MEEN363_HW03_Problems_Spring2023_Final (2)

.pdf

School

Texas A&M University *

*We aren’t endorsed by this school

Course

363

Subject

Mechanical Engineering

Date

Jan 9, 2024

Type

pdf

Pages

2

Uploaded by MateFreedom11959

Report
MEEN 363 Dynamics and Vibrations (Spring 2023) Dr. Yong Joe Kim and Ms. Wanyu Xu Assigned on 02/09/2023 Due: 11:59 pm on 02/16/2023 (Thursday) Homework Submission Instructions: An electric PDF copy of your homework needs to be submitted through Canvas by 11:59 PM on each due date. A scanned PDF copy of your handwritten homework is acceptable. Use the following file naming convention: HWXX_MEEN363_ Sp2023_LastName_FirstName.pdf where XX represents the homework number (e.g., 01 for homework #1). If you are requested to submit your Matlab or Python code along with the PDF copy , your code should be named as HWXX_MEEN363_Sp2023_LastName_FirstName_PYY.m where YY represents the problem (or task) number (e.g., 02 for problem #2). Then, all the files need to be compressed in a single ZIP file with the following filename. You do not need to compress your file if you are submitting only one file. HWXX_MEEN363_Sp2023_LastName_FirstName.zip Do not use nicknames, as they can make it difficult to discern whom the grade is assigned to. No late submission will be accepted even in case of wrong file submissions . Homework 3: Particle Kinetics (3 Problems) 1. Figure 1 shows a block of mass, ࠵? that is attached to a wall through two ideal springs and a viscous damper. (a) Derive the equation of motion (EOM) for the block, assuming that ࠵? is measured from its unstretched spring position (USP). (b) Find the symbolic expressions of the undamped natural angular frequency, critical damping coefficient, and damping ratio. (c) Given ࠵? = 0.2࠵?࠵? , ࠵? ! = 15࠵?/࠵? , ࠵? " = 35࠵?/࠵? , ࠵?̇(࠵? = 0) = 4 ࠵?/࠵? , and ࠵?(࠵? = 0) = 0 , derive the time solutions to the EOM in the underdamped, critically damped, and overdamped cases. In each case, clearly show the expressions of the unknown coefficients in the homogeneous time solution. (d) Draw the vibration responses during the three undamped cycles (i.e., 3࠵? = 3 × "# $ ! ) in a single plot using the damping ratios of ࠵? = 0.25, 1, and 2.5. Discuss the vibration characteristics in terms of the damping ratios, temporal decaying rates, and oscillatory behaviors.
Figure 1 : 1-DOF mass-damper-spring system. 2. A rotary air compressor with a mass of ࠵? = 100 ࠵?࠵? is rigidly mounted on a cart with a mass of ࠵? = 600 ࠵?࠵? as shown in Figure 2 . The undamped, natural angular frequency is measured as ࠵? % = 314 ࠵?࠵?࠵?/࠵? . A free vibration response in the horizontal direction (i.e., ࠵? -direction) is measured and shown in Figure 3 . Find the approximate viscous damping coefficient of the system in ࠵? ∙ ࠵?/࠵? using the Logarithmic Decrement. Figure 2 : Rotary air compressor on a cart. Figure 3 : Free vibration response. 0 0.05 0.1 0.15 0.2 0.25 0.3 Time [s] -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Displacement [m]
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help