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Consider a circular drumhead can be modelled by the vibrations of a circular membrane with a uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental mode. Find the free-vibration equation of motion, and the free-vibration solution with different mode shapes for circular membrane with radius r.

Consider a circular drumhead can be modelled by the vibrations of a circular membrane with a uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental mode. Find the free-vibration equation of motion, and the free-vibration solution with different mode shapes for circular membrane with radius r.

Elements Of Electromagnetics
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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Consider a circular drumhead can be modelled by the vibrations of a circular membrane with a uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental mode. Find the free-vibration equation of motion, and the free-vibration solution with different mode shapes for circular membrane with radius r.
Transcribed Image Text:Consider a circular drumhead can be modelled by the vibrations of a circular membrane with a uniform thickness, attached to a rigid frame. Due to the phenomenon of resonance, at certain vibration frequencies, its resonant frequencies, the membrane can store vibrational energy, the surface moving in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental mode. Find the free-vibration equation of motion, and the free-vibration solution with different mode shapes for circular membrane with radius r.
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