N/m, m? = =m4 = 450 kg, C?1 =.= C7 = 1000 Ns/mm F1(0) my m? www- 3 m? k3