In this solution some basic concepts and formulas of Vibration Mechanics are used. For more information, refer to any standard textbook or drop a comment below. Please give a Thumbs Up, if solution is helpful.
Solution :
NOTE : Feel free to ask further queries. Your positive rating would be appreciated and motivate me !
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www Problem 5 (20%) For the system shown in Figure...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2 For the system shown in Figure...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
1. A two story building is represented in the figure below by a lumped mass systen in which m1 = m2 and k1 = k2. The ground is given a harmonic motion y Ysin at. Draw the appropriate free body diagrams. (5 points) a. b. Write the equations of motion in matrix form. (5 points) c. Solve for the natural frequencies and mode shapes. (10 points) d. Solve for the displacement amplitude response of xi and x2. (10 points)
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
Problem 6: For the two systems shown below, separately, identify the degrees of freedom and then write the equations of motion, respectively. Also, for each system, determine the natural frequency and damping ratio. The two systems shown are set into motion via initial condition. For the first figure of problem 6 (the circular disc), the disc is performing fixed axis rotation about its center of mass, G. It has a radius of gyration kG about the axis through the center...
MatLab analysis preferred, but please show the process. II) 3-DOF Torsional System Using matrix algebra, analyze the natural frequencies of the following 3-DOF shaft system. First setup the equations of motion, express the system in matrix form, and then use MATLAB to calculate the natural frequencies and the mode shapes. K2 K3 K4 J1 J2 J3 Data: J: = 500 lb.in.s- J2 750 lb.in.s2 J3 1000 lb.in.s? K1-2x106 lb.in/rad K2 106 Ib.in/rad K3 106 Ib.in/rad K4 2x106 lb.in/rad
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
1. For the system shown in Figure 1. in determine the equations of motion taking degrees of freedom 01,02, X3, moment of inertia of slender rod about the center is 1G = m (10 points). 3 to m ki . > K2 Figure 1 Figure 1