Theory and Design for Mechanical Measurements
Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781119126317
Author: Richard S. Figliola; Donald E. Beasley
Publisher: Wiley Global Education US
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Chapter 3, Problem 3.23P
To determine

A measuring system which has a natural frequency of 0.5 rad/s, a damping ratio of 0.5, and a static sensitivity of 0.5 m/V. Estimate its 90% of rise time and setting time if F(t) = 2 U(t) and the initial condition is zero. Plot the response y(t) and indicate its transient and steady responses.

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For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to a(t) = a(0) exp(-4) (15.10) where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70 psi) after 30 s.
For the flows in Examples 11.1 and 11.2, calculate the magnitudes of the Δ V2 / 2 terms omitted in B.E., and compare these with the magnitude of the ℱ terms.
Calculate ℛP.M. in Example 11.2.
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