Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 5, Problem 5.23P
The period T of vibration of a beam is a function of its length L, area moment of inertia I, modulus of elasticity E, density
Take L,
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find the deflection under the load f in the following sketch using the following two approaches:
a. Assume the bar is rigid ( EI don't matter) using the Principe of Stationary Potentiel Energy.
b. Assume the bar is flexible (EI matter) using the rayleigh-ritz method. hint: you can assume a polynomial displacement field with two d.o.f.
c. How do the answers from parts (a) and (b) compare if, in part (b), you also assume that ei = kl3? in this case, you should be able to write your displacement for part (b) again in terms of only f, k, and maybe l.
For the system below, the mass, m is attached to the end of a cantilever beam of length, l, elasticity, E, and moment of inertia, I. Derive the equation of motions and find the natural frequencies in two cases by lagrange energy method
a) k1=k2=0
b) k1≠k2≠0
Given the vibration system with multiple degree of
freedom.
For string 1, k1 = 10kN/m
%3D
For string 2, k2 = 20KN/m
For string 3, k3 = 30 kN/m
%3D
mass = 500kg
mass of the beam will not be consider.
Solve for the following:
i. Frequency
j. Period
Chapter 5 Solutions
Fluid Mechanics
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