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Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with young's modulus E and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration longitudinal equation of motion of uniform bar is obtained as: 20² (x, t) = a (x, t) ax² at² where C= P

Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with young's modulus E and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration longitudinal equation of motion of uniform bar is obtained as: 20² (x, t) = a (x, t) ax² at² where C= P

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
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Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with young's modulus E and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration longitudinal equation of motion of uniform bar is obtained as: c² 20²² (x, t) = 0²/²² (x, t) 2²u ?t2 where And the General Solution of the free vibration equation of motion is: ωχ + B sin с u(x, t) = U(x)T(t) = (A cc A cos ωχ C = Р (C cos wt + D sin wt)
Transcribed Image Text:Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with young's modulus E and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration longitudinal equation of motion of uniform bar is obtained as: c² 20²² (x, t) = 0²/²² (x, t) 2²u ?t2 where And the General Solution of the free vibration equation of motion is: ωχ + B sin с u(x, t) = U(x)T(t) = (A cc A cos ωχ C = Р (C cos wt + D sin wt)
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