this is a text book example NOT for grading, how do they determine k Torsional natural frequency4₁ = 600 md₁ = 80mmG = 80GPaJ₁ = 900kgm²1₂ = 800 md₂ = 60mmG = 80GPaJ₂ = 400kgm²k₁0₁wwwJ₁J₂K₁1K124010K₁2(02-0₁)02Equation of motion for J₁:kt101 + kt201 - kt20₂ + J₁0₁ = 0(kt1+kt2)01(kt2)02-J₁w²0₁ = 0Equation of motion for J₂:Kt202 - Kt201 +J₂0₂ = 0-(kt2) 01 + (kt2)02-J₂w²0₂ = 0Equations of motion in matrix form:[(ker+ Kt2-J₁w²)(-ktz)0 (t) = Osin(wt)ä(t) = -w²0sin(wt)=(K²₂-12²)][82] [81 Torsional natural frequencyJ₁J₂K₁1K12010₂Calculate the natural frequencies:(ke1 + Ktz-J₁w²)(-Ktz)(-ktz)(ktz~1/26²) = 0360000w4379870910w² +68218704777.675003 = 0Wn1 = 28,73 rad/sfn1 = 4,57HzWn2 = 15,15 rad/sfn2 = 2,41Hz

Given Data: To Find: How to calculate kt1 and kt2?

Answered: how do they determine k

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Mechanical Engineering

how do they determine k

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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Question

this is a text book example NOT for grading, how do they determine k

Torsional natural frequency
4₁ = 600 m
d₁ = 80mm
G = 80GPa
J₁ = 900kgm²
1₂ = 800 m
d₂ = 60mm
G = 80GPa
J₂ = 400kgm²
k₁0₁
www
J₁
J₂
K₁1
K12
4010
K₁2(02-0₁)
02
Equation of motion for J₁:
kt101 + kt201 - kt20₂ + J₁0₁ = 0
(kt1+kt2)01(kt2)02-J₁w²0₁ = 0
Equation of motion for J₂:
Kt202 - Kt201 +J₂0₂ = 0
-(kt2) 01 + (kt2)02-J₂w²0₂ = 0
Equations of motion in matrix form:
[(ker
+ Kt2-J₁w²)
(-ktz)
0 (t) = Osin(wt)
ä(t) = -w²0sin(wt)
=
(K²₂-12²)][82] [81

Torsional natural frequency
J₁
J₂
K₁1
K12
01
0₂
Calculate the natural frequencies:
(ke1 + Ktz-J₁w²)
(-Ktz)
(-ktz)
(ktz~1/26²) = 0
360000w4379870910w² +68218704777.675003 = 0
Wn1 = 28,73 rad/s
fn1 = 4,57Hz
Wn2 = 15,15 rad/s
fn2 = 2,41Hz

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