-element bar -400 cm c 0, and simply suppor subject to flexura expressed as a function of the material density p, the cross-sectional area is A, the second moment of area I, and the Young's modulus, E, as: ΕΙ @²=b- PA Answer the following: • The number of degrees of freedom of the bar is The value of b is . The units of b are (give your answer to 2 decimal places) (in the international system, SI) Note local mass and stiffness matrices for bars subject to flexural vibrations are given here: 12 6L -12 6L 6L 4L² -6L 2L² -12 -6L 12 -6L 6L 2L² -6L 4L² M= 22L 54 -13L 4L² 13L -3L² 54 13L 156 -22L -13L-3L² -22L 4L² 156 PAL 22L 420 and K= tion. Its square natural frequency can ΕΙ L3

-element bar -400 cm c 0, and simply suppor subject to flexura expressed as a function of the material density p, the cross-sectional area is A, the second moment of area I, and the Young's modulus, E, as: ΕΙ @²=b- PA Answer the following: • The number of degrees of freedom of the bar is The value of b is . The units of b are (give your answer to 2 decimal places) (in the international system, SI) Note local mass and stiffness matrices for bars subject to flexural vibrations are given here: 12 6L -12 6L 6L 4L² -6L 2L² -12 -6L 12 -6L 6L 2L² -6L 4L² M= 22L 54 -13L 4L² 13L -3L² 54 13L 156 -22L -13L-3L² -22L 4L² 156 PAL 22L 420 and K= tion. Its square natural frequency can ΕΙ L3

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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Thermal Properties of Materials

In mechanical engineering, the thermal property is represented as the physical quantity that is relevant to the application of heat. The thermal properties are evaluated by variations in any specific material due to low heat or high heat. The quantities that influence the thermal property of the materials are mass, density, temperature, and many others.

Question

A one-element bar of length L=400 cm clamped at x=0, and simply supported at x=l. The bar is subject to flexural vibration. Its squared natural frequency can be
expressed as a function of the material density p, the cross-sectional area is A, the second moment of area I, and the Young's modulus, E, as:
ΕΙ
@²=b-
PA
Answer the following:
• The number of degrees of freedom of the bar is
The value of b is
. The units of b are
(give your answer to 2 decimal places)
(in the international system, SI)
Note local mass and stiffness matrices for bars subject to flexural vibrations are given here:
156 22L
54 -13L
4L² 13L -3L²
54 13L 156 -22L
-13L-3L² -22L 4L²
M=
PAL 22L
420
and K =
ΕΙ
L³
12 6L -12 6L
6L 4L2 -6L 2L²
-12 -6L 12 -6L
6L 2L² -6L 4L²

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