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ME 312 Project: Design for Vibration and Shock Suppression (Due Sunday 6/5/2012)

Introduction

To protect the electronic control module from fatigue and breakage, it is desirable to isolate the module from the vibration or shock induced in the car body by road and engine vibration. See Figure 1.

(a)
Figure 1. A schematic vibration system.

Model
Model this module vibration isolation system as a single-degree-of-freedom spring-mass-damper system with a moving base (Figure 1-b,c). The module ’s mass can be taken to be 0.5 kg. The car body on which the isolator mounted is modeled as the moving base. The base is subjected to harmonic or shock displacement conditions, y(t). The displacement excitations of the base can be approximated as
(a) (for harmonic loading) y(t)=(0.01)sin(200 t).
(b) (for shock loading )
i. y(t)=0.025 sin(100*p t) m for 0 < t < 0.01sec
ii. y(t)= 0 for t > 0.01 sec.

Objective and Constraints
Design a vibration and shock isolation systems (choose the parameters k and c for each system) to minimize module’s maximum displacement when subjected to the prescribed vibration and shock base excitation. Your design must also satisfy the following constraints:
(1) The maximum acceleration experienced by the hard drive should be less than 11g’s (g=9.8 m/s2) .
(2) Module’s static deflection (downward deflection caused by module weight) is less than 0.0050 m.
(3) k and c must be within the following ranges: 300 = k = 3500 N/m and 1= c = 500 N.s/m. Select k and c from Ref 2 if applicable or from a manufacturer catalog. Both k and c are assumed constants working at room temperature of 25oC.

Presentation of Results
In your report, include a table with your design choices for k and c and the resulting values of maximum deflection, maximum acceleration and static deflection.
In addition, create and show the following plots:
(1) Displacement ratio (T.R.) versus frequency ratio for harmonic loading only (similar to Figure 2.13 of Ref. 1).
(2) Force transmissibility versus frequency ratio for harmonic loading only (similar to Figure 2.14 of Ref. 1).
(3) Maximum acceleration versus frequency ratio.
(4) The displacement (x(t))) versus time. Plot it for at least 4 periods of oscillation.
(5) Use two values below and two values above the value you chose in your design.
(6) Compare the selected values of k and c for both loading conditions(i.e. for harmonic loading and shock loading). Are they similar? Why?

References:
(1) Inman, D. J. Engineering Vibration, 3rd edition.
(2) Mechanical Properties of Rubber.

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