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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