Copy of Vibration Models

8/12/2019 Copy of Vibration Models

1/14

Single Degree of Freedom Spring / Mass Vibration with Damping

Yellow cells can be changed, grey cells have formulae and should not be changed.

Parameter Setting Unit

Mass 50 kg Mass

Spring Constant 60 N/m Spring Constant

Natural Frequency 1.10 rad/second Natural Frequency

Natural Frequency 0.174 ! Natural Frequency

"eriod 5.74 seconds PeriodDamping #atio 0.8 a!ping "atio

Damped Natural Frequency 0.66 rad/second a!ped Natural Frequency

$nput Displacement 0.1 m #nput isplace!ent

Plotting step 0.7170 seconds

More Information(move mouse over cell)

0 1 $ % 4 5 6 7 8 & 10

'0.1

'0.08

'0.06

'0.04

'0.0$

0

0.0$0.04

0.06

0.08

0.1

Damped Vibration

%ime& se conds

Displacement&

Meters


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Forced Vibration Spring / Mass with Damping

Frequency of Forced Vibration 5 - Natural Frequency 10 -

"eak 'mplitude of Forced (ibration 1 !! 'mplitude #atio 1.%%

Damping #atio 0

0 0.05 0.1 0.15 0.$ 0.$5 0.% 0.%5 0.4 0.45 0.5

'10

'8

'6

'4

'$

0

$

4

6

8

10

Forced /i(ration input "esponse output

seconds

'mplitude&mm


3/14

Prepared (y ) Mc*auc+lan 0%,07,$014 Page %

Summing Vibrations

Vibration ) Vibration * Vibration +

'mplitude 5 'mplitude 1.5 'mplitude 1

Frequency 1 Frequency % Frequency 5

"hase, 0 "hase, 0 "hase, 0

0 0.1 0.$ 0.% 0.4 0.5 0.6 0.7 0.8 0.& 1

'6

'4

'$

0

$

4

6

/i(ration 1 /i(ration $ /i(ration %


4/14

Prepared (y ) Mc*auc+lan 0%,07,$014

Digital Sampling ModelSource Frequency )--- ! Sample Frequency .-- !

#atio of Sample to Source 0.5 21

'pparent Frequency - ! Data #ate)0 bit sample1 1 3(yte,second

'liasing& locked to !ero 0.06 M(yte,!inute

0 0.0005 0.001 0.0015 0.00$ 0.00$5 0.00% 0.00%5 0.0

'$

'1.5

'1

'0.5

0

0.5

1

1.5

$

%ime& seconds

'mplitude


5/14

Prepared (y ) Mc*auc+lan 0%,07,$014


6/14

Centre of 2ra(ity Calculation

Distance nter2 Mass nter2 Force& N Moments

D) - M) - 0 -

D* - M* - 0 -

D+ - M+ - 0 -

D3 - M3 - 0 -

D. - M. - 0 -

4nits5 m kg Newtons N m

Mass& Mt Force Moment%otals - - -

kg N Nm

Dc 6 Distance from ref7 to C of 2 Data8 metres

D)D*

D+D3

D.

M) M*M.

M3

M+

Dc

Mt


7/14

da!ping n

, 0 - 10 - 5 0 0

0.5 1.%% "ad,sec 6$.8%185 rad,sec %1.415&% 1 0.0$5

Period 0.1 Period 0.$ $ 0.05

ti!e step 0.0$5 % 0.075

a!plitude 1 4 0.15 0.1$5

6 0.15

7 0.175

p+i 0.00 0.00 8 0.$

& 0.$$5

10 0.$5

11 0.$75

1$ 0.%

1% 0.%$5

14 0.%5

15 0.%75

16 0.417 0.4$5

18 0.45

1& 0.475

$0 0.5

$1 0.5$5

$$ 0.55

$% 0.575

$4 0.6

$5 0.6$5

$6 0.65

$7 0.675

$8 0.7$& 0.7$5

%0 0.75

%1 0.775

%$ 0.8

%% 0.8$5

%4 0.85

%5 0.875

%6 0.&

%7 0.&$5

%8 0.&5

%& 0.&75

40 141 1.0$5

4$ 1.05

4% 1.075

44 1.1

45 1.1$5

46 1.15

47 1.175


8/14

48 1.$

4& 1.$$5

50 1.$5

51 1.$75

5$ 1.%

5% 1.%$5

54 1.%555 1.%75

56 1.4

57 1.4$5

58 1.45

5& 1.475

60 1.5

61 1.5$5

6$ 1.55

6% 1.575

64 1.6

65 1.6$5

66 1.6567 1.675

68 1.7

6& 1.7$5

70 1.75

71 1.775

7$ 1.8

7% 1.8$5

74 1.85

75 1.875

76 1.&

77 1.&$5

78 1.&57& 1.&75

80 $

81 $.0$5

8$ $.05

8% $.075

84 $.1

85 $.1$5

86 $.15

87 $.175

88 $.$

8& $.$$5

&0 $.$5&1 $.$75

&$ $.%

&% $.%$5

&4 $.%5

&5 $.%75

&6 $.4

&7 $.4$5


9/14

&8 $.45

&& $.475

100 $.5

101 $.5$5

10$ $.55

10% $.575

104 $.6105 $.6$5

106 $.65

107 $.675

108 $.7

10& $.7$5

110 $.75

111 $.775

11$ $.8

11% $.8$5

114 $.85

115 $.875

116 $.&117 $.&$5

118 $.&5

11& $.&75

1$0 %

1$1 %.0$5

1$$ %.05

1$% %.075

1$4 %.1

1$5 %.1$5

1$6 %.15

1$7 %.175

1$8 %.$1$& %.$$5

1%0 %.$5

1%1 %.$75

1%$ %.%

1%% %.%$5

1%4 %.%5

1%5 %.%75

1%6 %.4

1%7 %.4$5

1%8 %.45

1%& %.475

140 %.5141 %.5$5

14$ %.55

14% %.575

144 %.6

145 %.6$5

146 %.65

147 %.675


10/14

148 %.7

14& %.7$5

150 %.75

151 %.775

15$ %.8

15% %.8$5

154 %.85155 %.875

156 %.&

157 %.&$5

158 %.&5

15& %.&75

160 4


11/14

"esponse

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'1 46 1.15 '1.%%%%%%

'0.707107 47 1.175 '0.&4$80&


12/14

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1 50 1.$5 1.%%%%%%

0.707107 51 1.$75 0.&4$80&

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1 58 1.45 1.%%%%%%

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5.4'015 60 1.5 7.$'015

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'1 70 1.75 '1.%%%%%%

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0.707107 7% 1.8$5 0.&4$80&

1 74 1.85 1.%%%%%%

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'1 86 $.15 '1.%%%%%%

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4.4'015 88 $.$ 5.&'015

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1.1'014 &6 $.4 1.5'014

0.707107 &7 $.4$5 0.&4$80&


13/14

1 &8 $.45 1.%%%%%%

0.707107 && $.475 0.&4$80&

'5'016 100 $.5 '7'016

'0.707107 101 $.5$5 '0.&4$80&

'1 10$ $.55 '1.%%%%%%

'0.707107 10% $.575 '0.&4$80&

%.&'015 104 $.6 5.$'0150.707107 105 $.6$5 0.&4$80&

1 106 $.65 1.%%%%%%

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'7'015 108 $.7 '1'014

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'1 110 $.75 '1.%%%%%%

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1.1'014 11$ $.8 1.4'014

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1 114 $.85 1.%%%%%%

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7.%'015 1$4 %.1 &.8'015

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14/14

&.8'016 148 %.7 1.%'015

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'5'015 160 4 '7'015

Copy of Vibration Models

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