{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

SolSec7.4

# SolSec7.4 - Problems and Solutions for Section...

This preview shows pages 1–4. Sign up to view the full content.

Problems and Solutions for Section 7.4 (7.10-7.19) 7.10 Consider the magnitude plot of Figure P7.10. How many natural frequencies does this system have, and what are their approximate values? Solution: The system looks to have 8 modes with approximate natural frequencies of 2, 4, 10, 15, 22, 29, 36, and 47 Hz.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
7.11 Consider the experimental transfer function plot of Figure P7.11. Use the methods of Example 7.4.1 to determine i ζ and i ϖ . Solution: For each mode: i ai bi i ϖ ϖ ϖ ζ 2 - = where bi ϖ and ai ϖ are the frequencies where the magnitude is 2 1 of the resonant magnitude. All values given in the following table are approximate. Mode i ϖ (Hz) ) ( i H ϖ 2 ) ( i H ϖ ai ϖ (Hz) bi ϖ (Hz) i ζ 1 4.80 0.089 0.063 4.56 5.04 0.049 2 15.20 1.050 0.742 14.76 15.48 0.024 3 30.95 1.800 1.270 30.47 31.19 0.012 4 52.62 2.000 1.414 52.14 52.85 0.007 5 80.00 2.100 1.480 79.05 80.48 0.009
7.12 Consider a two-degree-of-freedom system with frequencies 1 ϖ = 10 rad/s, 2 ϖ = 15 rad/s, and damping ratios 1 ζ = 2 ζ = 0.01. With modal s = 1 2 1 -1 1 1 , calculate the transfer function of this system for an input at 1 x and a response measurement at 2 x . Solution: Since the natural frequencies, damping ratios and mode shapes are given, the system can be expressed in modal coordinates as 1 0 0 1  ρ+ 2(.01 29 10 0 0 2(.01 29 15 ρ+ 10 2 0 0 15 2 ρ = 1 2 1 1 -1 1 1 0 φ ( τ 29 = 1 2 1 -1 φ ( τ 29 y = 1 2 0 1 { } 1 -1 1 1 ρ= 1 2 1 1 { This is the representation of the system in modal coordinates, if proportional damping is assumed. The transfer function is: Y ( s ) = 1 2 1 1 { } Ρ ( σ 29 where R ( s ) = 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}