Question

A 45 kg machine is place at the end of a 1.6 m cantilever beam of elastic modulus of 200x109 N/m2 and cross-sectional Moment of Inertia of 1.6X10-5m4. The machine produces a harmonic force of magnitude 125 N. Find allowable value of magnification factor in order to restrict the steady-state amplitude to 0.2 mm is

Answer 1

Increase in energy

ΔE=

2

1 × stress × strain × volume

ΔE=

2

1

×

A

F

×

A×Y

F

×(A×L)

ΔE=

2

1

×

A

F

×

Y

FL

=

2

1

×

10

−4

10

×

10

11

10×0.1