تحلیل سه بعدی ارتعاشات و سرعت بحرانی پوسته های استوانه ای کامپوزیتی با تقویت کننده های متعامد تحت بار محوری و فشار

(1)

ﻪﭽﺨ ﻪﻟﺎﻘﻣ :

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شﺮ 20 / 6 / 91

رد ﻪﺋارا ﺎﺳ ﻳ ﺖ 30 / 9 /

91

ﻪﻧاﻮﺘﺳا يﺎﻫ يا

رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

ﺖﺧاﻮﻨﻜ و

،رﺎﺸﻓ ﺎﺑ

ﺲﻨﺟ ﻳ ﻧﺎﺴﻜ ﻲ ﻣ ﻲ

هدﺎﻔﺘﺳا هﺪﺷ ﺖﺳا .

ﻪﺘ هدﺎﻔﺘﺳا هﺪﺷ

ﺮﺑ ور ي تﻻدﺎﻌﻣ

ﻪﺘﻓﺮﮔ هﺪﺷ ﺖﺳا .

ﻴ ﺮ ﻪﺳﺪﻨﻫ و عﻮﻧ

راﺮﻗ ﻪﺘﻓﺮﮔ ﺖﺳا .

Three

rotating orthogonally stiffened laminated cylindrical shells

Abstract- In this paper, an approximate solution using layer

laminated cylindrical shells with ring and stringer stiffeners under axial load and pressure i

shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties and cylindrical shell reinforced by outer stiffeners while stiffeners are treated as discrete elem

equations of motion are derived by the Hamilton’s principle. In

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial hoop tension.

through the thickness of the shells. The edges of the shell are restrained presented results are com

agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffened cylindrical shell and different geometry of

and amplitude of axial load.

Keywords: Rotating Cylindrical Shell, Ring wise Theory

رﺎﺗ ﻳ ﻪﭽﺨ رد ﻳ ﺖﻓﺎ ﺬﭘ ﻳ شﺮ رد ﻪﺋارا

ﻪﻧاﻮﺘﺳا يﺎﻫ

رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

رﺎﺑ رﻮﺤﻣ ﻳ ي ﺖﺧاﻮﻨﻜ

اراد ي ﻪﺳﺪﻨﻫ و ﺲﻨﺟ

نﺎﻤﻟا ﻪﻧﺎﮔاﺪﺟ هدﺎﻔﺘﺳا

ﻪﺳ ﺪﻌﺑ ي ﺘﺳﻻا ﻴ ﺴ ﻴ ﻪﺘ

ﻪﺳ ﺪﻌﺑ ي ﻻ ﻳ ﻪ ا ي

، ﺮﺑ

هﺎﮔ هدﺎﺳ ﺮﻈﻧرد ﻪﺘﻓﺮﮔ

ﺖﺳا . رد ﺎﻬﻧ ﻳ ﺖ ﺛﺎﺗ ﻴ

هﺪﺷ درﻮﻣ ﻪﻌﻟﺎﻄﻣ راﺮﻗ

ﻪﻳﻻ

يا

Three-dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

In this paper, an approximate solution using layer

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial nsion.The layer -wise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. The edges of the shell are restrained

presented results are com

Rotating Cylindrical Shell, Ring

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ ﻪﻧاﻮﺘﺳا يﺎﻫ

رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

ﻲﺗﻮﺗ ﻲﺒﻟﺎﻃ ﻲﻔﻄﺼﻣ ، 3

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ دﺎﺘﺳا

ناﺮﻬﺗ ،

ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ناﺮﻬﺗ ،

madoliat

ي ﺪﻣﺎﻌﺘﻣ ﺖﺤﺗ

راﺮﻗ ﻪﺘﻓﺮﮔ ﺪﻧا و اراد

هﺪﻨﻨﻛ ﺎﻫ زا شور نﺎﻤﻟا

ﺖﻛﺮﺣ زا رﻮﺌﺗ ي ﻪﺳ

هدﺎﻔﺘﺳا زا رﻮﺌﺗ ي ﻪﺳ

رد ود ﺮﺳ ﻜﺗ ﻴ ﻪ هﺎﮔ

هﺪﻫﺎﺸﻣ هﺪﺷ ﺖﺳا

ﻪﻧاﻮﺘﺳا ا ي ﻮﻘﺗ ﻳ ﺖ هﺪﺷ

،ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ ،ﻪﺘﻴﺴﻴﺘﺳﻻا يﺪﻌﺑ يرﻮﺌﺗ

ﻪﻳﻻ

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

under axial load and

K. Daneshjou

1- Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran 2- Assoc. Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran 3- PhD Student, Mech. Eng., Iran Univ. Sci. & Tech., Tehran

* P. O. B.

In this paper, an approximate solution using layer

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. The edges of the shell are restrained

presented results are compared with those available in the literature and also with the FE results

Rotating Cylindrical Shell, Ring

http://mechanics.journals.modares.ac.ir

80 - 94

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

ﻲﺗﻮﺗ ﻲﺒﻟﺎﻃ ﻲﻔﻄﺼﻣ ،

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ دﺎﺘﺳا ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد

ناﺮﻬﺗ ،

ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد madoliat@iust.ac.ir

ﺎﺑ ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ي

وﺎﺴﻣ ي زا ﻳ ﺪﻜ ﻳ ﺮﮕ راﺮﻗ

ﻳ ﺿﺎ ﻲ ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ

جاﺮﺨﺘﺳا تﻻدﺎﻌﻣ ﺖﻛﺮﺣ

هﺪﺷ ﺖﺳا . ﺎﺑ هدﺎﻔﺘﺳا

ﻂ زﺮﻣ ي ﻪﺘﺳﻮﭘ رد

ﻖﺑﺎﻄﺗ ﺒﺳﺎﻨﻣ ﻲ هﺪﻫﺎﺸﻣ

ﺒﻃ ﻴ ﻌ ﻲ ﻪﺘﺳﻮﭘ ﻪﻧاﻮﺘﺳا

،ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ ،ﻪﺘﻴﺴﻴﺘﺳﻻا يﺪﻌﺑ

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

under axial load and

K. Daneshjou¹, R. Madoliat

Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran Assoc. Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran PhD Student, Mech. Eng., Iran Univ. Sci. & Tech., Tehran

P. O. B. 16846-13114 Tehran, In this paper, an approximate solution using layer

pared with those available in the literature and also with the FE results

Rotating Cylindrical Shell, Ringand Stringer Stiffeners, Three

mechanics.journals.modares.ac.ir ﻲﺸﻫوﮋﭘ ﻲﻤﻠﻋ ﻪﻠﺠﻣ

هرﺎﻤﺷ 6

، ﺪﻨﻔﺳا 1391 ص ص 80

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

ﺖﻴﻟوﺪﻌﻣ ﺎﺿر ،

2

ﻲﺗﻮﺗ ﻲﺒﻟﺎﻃ ﻲﻔﻄﺼﻣ ،*

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ دﺎﺘﺳا ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻴﺸﻧاد ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد

،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد

13114 - 16846 ،

@iust.ac.ir

زﻮﭙﻣﺎﻛ ﻳﺘ ﻲ راود

، ﺎﺑ

هﺪﻨﻨﻛ ﺎﻫ ﺎﺑ ﻞﺻاﻮﻓ وﺎﺴﻣ

ﺪﺼﻗ زﺎﺴﻟﺪﻣ ي رﻳ

ﻲﻣ ﺪﻧدﺮﮔ . رد جاﺮﺨﺘﺳا

ﻟوا ﻴ ﻪ ﺮﻈﻧرد ﻪﺘﻓﺮﮔ

ﻪﺘﻓﺮﮔ ﺖﺳا . اﺮﺷ ﻳ ﻂ

دﺪﻋ ي ﺎﻘﻣ ﻳ ﻪﺴ و

ﻲ ﺮﺑ ﺲﻧﺎﻛﺮﻓ ﺒﻃ

ﻪﺳ يرﻮﺌﺗ ،ﻲﻄﻴﺤﻣ و ﻲﻟﻮﻃ يﺎﻫ ،ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ ،ﻪﺘﻴﺴﻴﺘﺳﻻا يﺪﻌﺑ

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

under axial load and

, R. Madoliat

Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran Assoc. Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran PhD Student, Mech. Eng., Iran Univ. Sci. & Tech., Tehran

13114 Tehran, madoliat In this paper, an approximate solution using layer

agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure and Stringer Stiffeners, Three

mechanics.journals.modares.ac.ir

هرود 12 هرﺎﻤﺷ

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ

ﺖﻳﻮﻘﺗ ﺎﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ هﺪﻨﻨﻛ

رﺎﺸﻓ و يرﻮﺤﻣ رﺎﺑ ﺖﺤﺗ ﺪﻣﺎﻌﺘﻣ يﺎﻫ

ﻮﺠﺸﻧاد ناﺮﻣﺎﻛ ﺖﻴﻟوﺪﻌﻣ ﺎﺿر ،1

ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ دﺎﺘﺳا ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻴﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد

ناﺮﻬﺗ ﻲﺘﺴﭘ قوﺪﻨﺻ ، 13114

ﺎﻫ ي ﻪﻧاﻮﺘﺳا ا ي زﻮﭙﻣﺎﻛ

ﺖﺳا . ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ

ﻪﺘﺳﻮﭘ هدﻮﺑ و ﻪﺑ ﺪﺼﻗ

ﻤﻫ ﻴ نﻮﺘﻠ ﻞﺻﺎﺣ ﻲﻣ

ﺶﺸﻛ ﻮﻘﻠﺣ ي ﻟوا

زﺎﺳاﺪﺟ ي ترﻮﺻ ﻪﺘﻓﺮﮔ

ن و ﺎﺘﻧ ﻳ ﺞ ﻠﺤﺗ ﻴ ﻞ دﺪﻋ

رﻮﺤﻣ ي و رﺎﺸﻓ ﻠﺧاد ﻲ

ﻪﺳ يرﻮﺌﺗ ،ﻲﻄﻴﺤﻣ و ﻲﻟﻮﻃ يﺎﻫ

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

under axial load and pressure

, R. Madoliat^2*, M. Talebitooti

Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran Assoc. Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran PhD Student, Mech. Eng., Iran Univ. Sci. & Tech., Tehran madoliat@iust.ac.ir

In this paper, an approximate solution using layer-wise theory for the vibration analysis of rotating laminated cylindrical shells with ring and stringer stiffeners under axial load and pressure i

equations of motion are derived by the Hamilton’s principle. In deriving the governing equations three

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions through the thickness of the shells. The edges of the shell are restrained by simply supported boundary conditions. The

agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure and Stringer Stiffeners, Three-Dimensional Elasticity Theory, Critical Speed, Layer

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ

ﺖﻳﻮﻘﺗ ﺎﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

ﻮﺠﺸﻧاد ناﺮﻣﺎﻛ

1 - ناﺮﻬﺗ ،ناﺮﻳا ﺖﻌﻨﺻ و ﻢﻠﻋ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ دﺎﺘﺳا

2 - ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻴﺸﻧاد

3 - ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ياﺮﺘﻛد يﻮﺠﺸﻧاد

* ناﺮﻬﺗ

تﺎﺷﺎﻌﺗرا دازآ ﻪﺘﺳﻮﭘ ﺎﻫ

ﻪﻌﻟﺎﻄﻣ راﺮﻗ ﻪﺘﻓﺮﮔ ﺖﺳا

ﺢﻄﺳ ﺟرﺎﺧ ﻲ ﻪﺘﺳﻮﭘ

سﺎﺳاﺮﺑ ﻞﺻا ﻤﻫ

ﺐﻧﺎﺟ ﻪﺑ ﺰﻛﺮﻣ و ﺶﺸﻛ

ي ﺖﻣﺎﺨﺿ زﺎﺳاﺪﺟ

ﻳ ﺞ ﺎﺳ ﻳ ﺮ ﻘﻘﺤﻣ ﺎ ن

راﺪﻘﻣ ﻧ ﻴ وﺮ ي رﻮﺤﻣ

ﺖﻳﻮﻘﺗ ،راود يا هﺪﻨﻨﻛ

ﻪﺳ يرﻮﺌﺗ ،ﻲﻄﻴﺤﻣ و ﻲﻟﻮﻃ يﺎﻫ

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

pressure

, M. Talebitooti³

Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran, Iran Assoc. Prof., Mech. Eng., Iran Univ. Sci. & Tech., Tehran, Iran PhD Student, Mech. Eng., Iran Univ. Sci. & Tech., Tehran, Iran

@iust.ac.ir

wise theory for the vibration analysis of rotating laminated cylindrical shells with ring and stringer stiffeners under axial load and pressure is presented. The cylindrical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties and cylindrical shell reinforced by outer stiffeners while stiffeners are treated as discrete elem

deriving the governing equations three

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions by simply supported boundary conditions. The pared with those available in the literature and also with the FE results

agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure Dimensional Elasticity Theory, Critical Speed, Layer

ﻪﺳ ﻞﻴﻠﺤﺗ ﺑ

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ

ﺖﻳﻮﻘﺗ ﺎﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

ﻪﻟﺎﻘﻣ

،ﺮﺿﺎﺣ تﺎﺷﺎﻌﺗرا

ﻻ ﻳ ﻪ ا ي درﻮﻣ ﻪﻌﻟﺎﻄﻣ

ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ﺮﺑ ﺢﻄﺳ

ﺎﺑ شﺮﮕﻧ يژﺮﻧا و

ﺮﻛ ﻳ ﻟﻮ ﻴ

،ﺲ بﺎﺘﺷ ﺐﻧﺎﺟ

زﺮﻣ ي رد ﺎﺘﺳار ي

شور ﺮﺿﺎﺣ ﺎﺑ ﺎﺘﻧ ﻳ

ﺖﻋﺮﺳ ﻧارود ﻲ و راﺪﻘﻣ

ﻪﻧاﻮﺘﺳا ﻪﺘﺳﻮﭘ ﺖﻳﻮﻘﺗ ،راود يا

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

wise theory for the vibration analysis of rotating s presented. The cylindrical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties and cylindrical shell reinforced by outer stiffeners while stiffeners are treated as discrete elem

deriving the governing equations three

elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions by simply supported boundary conditions. The pared with those available in the literature and also with the FE results and excellent agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure Dimensional Elasticity Theory, Critical Speed, Layer

ﻪﺳ ﻞﻴﻠﺤﺗ ﺖﻳﻮﻘﺗ ﺎﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

هﺪﻴﻜﭼ رد-

ﻪﻟﺎﻘﻣ

رﻮﺌﺗ ي ﻪﺳ ﺪﻌﺑ ي ﻻ

ﺪﻨﺷﺎﺑ . لﺎﺼﺗا ﻮﻘﺗ

تﻻدﺎﻌﻣ ﺖﻛﺮﺣ ﺎﺑ

و تاﺮﺛا ﻧ ﻴ وﺮ ي ﺮﻛ

ﺖﻛﺮﺣ و اﺮﺷ ﻳ ﻂ

ﺎﺘﻧ ﻳ ﺞ ﻞﺻﺎﺣ زا شور

ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ

،ﺎﻫ ﺖﻋﺮﺳ

ﺪﻴﻠﻛ نﺎﮔژاو ﻪﻧاﻮﺘﺳا ﻪﺘﺳﻮﭘ:

dimensional vibration analysis and critical speed of rotating orthogonally stiffened laminated cylindrical shells

wise theory for the vibration analysis of rotating s presented. The cylindrical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties and cylindrical shell reinforced by outer stiffeners while stiffeners are treated as discrete elements. The deriving the governing equations three-dimensional elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions by simply supported boundary conditions. The and excellent agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure Dimensional Elasticity Theory, Critical Speed, Layer-

هﺪﻴﻜﭼ رﻮﺌﺗ ﺪﻨﺷﺎﺑ تﻻدﺎﻌﻣ و ﺖﻛﺮﺣ ﺎﺘﻧ ﻮﻘﺗ ﺪﻴﻠﻛ

rotating orthogonally stiffened laminated cylindrical shells

wise theory for the vibration analysis of rotating s presented. The cylindrical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric ents. The dimensional elasticity theory are used and the study includes the effects of the Coriolis and centrifugal accelerations and the initial wise theory is used to discretize the equations of motion and the related boundary conditions by simply supported boundary conditions. The and excellent agreement is observed. Finally, the results obtained include the relationship between frequency characteristics of stiffeners, stiffener type, rotating velocities, amplitude of pressure -

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1 - ﻪﻣﺪﻘﻣ

ﻪﺘﺳﻮﭘ ﺎﻫ ي ﻪﻧاﻮﺘﺳا ا ي راود رد ﺴﺑ ﻴ رﺎ ي زا ﺎﻫدﺮﺑرﺎﻛ ي ﺘﻌﻨﺻ ﻲ زا

ﺒﻗ ﻴ ﻞ رﻮﺗور ﺑرﻮﺗ ﻴ ﻦ

،زﺎﮔ ﺮﺘﻧﺎﺳ ﻳ ﻔ ﻴ

،ﺎﻫژﻮ هرﻮﻛ ﺎﻫ ي ﺖﺨﭘ ﺳ ﻴ نﺎﻤ و

ﺳ ﻴ ﻢﺘﺴ ﺎﻫ ي راود هدﺎﻔﺘﺳا ﻣ ﻲ دﻮﺷ . اﺮﺑ ي ندﺮﺑﻻﺎﺑ ﺘﻔﺳ ﻲ ﻪﺘﺳﻮﭘ

زا ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ هدﺎﻔﺘﺳا ﻣ ﻲ دﻮﺷ . ﻪﺘﺳﻮﭘ ﺎﻫ ي ﻪﻧاﻮﺘﺳا ا ي

، ﻪﻛ ﺎﺑ

نﺎﻤﻟا ﺎﻫ ﻲﻳ زا عﻮﻧ ﺗ ﻴ ﺮ ﻮﻘﺗ ﻳ ﺖ هﺪﺷ ﺪﻧا

، ﻪﺑ ترﻮﺻ هدﺮﺘﺴﮔ ا ي رد

هزﺎﺳ ﺎﻫ ي ﻧﺎﻜﻣ ﻴ ﻜ ﻲ زا ﺒﻗ ﻴ ﻞ

،ﻚﺷﻮﻣ زﻳ ردﺮ ﻳﺎ ﻲﻳ

، ﻚﺸﺧ هﺪﻨﻨﻛ ﺎﻫ ي

راود و نزﺎﺨﻣ ﺖﺧﻮﺳ ﭘاﻮﻫ ﻴ ﺎﻤ هدﺎﻔﺘﺳا ﻣ ﻲ ﺪﻧﻮﺷ . رد ﺮﺜﻛا ﻦﻳا

دراﻮﻣ ﻪﺘﺳﻮﭘ ﺖﺤﺗ يﺎﻫرﺎﺑ ﻲﻜﻴﻣﺎﻨﻳد راﺮﻗ

دراد و ﻦﻜﻤﻣ ﺖﺳا

رﺎﭼد شﺎﻌﺗرا و ﺶﻧﺎﻤﻛ و ﻲﮕﺘﺴﺧ دﻮﺷ

. ﻦﻳاﺮﺑﺎﻨﺑ ﺖﺧﺎﻨﺷ

تﺎﻴﺻﻮﺼﺧ ﻦﻳا

هزﺎﺳ ﺎﻫ زا ﻪﻠﻤﺟ ﺲﻧﺎﻛﺮﻓ ﻲﻌﻴﺒﻃ و رﺎﺑ ﺶﻧﺎﻤﻛ

بﺎﻨﺘﺟا ﺬﭘﺎﻧ ﻳ ﺮ ﺖﺳا . زا ﻲﻓﺮﻃ

، ﺎﺑ ﻪﺟﻮﺗ ﻪﺑ زﺎﻴﻧ نوﺰﻓازور ﻲﺣاﺮﻃ

هزﺎﺳ يﺎﻫ ﻚﺒﺳ نزو ﺎﺑ مﺎﻜﺤﺘﺳا

،ﻻﺎﺑ مزﻻ ﺖﺳا ﻪﻛ ﺖﺒﺴﻧ

مﺎﻜﺤﺘﺳا ﻪﺑ

نزو ﻦﻳا هزﺎﺳ ﺎﻫ ﺎﺗ ﺪﺣ نﺎﻜﻣا ﻻﺎﺑ ﺪﺷﺎﺑ ﺎﺗ هزﺎﺳ

ﻲﺣاﺮﻃ هﺪﺷ زا ﺮﻈﻧ فﺮﺼﻣ

،داﻮﻣ يژﺮﻧا و ﻪﻨﻳﺰﻫ ﻪﻨﻴﻬﺑ ﺪﺷﺎﺑ . زا

ﻪﻠﻤﺟ هار يﺎﻫ نﺪﻴﺳر ﻪﺑ ﻦﻳا

،فﺪﻫ ﺖﻳﻮﻘﺗ ﻪﻨﻴﻬﺑ ﻪﺘﺳﻮﭘ ﺎﺑ

نﺎﻤﻟا يﺎﻫ ﺖﻳﻮﻘﺗ هﺪﻨﻨﻛ ﻲﻄﻴﺤﻣ و ﻲﻟﻮﻃ و ﻦﻴﻨﭽﻤﻫ هدﺎﻔﺘﺳا

زا

داﻮﻣ ﺐﻛﺮﻣ ﻲﻣ ﺪﺷﺎﺑ .

ﻔﻄﺼﻣ ﻲ و ﻠﻋ ﻲ 1] زا[ شور ژﺮﻧا ي اﺮﺑ ي ﻠﺤﺗ ﻴ ﻞ تﺎﺷﺎﻌﺗرا دازآ

ﻪﺘﺳﻮﭘ ﺎﻫ ي ﻪﻧاﻮﺘﺳا ا ي ﻮﻘﺗ ﻳ ﺖ هﺪﺷ

، ﺎﺑ ﺮﻈﻧرد ﻦﺘﻓﺮﮔ ﻤﺧ ﻴ ﮔﺪ ﻲ

،

ﺸﻛ ﻴ ﮔﺪ ﻲ و ﭘ ﻴ ﭽ ﻴ ﮔﺪ ﻲ ﻮﻘﺗ ﻳ ﺖ

،هﺪﻨﻨﻛ هدﺎﻔﺘﺳا ﺪﻧدﺮﻛ . ﮓﻧ و

ﻢﻟ 2] تﺎﺷﺎﻌﺗرا [ دازآ

و ﺖﻋﺮﺳ ﻧاﺮﺤﺑ ﻲ ﻪﺘﺳﻮﭘ ﺎﻫ ي اﻳ ﭘوﺮﺗوﺰ ﻴ ﻚ

راود ﺖﺤﺗ رﺎﺑ رﻮﺤﻣ ي ﺖﺑﺎﺛ ار ﻠﺤﺗ ﻴ ﻞ ﺪﻧدﺮﻛ .

،ﻮﻫاژ ﻟ ﻴ ﻮ و ﮓﻧ 3] [

تﺎﺷﺎﻌﺗرا ﻪﺘﺳﻮﭘ

ﺎﻫ ي زﻮﭙﻣﺎﻛ ﻳﺘ ﻲ راود ﺎﺑ ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ي ﺪﻣﺎﻌﺘﻣ

ار ﺳرﺮﺑ ﻲ ﺮﻛ ﺪﻧد يﺮﻔﻌﺟ . و يﺮﻗﺎﺑ 4] ﺎﺑ [ شور يﺎﻫ

،يدﺪﻋ

ﻲﻠﻴﻠﺤﺗ و ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﻪﺑ

ﻲﺳرﺮﺑ تﺎﺷﺎﻌﺗرا دازآ

ﻪﺘﺳﻮﭘ يﺎﻫ

ﻪﻧاﻮﺘﺳا يا ﻚﻴﭘوﺮﺗوﺰﻳا ﺎﺑ

ﺖﻳﻮﻘﺗ هﺪﻨﻨﻛ يﺎﻫ ﻲﻄﻴﺤﻣ ﺪﻨﺘﺧادﺮﭘ و

ﺞﻳﺎﺘﻧ ﻞﺻﺎﺣ زا ﻪﺳ شور قﻮﻓ ار ﺎﺑ ﻢﻫ ﻪﺴﻳﺎﻘﻣ ﺪﻧدﺮﻛ . ﻣﺮﺧ ﻲ و

ﺴﺣ ﻴ ﻨ ﻲ ﻤﺷﺎﻫ ﻲ 5] ﺎﺑ [ هدﺎﻔﺘﺳا زا شور د ﻳ ﺴﻧاﺮﻔ ﻴ ﻞ ﺮﭼارداﻮﻛ و1

رﻮﺌﺗ ي ﻪﺒﺗﺮﻣ لوا ﻐﺗ ﻴﻴ ﺮ ﻞﻜﺷ ﺷﺮﺑ ﻲ ﻪﺑ ﺳرﺮﺑ ﻲ تﺎﺷﺎﻌﺗرا ﻪﺘﺳﻮﭘ

ﻪﻧاﻮﺘﺳا ا ي ﻪﺘﺧﺎﺳ هﺪﺷ زا داﻮﻣ ﺪﻨﻤﻓﺪﻫ ﺪﻨﺘﺧادﺮﭘ

. رد ﻪﻨﻴﻣز

تﺎﻌﻟﺎﻄﻣ مﺎﺠﻧا

ﻪﺘﻓﺮﮔ ﺎﺑ هدﺎﻔﺘﺳا زا يرﻮﺌﺗ

ﻪﺳ يﺪﻌﺑ ﻪﺘﻴﺴﻴﺘﺳﻻا رد

ﻪﺴﻳﺎﻘﻣ ﺎﺑ ﺮﮕﻳد يرﻮﺌﺗ ﺎﻫ

، ﻪﺑ ﻞﻴﻟد

ﻲﮔﺪﻴﭽﭘ نآ

و رد ﺮﻈﻧ ﻦﺘﻓﺮﮔ ﺮﻫ ﺶﺷ ءﺰﺟ ناﺪﻴﻣ ﺶﻨﺗ و

ﺶﻧﺮﻛ

، رﺎﻴﺴﺑ ﻢﻛ ﻲﻣ ﺪﺷﺎﺑ . زا ﻪﻠﻤﺟ ﻦﻳا تﺎﻘﻴﻘﺤﺗ ﻲﻣ

ناﻮﺗ ﻪﺑ

1. Differential Quadrature Method

ﻪﻟﺎﻘﻣ نﻮﺴﻠﻧ 6] رد [ ﻪﻨﻴﻣز تﺎﺷﺎﻌﺗرا ﻪﺘﺳﻮﭘ

ﻪﻧاﻮﺘﺳا يا ﺎﺑ لﻮﻃ

دوﺪﺤﻣﺎﻧ هرﺎﺷا دﺮﻛ . ﻦﻴﻨﭽﻤﻫ ياﺮﺑ

ﻪﻧاﻮﺘﺳا ﺎﺑ لﻮﻃ دوﺪﺤﻣ ﻲﻣ

ناﻮﺗ رﺎﻛ يﺎﻫ نﻮﺴﻴﻨﭽﺗﺎﻫ و

يﺮﻫزﻻا 7] و[ ﺎﺴﻴﻟ 8] ار[ مﺎﻧ دﺮﺑ ﻪﻛ

ﺎﺑ هدﺎﻔﺘﺳا زا شور ﻲﻠﻳر ﺰﺘﻳر ﻦﻳا ﻪﻠﺌﺴﻣ ار درﻮﻣ ﻲﺳرﺮﺑ راﺮﻗ

ﺪﻧداد . ﻚﻠﻣ هداز و ﺶﻧارﺎﻜﻤﻫ 9]

ﺎﺑ [ هدﺎﻔﺘﺳا زا يرﻮﺌﺗ ﻻ ﻳ ﻪ ا ي و

هدﺎﻔﺘﺳا زا شور د ﻳ ﺴﻧاﺮﻔ ﻴ ﻞ ﺮﭼارداﻮﻛ ﻪﺑ

ﻠﺤﺗ ﻴ ﻞ تﺎﺷﺎﻌﺗرا ﻪﺘﺳﻮﭘ

ﻪﻧاﻮﺘﺳا ا ي زﻮﭙﻣﺎﻛ ﻳﺘ ﻲ ﺪﻨﺘﺧادﺮﭘ . رد ﻪﻣادا ﻲﻠﻋ ﻮﻠﮕﻴﺑ 10] ﻪﺑ [

ﻪﻌﻟﺎﻄﻣ تﺎﻴﺻﻮﺼﺧ ﻲﻜﻴﺗﺎﺘﺳا

و ﻲﺗﺎﺷﺎﻌﺗرا ﻪﺘﺳﻮﭘ

ﻲﺘﻳزﻮﭙﻣﺎﻛ ﺎﺑ

ﻻ ﻳ ﻪ ﺎﻫ ﻲﻳ اراد ي واز ﻳ ﻪ ﻟا ﻴ فﺎ 0 و 90

2ﻪﺟرد ﺎﺑ هدﺎﻔﺘﺳا زا يرﻮﺌﺗ

ﻪﺳ يﺪﻌﺑ ﻻ ﻳ ﻪ ا ي ﻪﺘﻴﺴﻴﺘﺳﻻا و

هدﺎﻔﺘﺳا زا يﺎﻀﻓ ﺖﻟﺎﺣ ﻪﺑ هاﺮﻤﻫ

شور د ﻳ ﺴﻧاﺮﻔ ﻴ ﻞ ﺮﭼارداﻮﻛ ﺖﺧادﺮﭘ

. ﻨﭽﻤﻫ ﻴ ﻦ ﻨﻛ ﻲ و ﻠﻋ ﻲ

ﺑﻴ ﻮﻠﮕ 11]

،[ ﺎﺑ هدﺎﻔﺘﺳا زا رﻮﺌﺗ ي ﻪﺳ ﺪﻌﺑ ي و شور ﻠﺤﺗ ﻴﻠ ﻲ

،

ﻪﻧاﻮﺘﺳا ا ي ﻻﺪﻨﭼ ﻳ ﻪ ﺎﺑ ﻻ ﻳ ﻪ ﭘ ﻴ ﺮﺘﻜﻟاوﺰ ﻳ ﻚ ار درﻮﻣ

ﺳرﺮﺑ ﻲ راﺮﻗ ﺪﻧداد .

رد ا ﻳ ﻦ

،ﻪﻟﺎﻘﻣ ﻞﻴﻠﺤﺗ ﻲﻜﻴﻣﺎﻨﻳد ﻪﺘﺳﻮﭘ

ﺎﻫ ي ﻪﻧاﻮﺘﺳا ا ي

زﻮﭙﻣﺎﻛ ﻳﺘ ﻲ راود ﻮﻘﺗ ﻳ ﺖ هﺪﺷ ﺖﺤﺗ ﺮﺛا رﺎﺑ رﻮﺤﻣ ي ﺖﺑﺎﺛ و رﺎﺸﻓ

،

ﺎﺑ اﺮﺷ ﻳ ﻂ زﺮﻣ ي ﻜﺗ ﻴ ﻪ هﺎﮔ هدﺎﺳ رد ﺮﺳود

، ﺎﺑ هدﺎﻔﺘﺳا زا رﻮﺌﺗ ي

ﻪﺳ ﺪﻌﺑ ي ﻻ ﻳ ﻪ ا ي

، ﻪﻌﻟﺎﻄﻣ ﻣ ﻲ دﻮﺷ . اﺮﺑ ي جاﺮﺨﺘﺳا تﻻدﺎﻌﻣ

ﻪﻠﻜﺸﺘﻣ ﻢﻛﺎﺣ ﺮﺑ ﻪﺘﺳﻮﭘ زا شور ژﺮﻧا ي و ﻞﺻا ﻤﻫ ﻴ نﻮﺘﻠ هدﺎﻔﺘﺳا

ﻣ ﻲ دﻮﺷ . ﺛﺎﺗ ﻴ ﺮ ﺎﻫﺮﺘﻣارﺎﭘ ي ﻒﻠﺘﺨﻣ ﻈﻧ ﻴ ﺮ ﺖﻋﺮﺳ ﻧارود ﻲ

،ﻪﺘﺳﻮﭘ

ﻣ ﻴ ناﺰ رﺎﺑ رﻮﺤﻣ ي

، رﺎﺸﻓ و ﺖﺒﺴﻧ عﺎﻔﺗرا ﻪﺑ ﺎﻨﻬﭘ ي ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ

ﺮﺑ ور ي ﺲﻧﺎﻛﺮﻓ ﺒﻃ ﻴ ﻌ ﻲ و ﺖﻋﺮﺳ ﻧاﺮﺤﺑ ﻲ ﺳرﺮﺑ ﻲ هﺪﺷ ﺖﺳا . ﺮﺛا

ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ﺎﺑ هدﺎﻔﺘﺳا زا شور ﻪﻧﺎﮔاﺪﺟ دراو تﻻدﺎﻌﻣ هﺪﺷ و

رد ﺖﻳﺎﻬﻧ ﺎﺘﻧ ﻳ ﺞ ﻪﻠﺻﺎﺣ ﺎﺑ ﺎﺘﻧ ﻳ ﺞ دﻮﺟﻮﻣ رد تﻻﺎﻘﻣ ﺮﮕﻳد ﺎﻘﻘﺤﻣ ن

و ﻨﭽﻤﻫ ﻴ ﻦ ﺎﺘﻧ ﻳ ﺞ ﻞﺻﺎﺣ زا ﻠﺤﺗ ﻴ ﻞ دﺪﻋ ي ﻂﺳﻮﺗ مﺮﻧ راﺰﻓا

سﻮﻛﺎﺑا ﺎﻘﻣ3

ﻳ ﻪﺴ هﺪﺷ ﻪﻛ اراد ي ﻧاﻮﺨﻤﻫ ﻲ ﺒﺳﺎﻨﻣ ﻲ ﻣ ﻲ ﺪﺷﺎﺑ .

2 - رﻮﺌﺗ ي ﻪﻠﺌﺴﻣ

2 - 1 - ﻪﺳﺪﻨﻫ ﻪﻠﺌﺴﻣ

ﻪﺘﺳﻮﭘ ﻪﻧاﻮﺘﺳا ا ي زﻮﭙﻣﺎﻛ ﻳﺘ ﻲ ﺎﺑ ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ي ﺪﻣﺎﻌﺘﻣ

، ﺎﺑ

ﺖﻋﺮﺳ واز ﻳ ﻪ ا ي ﻪﺑ Ω رود رﻮﺤﻣ نرﺎﻘﺗ ﻟﻮﻃ ﻲ

، درﻮﻣ ﺳرﺮﺑ ﻲ ﻊﻗاو

هﺪﺷ ﺖﺳا . ﺳ ﻴ ﻢﺘﺴ تﺎﺼﺘﺨﻣ ﺪﻣﺎﻌﺘﻣ

(x,θ,z) ﺮﺑ ﺢﻄﺳ ﻊﺟﺮﻣ ﺮﺑ

ور ي ﻻ ﻳ ﻪ ﻣ ﻴ ﻧﺎ ﻲ ﻪﺘﺳﻮﭘ راﺮﻗ دراد . ﻖﺑﺎﻄﻣ ﻞﻜﺷ 1

، رد رﻮﺌﺗ ي

ﻻ ﻳ ﻪ ا ي

، ﻪﺘﺳﻮﭘ ﻪﺑ Nl

ﻻ ﻳ ﻪ هاﻮﺨﻟد ﺿﺮﻓ ﻲ ﺴﻘﺗ ﻴ ﻢ ﻣ ﻲ دﻮﺷ . عﺎﻌﺷ

2. Cross-ply 3. Abaqus

(3)

ﻮﺠﺸﻧاد ناﺮﻣﺎﻛ رﺎﻜﻤﻫ و

نا

ةرﺎﻤﺷ 6 ، ﺪﻨﻔﺳا 1391

ﺲﻳﺮﺗﺎﻣ ﺎﺑ ﻪﺘﻓﺎ

[ ]

¹

C T ⁻ C T

 =

 

ﻪﺑ هدﺎﻣ تﺎﺼﺘﺨﻣ زا لﺎﻘﺘﻧا ﺲﻳﺮﺗﺎﻣ

[ ]

2 2

0 0 1 0 0 0

0 0 0 0

cos , sin

m n mn

n m mn

T

mn mn m n

m n

 

 

= 

 

− −

 

= =

ﺖﻬﺟ و ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ فﺎﻴﻟا ﻦﻴﺑ ﻪﻳواز ﻦﻴﻨﭽﻤﻫ

[ ]

^C

ﺲﻳﺮﺗﺎﻣ

ﻪﻳﻻ ﻚﻳ ياﺮﺑ و ﺪﺷﺎﺑ

[ ]

11 12 13

21 22 23

31 32 33

0 0 0 0 0

C C C

C

 

 

= 

 

 

11 11 22 22

33 33

12 21 11

13 31 22

23 32 33

44 23 55 13 66 12

12 21 23 32 31 13 21 32 13

1 1

1

, ,

1 2

C E C E

C E

C C E

C G C G C G

υ υ υ υ υ υ υ υ υ

= =

=

= =

= = =

∆ = − − − −

و ﻲﺷﺮﺑ لوﺪﻣ ν_ij

ﻪﺑﺎﺟ ﻲﻳﺎﺟ ياﺮﺑ

ﻮﺷ د ] 10 .[

{ }

^ε ⁼

[ ]

^D

{

^χ

ﻮﺠﺸﻧاد ناﺮﻣﺎﻛ

سرﺪﻣ ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ

ةرود 12 ةرﺎﻤﺷ

لﺎﻘﺘﻧا ﻲﺘﻔﺳ ﺲﻳﺮﺗﺎﻣ ﻪﻄﺑار ﻳ

ﺲﻳﺮﺗﺎﻣ ﺎﺑ ﻪﺘﻓﺎ

[ ][ ]

C T ⁻1 C T

ﻲﻣ ﺮﻳز ترﻮﺻ ﻪﺑ و ﻲﻠﺻا تﺎﺼﺘﺨﻣ ﺪﺷﺎﺑ

.

2 2

0 0 0 2

0 0 1 0 0 0

0 0 0 0

0 0 0

cos , sin

m n mn

n m mn

mn mn m n

m α n α

 

 

− −

 

= =

ﺖﻬﺟ و ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ فﺎﻴﻟا ﻦﻴﺑ ﻪﻳواز ﺪﺷﺎﺑ

. ﻦﻴﻨﭽﻤﻫ

ﻲﻣ هدﺎﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد رد ﻲﺘﻔﺳ ﻪﻳﻻ ﻚﻳ ياﺮﺑ و ﺪﺷﺎﺑ

ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳز ترﻮﺻ ﻪﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ ددﺮﮔ

.

11 12 13

21 22 23

31 32 33

0 0 0 0 0

C C C

 

 

 

23 32 31 13

11 11 22 22

21 12

21 31 23

12 21 11

13 12 23

13 31 22

23 21 13

23 32 33

44 23 55 13 66 12

12 21 23 32 31 13 21 32 13

1 1

, 1

, ,

1 2

C E C E

C C E

C G C G C G

υ υ υ υ

υ υ

− −

= =

∆ ∆

−

∆

= = +

∆

= = +

∆

= = +

∆

= = =

∆ = − − − −

،ﻪﺘﻴﺴﻴﺘﺳﻻا لوﺪﻣ Gij

و ﻲﺷﺮﺑ لوﺪﻣ

ﻲﻣ ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ ياﺮﺑ نﺎﺳﻮﭘ يﺎﻫ ﺪﻨﺷﺎﺑ

.

ﻪﺘﻴﺴﻴﺘﺳﻻا ﻪﻄﺑار

ﺶﻧﺮﻛ - ﻪﺑﺎﺟ

ﺮﻳز ﻲﺴﻳﺮﺗﺎﻣ نﺎﻴﺑ

ﻲﻣ ﻮﺷ

}

ε χ

لﺎﻘﺘﻧا ﻲﺘﻔﺳ ﺲﻳﺮﺗﺎﻣ ﻪﻄﺑار

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ هدﺎﻣ ﻲﺘﻔﺳ .

قﻮﻓ ﻪﻄﺑار رد ﻪﻛ

[ ]

^T

ﻲﻣ ﺮﻳز ترﻮﺻ ﻪﺑ و ﻲﻠﺻا تﺎﺼﺘﺨﻣ

2 2

0 0 0 2

0 0 1 0 0 0

0 0 0 0

0 0 0

cos , sin

m n mn

n m mn

m n n m

mn mn m n

α α

 

 

 − 

 

 − 

 

− −

 

قﻮﻓ ﻪﻄﺑار رد ﺖﻬﺟ و ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ فﺎﻴﻟا ﻦﻴﺑ ﻪﻳواز α

ﻲﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد ﺪﺷﺎﺑ

ﻲﻣ هدﺎﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد رد ﻲﺘﻔﺳ ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳز ترﻮﺻ ﻪﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

21 22 23

31 32 33

44 55

0 0 0

0 0 0 0 0

C C

 

 

 

23 32 31 13

11 11 22 22

21 31 23

13 12 23

23 21 13

44 23 55 13 66 12

12 21 23 32 31 13 21 32 13

1 1

, ,

1 2

C E C E

C G C G C G

υ υ υ υ

− −

= =

∆ ∆

∆

= = =

∆ = − − − −

Eij

،ﻪﺘﻴﺴﻴﺘﺳﻻا لوﺪﻣ

ﻲﻣ ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ ياﺮﺑ نﺎﺳﻮﭘ يﺎﻫ يﺪﻌﺑ

ﻪﺘﻴﺴﻴﺘﺳﻻا ترﻮﺻ ﺮﻳز ﻲﺴﻳﺮﺗﺎﻣ

ﻦﻴﻨﭽﻤﻫ

، لﺎﻘﺘﻧا ﻲﺘﻔﺳ ﺲﻳﺮﺗﺎﻣ ﻪﻄﺑار

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ هدﺎﻣ ﻲﺘﻔﺳ قﻮﻓ ﻪﻄﺑار رد ﻪﻛ ﻲﻣ ﺮﻳز ترﻮﺻ ﻪﺑ و ﻲﻠﺻا تﺎﺼﺘﺨﻣ

2 2

0 0 0 2

0 0 1 0 0 0

0 0 0 0

m n mn

n m mn

mn mn m n

 

 

 − 

 

− −

 

قﻮﻓ ﻪﻄﺑار رد ﻪﺼﺘﺨﻣ ﻲﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد x

ﻲﻣ هدﺎﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد رد ﻲﺘﻔﺳ ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳز ترﻮﺻ ﻪﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

66

0 0 0

0 0 0 0 0

C

 

 

 

(

23 32 31 13

44 23 55 13 66 12

12 21 23 32 31 13 21 32 13

υ υ υ υ

− −

∆ ∆

قﻮﻓ ﻪﻄﺑار رد ﻪﻛ Eij

ﺖﺒﺴﻧ ﻲﻣ ﻲﺘﻳزﻮﭙﻣﺎﻛ ﻪﻳﻻ ياﺮﺑ نﺎﺳﻮﭘ يﺎﻫ

رد يرﻮﺌﺗ ﻪﺳ يﺪﻌﺑ

ﻪﺘﺳﻮﭘ ﻪﻧاﻮﺘﺳا ﻪﺑ يا

ﻴ

ﺐ

لﻮﻃ

ﻞﻜﺷ

ﺢﻄﺳ ددﺮﮔ .

ياﺮﺑ ﺶﻧﺮﻛ

{

^σ ^ε

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ ﺶﻧﺮﻛ و ﺶﻨﺗ يﺎﻫ .

{ {

σ σ σ σ τ τ τ

ε ε ε ε γ γ γ

دﻮﺷ .

 C

  ﻦﻴﻨﭽﻤﻫ

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ هدﺎﻣ ﻲﺘﻔﺳ ) 4 ( قﻮﻓ ﻪﻄﺑار رد ﻪﻛ ﻲﻣ ﺮﻳز ترﻮﺻ ﻪﺑ و ﻲﻠﺻا تﺎﺼﺘﺨﻣ ) 5 ( قﻮﻓ ﻪﻄﺑار رد

ﻪﺼﺘﺨﻣ ﻲﻣ هدﺎﻣ تﺎﺼﺘﺨﻣ هﺎﮕﺘﺳد رد ﻲﺘﻔﺳ ﻲﻣ ﻒﻳﺮﻌﺗ ﺮﻳز ترﻮﺻ ﻪﺑ ﻲﺘﻳزﻮﭙﻣﺎﻛ

) 6 (

) 7 ( قﻮﻓ ﻪﻄﺑار رد ﻪﻛ

ﺖﺒﺴﻧ رد ﻪﺘﺳﻮﭘ

) 8 (

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ يﺎﻫ

،

v^j و w^j ﻪﺑ ﺗﺮﺗ ﻴ

ﻪﺘﺳﻮﭘ اراد ي لﻮﻃ

ترﻮﺻ ﻄﺘﺴﻣ ﻴ ﻞ ﻞﻜﺷ

ﻪﻠﺻﺎﻓ ﺰﻛﺮﻣ ﺢﻄﺳ

ﺺﺨﺸﻣ ﻣ ﻲ ددﺮﮔ

شﺮﺑ

،A-A

ﻊﻄﻘﻣ ﺢﻄﺳ ﮓﻨﻳر

ا ي ﻮﻘﺗ ﻳ ﺖ هﺪﺷ

ﺶﻨﺗ ﻪﻄﺑار ،ﻪﺘﻴﺴﻴﺘﺳﻻا -

ياﺮﺑ ﺶﻧﺮﻛ

}

^C

{ }

σ =^{ }  ε

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ ﺶﻧﺮﻛ و ﺶﻨﺗ يﺎﻫ

} {

T

x z z xz x

T

x θ z θz xz xθ

=

ﺮﻳز ﻒﻳﺮﻌﺗ ﻲﻣ دﻮﺷ

11 12 13 16

21 22 23 26

31 32 33 36

16 26 36 66

0 0 0 0

C C C C

C

C C C C

 

 

 = 

   

 

 

ﻪﺘﺳﻮﭘ ﻲﻧاﺮﺤﺑ ﺖﻋﺮﺳ و تﺎﺷﺎﻌﺗرا يﺪﻌ

ﻪﺑﺎﺟ

ﺎﺟ ﻲﻳ ﺎﻫ ي u^j ،

ﻪﺘﻓﺮﮔ ﻣ ﻲ دﻮﺷ . ﻪﺘﺳﻮﭘ

هﺪﻨﻨﻛ ﺎﻫ ﻪﺑ ترﻮﺻ

bs/r

ﻣ ﻲ ﺪﻨﺷﺎﺑ . ﻪﻠﺻﺎﻓ

ﻲ ﻪﺘﺳﻮﭘ ﺎﺑ zs/r

ﺺﺨﺸﻣ

شﺮﺑ ﻊﻄﻘﻣ ﺢﻄﺳ

ي ﻪﺘﺳﻮﭘ ﻪﻧاﻮﺘﺳا ا

ﺘﺳﻻا ﻴ ﺴ ﻴ ﻪﺘ

ﺶﻨﺗ ﻪﻄﺑار ،ﻪﺘﻴﺴﻴﺘﺳﻻا

ﻲﻣ نﺎﻴﺑ ﺮﻳز ترﻮﺻ ﻪﺑ ﻪﻳﻻﺪﻨﭼ ﻪﺘﺳﻮﭘ دﻮﺷ

.

ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ ﺶﻧﺮﻛ و ﺶﻨﺗ يﺎﻫ

x z z xz x

θ θ θ

=

 C ﻪﺑ   ترﻮﺻ ﺮﻳز

11 12 13 16

21 22 23 26

31 32 33 36

16 26 36 66

0 0 0 0

C C C C

C C

C C C C

 

 

= 

 

 

ﻻ

ﻳ ﻪ ما j و ﻪﺑﺎﺟ

و θ ﺮﻈﻧرد z ﻪﺘﻓﺮﮔ

ﻮﻘﺗو h ﻳ ﺖ هﺪﻨﻨﻛ

ds/r

و ﺎﻨﻬﭘ ي

s/r

ﺎﺗ ﺢﻄﺳ ﺟرﺎﺧ ﻲ

،B-B

ﺮﮕﻨﻳﺮﺘﺳا ﻊﻄﻘﻣ ﺢﻄﺳ

ﻪﺳﺪﻨﻫ و راﺬﮔدﺎﻤﻧ ي

ﻪﺳ ﺪﻌﺑ ي ﺘﺳﻻا

ﻪﺳ يرﻮﺌﺗ ﻖﺒﻃ يﺪﻌﺑ

ﺶﻨﺗ ﻪﻄﺑار ،ﻪﺘﻴﺴﻴﺘﺳﻻا

ﻲﻣ نﺎﻴﺑ ﺮﻳز ترﻮﺻ ﻪﺑ ﻪﻳﻻﺪﻨﭼ ﻪﺘﺳﻮﭘ ﻪﻔﻟﻮﻣ قﻮﻓ ﻪﻄﺑار رد ﻪﻛ ﺖﺳا ﺮﻳز ترﻮﺻ ﻪﺑ ﺶﻧﺮﻛ و ﺶﻨﺗ يﺎﻫ

} }

x z z xz x

θ θ θ

=

ﻲﺘﻔﺳ ﺶﻫﺎﻛ ﻳ ﻪﺘﻓﺎ

 C

 

11 12 13 16

21 22 23 26

31 32 33 36

44 45

45 55

16 26 36 66

0 0

0 0 0 0

0 0

C C C C

C C

C C C C

 

 

= 

 

 

ﻪﺳ ﻞﻴﻠﺤﺗ ﺑ

82

ﺖﺑﺎﺛ Rj

اﺮﺑ ي ﻻ

رد تﺎﻬﺟ

،x θ

و L ﺖﻣﺎﺨﺿ

اراد ي عﺎﻔﺗرا

s/r

ﻮﻘﺗ ﻳ ﺖ هﺪﻨﻨﻛ ﺎﻫ ﺎﺗ

شﺮﺑ B

ﺮﮕﻨﻳﺮﺘﺳا ﻊﻄﻘﻣ ﺢﻄﺳ ﻞﻜﺷ ﻪﺳﺪﻨﻫ1

2 - 2 - رﻮﺌﺗ ي ﻪﺳ

ﻪﺳ يرﻮﺌﺗ ﻖﺒﻃ ﻲﻣ نﺎﻴﺑ ﺮﻳز ترﻮﺻ ﻪﺑ ﻪﻳﻻﺪﻨﭼ ﻪﺘﺳﻮﭘ ) 1 ( ﻪﻔﻟﻮﻣ قﻮﻓ ﻪﻄﺑار رد ﻪﻛ

) 2 (

و ﺲﻳﺮﺗﺎﻣ ﻲﺘﻔﺳ

) 3 (

11 12 13 16

21 22 23 26

31 32 33 36

16 26 36 66

0 0 0 0

C C C C

 

 

= 

 

 

82 ﺖﺑﺎﺛ رد L اراد ﻮﻘﺗ

2 ﻪﺳ يرﻮﺌﺗ ﻖﺒﻃ ﻲﻣ نﺎﻴﺑ ﺮﻳز ترﻮﺻ ﻪﺑ ﻪﻳﻻﺪﻨﭼ ﻪﺘﺳﻮﭘ ﻪﻔﻟﻮﻣ قﻮﻓ ﻪﻄﺑار رد ﻪﻛ

و

)