Find the frequency Equation, Mode shapes (Normal Function), and expression Bl for a uniform beam with young's modulus E, mass density p, cross-sectional area A, second moment of cross- sectional area I, and a length / with Pinned - Free boundary conditions. Whereas the free-vibration lateral equation of motion of the beam is obtained as: aw a²w + Əx4 at² c²5 =0 where C= EI VPA And the General Solution of the free vibration equation of motion is: w(x, t) = [C₁ cos ßx + C₂ sin ßx + C3 cosh Bx + C4 sinh ßx][A cos wt + P sin wt] 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.
Find the frequency Equation, Mode shapes (Normal Function), and expression Bl for a uniform beam with young's modulus E, mass density p, cross-sectional area A, second moment of cross- sectional area I, and a length / with Pinned - Free boundary conditions. Whereas the free-vibration lateral equation of motion of the beam is obtained as: aw a²w + Əx4 at² c²5 =0 where C= EI VPA And the General Solution of the free vibration equation of motion is: w(x, t) = [C₁ cos ßx + C₂ sin ßx + C3 cosh Bx + C4 sinh ßx][A cos wt + P sin wt] 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
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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![Problem No.5:
Find the frequency Equation, Mode shapes (Normal Function), and expression ßl for a uniform
beam with young's modulus E, mass density p, cross-sectional area A, second moment of cross-
sectional area I, and a length / with Pinned - Free boundary conditions.
Whereas the free-vibration lateral equation of motion of the beam is obtained as:
24w a²w
+ <=0
Əx4 at²
c²
where
C =
EI
VPA
And the General Solution of the free vibration equation of motion is:
w(x, t) = [C₁ cos ßx + C₂ sin ßx + C3 cosh Bx + C4 sinh ßx][A cos wt + P sin wt]
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d6d14a7-e5eb-4378-8510-35ec92c02df5%2F46453180-1658-4b3e-b50b-dea1f627640d%2Fzw6band_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem No.5:
Find the frequency Equation, Mode shapes (Normal Function), and expression ßl for a uniform
beam with young's modulus E, mass density p, cross-sectional area A, second moment of cross-
sectional area I, and a length / with Pinned - Free boundary conditions.
Whereas the free-vibration lateral equation of motion of the beam is obtained as:
24w a²w
+ <=0
Əx4 at²
c²
where
C =
EI
VPA
And the General Solution of the free vibration equation of motion is:
w(x, t) = [C₁ cos ßx + C₂ sin ßx + C3 cosh Bx + C4 sinh ßx][A cos wt + P sin wt]
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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