Page 350 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 10 Problems 337

equation for w,.
420 £/ 420A, £ /
Ù), = w A = 4
420£:/ m {l/2 y m r

With this change, the computer results for A, and the natural frequencies of a
two-element beam of length / are shown in Table 10.8-1. The case for il = 0 is
compared to exact values, which shows that the results are quite good for the first
two modes.
Shown in Figures 10.8-4 and 10.8-5 are two helicopters of different size. The
Robinson Helicopter, Model R22, shown in Figure 10.8-4 is a small two-seater
vehicle used mainly for pleasure flying. The descriptive data accompanying the
photo indicates some of its specifications and size.
In contrast, the commercial helicopter, shown in Figure 10.8-5, used for
hauling material and workers between shore and oil platforms is a large vehicle
capable of transporting a maximum load of 6000 lbs. As in all helicopters, the rotor
blades are very flexible. Their rotational speed is governed by the requirement of
keeping the tip speed below the speed of sound.

R E F E R E N C E S
111 Cook, R. D. Concepts and Applications of Finite Element Analysis. New York: John
Wiley & Sons, 1974.
12] Gallagher, R. H. Finite Element Analysis Fundamentals. Englewood Cliffs, NJ:
Prentiee-Hall, 1975.
131 Rockey, K. C., Evans, H. R., G rieehh, D. W. and N etheroot, D. A. The Finite
Element Method. New York: Halsted Press Book, John Wiley & Sons, 1975.
[4] Yang, T. Y., Finite Element Structural Analysis. Englewood Cliffs, NJ: Prentiee-Hall,
1986.
[5] Weaver, W., and Johnston, P. R. Structural Dynamics by Finite Elements. Engle­
wood Cliffs, NJ: Prentiee-Hall, 1987.
[6] Clough, R. W. and Penzien, J. Dynamics of Structures. New York: McGraw-Hill,
1975.
[71 Craig, R. R. Jr. Structural Dynamics. John Wiley & Sons, 1981.

P R O B L E M S

10-1 Determine the two natural frequencies in axial vibration for the uniform rod, fixed at
one end and free at the other end, using two elements with the intermediate station
at //3 from the fixed end. Compare results with those when the station is chosen at
midlength. What conclusion do you come to regarding choice of station location?