Does an automobile radio antenna vibrate in resonance dueto vortex shedding? Consider an antenna of length L anddiameter D . According to beam vibration theory [, the fi rst mode natural frequency of a solidcircular cantilever beam is ω n = 3.516[ EI /( ρ AL 4 )] 1/2 ,where E is the modulus of elasticity, I is the area momentof inertia, ρ is the beam material density, and A is the beamcross-section area. ( a ) Show that ω n is proportional to theantenna radius R . ( b ) If the antenna is steel, with L = 60 cmand D =4 mm, estimate the natural vibration frequency, inHz. ( c ) Compare with the shedding frequency if the carmoves at 65 mi/h.
Does an automobile radio antenna vibrate in resonance dueto vortex shedding? Consider an antenna of length L anddiameter D . According to beam vibration theory [, the fi rst mode natural frequency of a solidcircular cantilever beam is ω n = 3.516[ EI /( ρ AL 4 )] 1/2 ,where E is the modulus of elasticity, I is the area momentof inertia, ρ is the beam material density, and A is the beamcross-section area. ( a ) Show that ω n is proportional to theantenna radius R . ( b ) If the antenna is steel, with L = 60 cmand D =4 mm, estimate the natural vibration frequency, inHz. ( c ) Compare with the shedding frequency if the carmoves at 65 mi/h.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
Does an automobile radio antenna vibrate in resonance due
to vortex shedding? Consider an antenna of length L and
diameter D . According to beam vibration theory [, the fi rst mode natural frequency of a solid
circular cantilever beam is ω n = 3.516[ EI /( ρ AL 4 )] 1/2 ,
where E is the modulus of elasticity, I is the area moment
of inertia, ρ is the beam material density, and A is the beam
cross-section area. ( a ) Show that ω n is proportional to the
antenna radius R . ( b ) If the antenna is steel, with L = 60 cm
and D =4 mm, estimate the natural vibration frequency, in
Hz. ( c ) Compare with the shedding frequency if the car
moves at 65 mi/h.
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