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Consider axial vibration of the uniform bar in Fig. 1 Obtain the characteristic equation from which eigenvalues can be determined. Salve for the fundamental axial frequency of the bar. Sketch the fundamental mode shape by plotting values at increments of L/S along the bar. (E₁ªH ) = p Hint EA =pAü where c²=E/p (see Eq. 12.18) Characteristic equation (x)=a, cos-x+b sinx with (0)=0, (L)=0 Konfor to Fren de 12 Chap 12) L Fig. 1 PALIA

Consider axial vibration of the uniform bar in Fig. 1 Obtain the characteristic equation from which eigenvalues can be determined. Salve for the fundamental axial frequency of the bar. Sketch the fundamental mode shape by plotting values at increments of L/S along the bar. (E₁ªH ) = p Hint EA =pAü where c²=E/p (see Eq. 12.18) Characteristic equation (x)=a, cos-x+b sinx with (0)=0, (L)=0 Konfor to Fren de 12 Chap 12) L Fig. 1 PALIA

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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1. Consider axial vibration of the uniform bar in Fig. (a) Obtain the characteristic equation from which eigenvalues can be determined. (b) Salve for the fundamental axial frequency of the bar. (c) Sketch the fundamental mode shape by plotting values at increments of L/5 along the bar. du 104 ) = p ax EA Hint =pAu where c²=E/p (see Eq. 12.18) Characteristic equation (x)=a, cos-x+b sinx с with (0)=0, '(L) = 0 (refer to Example 12, Chap. 12) L Fig. 1 -PALIA
Transcribed Image Text:1. Consider axial vibration of the uniform bar in Fig. (a) Obtain the characteristic equation from which eigenvalues can be determined. (b) Salve for the fundamental axial frequency of the bar. (c) Sketch the fundamental mode shape by plotting values at increments of L/5 along the bar. du 104 ) = p ax EA Hint =pAu where c²=E/p (see Eq. 12.18) Characteristic equation (x)=a, cos-x+b sinx с with (0)=0, '(L) = 0 (refer to Example 12, Chap. 12) L Fig. 1 -PALIA
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