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Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with shear modulus G and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration torsional equation of motion of the rod is obtained as: 8²0 əx² c². (x, t): = 8²0 at² -(x, t) And the General Solution of the free vibration equation of motion is: ωχ ωχ cos + B sin C where 8(x, t) = (A co C= 1012 (C cos wt + D sin wt)

Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with shear modulus G and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration torsional equation of motion of the rod is obtained as: 8²0 əx² c². (x, t): = 8²0 at² -(x, t) And the General Solution of the free vibration equation of motion is: ωχ ωχ cos + B sin C where 8(x, t) = (A co C= 1012 (C cos wt + D sin wt)

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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Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with shear modulus G and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration torsional equation of motion of the rod is obtained as: a²0 dx2 c² 2²0 at² -(x, t) = (x, t) where 0 (x, t) = (A co C = P And the General Solution of the free vibration equation of motion is: ωχ ωχ +B sin (C cos wt + D sin wt) C
Transcribed Image Text:Problem No.2: Find the natural longitudinal frequencies, the frequency Equation and Mode shapes of a uniform bar with shear modulus G and mass density p, and a fixed - fixed at both ends boundary conditions. Whereas the free-vibration torsional equation of motion of the rod is obtained as: a²0 dx2 c² 2²0 at² -(x, t) = (x, t) where 0 (x, t) = (A co C = P And the General Solution of the free vibration equation of motion is: ωχ ωχ +B sin (C cos wt + D sin wt) C
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