QuestionQuestion

Transcribed TextTranscribed Text

1. A system is vibrating with very small angle 0, which is shown in figure 1 with massless lever a =0.8 m and b = 1 m and mass m1 = 1.5 kg and m2 = 2.0 kg. A stiffness k = 100 N/m and a damper c = 0.5 N/m-s are vertically connected to mi and m2, respectively. The force f = 10 N cos(2t) / / m2 k f b c m, a 45° / 7 4 X Figure 1. Problem 1 a) Derive the equation of motion in terms of coordinate y. b) Find the natural frequency and damping ratio. 2. A machine is subjected to harmonic ground excitation. The driving frequency f = 2 Hz. The machine with base isolator can be modeled a SDOF system. The mass is, m = 500kg and the damping ratio is E = 0.05. a) Calculate the damping coefficient. b) Calculate the corresponding relative displacement c) Determine the stiffness of the base isolator so that the acceleration of the machine can be reduced to 1/2 of the level when the stiffness is considered to be infinity. 3. An under-damped 2-DOF system has mass and stiffness matrix M and K. We also know that the system has damping ratio E1 = 0.5 and E2 = 0.4. The damping matrix is written as a) Try to find the coefficients a., ß and Y- b) Find if this system proportionally damped? 4. Write the equation of motion of the system shown in figure 2. a) Calculate the natural frequency and modal shape by assuming c = 0, where the rotating stiffness k1 = k2 = k; the moment of inertia J1 = 3 J2. 01 w 02 . V k1 J1 k2 J2 2/1 c Figure 2 Problem 4 5. A system has mass matrix M = 0 1 4 0 and eigenvector matrix U = "1 U2 0.9673 0.2535 0.9979 -0.0654 And the natural frequencies of the system are: Onl = 1.3582 and On2 = 6.3761. a) Normalize U with respect to M. (Hint: Uc is an eigenvector of M-K. Let =1) 7. A system has = and K = -100 400 -100 100 and its natural frequencies are 50 and 150 respectively. Check which of the following can be eigenvectors of matrix M-1/2 KM-1/2 2 Suppose this system has initial conditions: x(0) 2 and x(0) = {-0.05} 0 = Calculate the responses of displacements. 8. a) Find the dynamic magnification factor (amplitude of the transfer function) for a first order vibration system = = - - (p8) and E are respectively the natural frequency and damping ratio of this system. b) if equation (p8) is the equation of a modal response of one part of a complex conjugate pair, then can you find the transfer function of this particular mode? plot the transfer function by letting E = 0.3 and On = 10.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $100.00
    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mechanical Engineering Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats