SolSec8.6

# SolSec8.6 - Problems and Solutions Section 8.6(8.50 through...

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Unformatted text preview: Problems and Solutions Section 8.6 (8.50 through 8.54) 8.50 Consider the machine punch of Figure P8.15. Recalculate the fundamental natural frequency by reducing the model obtained in Problem 8.16 to a single degree of freedom using Guyan reduction. Solution: From the results of 8.16 K = 4-2-2 2 × 10 8 , Μ = .052 .013 .013 .026 Φρομ(8.10429 Θ Τ ΜΘ = .052 + .013 + .013 + .026 = .104 Φρομ(8.10529 Θ Τ ΚΘ = (4 - 229 ×10 8 = 2 ×10 8 ϖ = 2 ×10 8 .104 = 43852.9ραδ/σ which is a poor prediction of the first natural frequency. If we reorder K and M (reducing to coordinate 2) we get Q T MQ = .026 + .013 + .013 = .052 Θ Τ ΚΘ = (2 -129 ×10 8 = 1 ×10 8 ϖ = 43852.9ραδ/σ which is the same result as reducing to coordinate 1. 8.51 Compute a reduced-order model of the three-element model of a cantilevered bar given in Example 8.3.2 by eliminating u 2 and u 3 using Guyan reduction. Compare the frequencies of each model to those of the distributed model given in Window...
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SolSec8.6 - Problems and Solutions Section 8.6(8.50 through...

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