پایان نامه تحلیل غیر خطی دینامیکی و ارتعاشی نانو لوله کربنی در سیستم نانو الکترومکانیک‌سوییچ با استفاده از تئوری غیر‌محلی الاستیسیته

فهرست:

1-فصل اول : مقدمه    1

1-1-سیستم‌های میکرو و نانو الکترومکانیکی      1

1-1-1-  سوییچ‌های الکترواستاتیک... 5

1-1-1-1-مزایا و معایب میکرو و نانوسوییچ‌ها  6

1-1-2-سیستم‌های میکرو و نانو الکترومکانیکی در شناسایی ذره‌ خارجی   9

1-1-3-  تئوری‌های کلاسیک و غیر موضعی.. 10

1-1-4-فصل‌بندی پژوهش... 11

1-2-مفاهیم پایه و اصلی   13

1-2-1-تحریک الکترواستاتیک در میدان الکتریکی   13

1-2-2-نیروی بین ملکولی واندروالس    16

1-2-2-1-مقدمه    16

1-2-2-2-تعامل نیروی واندروالس و الکترواستاتیک در نانوسوییچ.. 17

1-2-3-تئوری تنش غیرمحلی.. 18

1-2-4-حسگر جرمی.. 20

1-3-مروری بر ادبیات و تاریخچه موضوع تحقیق    22

1-3-1-مروری بر تاریخچه مدلسازی و طراحی میکرو/نانوسوییچ‌های کربنی   22

1-3-2- مروری بر روش‌های حل عددی و تحلیلی میکرو/نانو تیرهای تحریک‌شده با میدان الکتریکی   25

1-3-3-پیشرفت‌های انجام شده در زمینه سنسورها 29

1-3-4-اهداف پژوهش و سازماندهی.. 32

2-فصل دوم : مدلسازی مسأله. 34

2-1-استخراج معادله حاکم بر مسأله  34

2-2-استخراج شرایط مرزی   38

2-2-1-سوییچ یکسرگیردار 38

2-3-  بی‌بعد‌سازی معادلات.. 40

2-4-بسط تیلورنیروهای غیر خطی   41

2-5-حل خطی مسأله. 41

2-6-تاثیر ولتاژ روی فرکانس طبیعی تیر    43

3-فصل سوم : تحلیل استاتیکی و دینامیکی سیستم.. 46

3-1-تحلیل استاتیکی   46

3-1-1-روش حل معادلات مقدار مرزی در متلب   47

3-1-2-نتایج و نمودارهای تحلیل استاتیک    48

3-2-تحلیل دینامیکی   59

3-2-1-  مقدمه. 59

3-2-2-استخراج معادله خطی و همگن برای ارتعاش آزاد. 60

3-2-3-حل ارتعاش آزاد مسأله. 62

3-2-3-1-شرایط مرزی طبیعی در    64

3-2-4-روش گالرکین، و حذف وابستگی به مکان در مسئله  66

3-2-5-حل عددی معادله دیفرانسیل غیرخطی وابسته به زمان  68

3-2-6-نمودار ها و نتایج تحلیل دینامیک    69

4-فصل چهارم : بررسی ناپایداری سیستم با حضور ذره جرمی محرک... 77

4-1-مقدمه 77

4-1-1-ارتعاش سازه‌ها تحت بار یا ذره محرک    77

4-1-2-نانو ذره محرک در سیستم‌های نانو الکترومکانیک    78

4-2-فرضیات لازم جهت مدلسازی مسأله  79

4-3-فرموله کردن مسأله  80

4-3-1-معرفی پارامترهای بدون بعد ذره 82

4-4-نتایج عددی و بحث‌ها 83

5-فصل پنجم : ناپایداری استاتیکی غیرخطی غیرمحلی نانوسوییچ ‌نیترید-بور. 88

5-1-         مقدمه. 88

5-2-نانوسوییچ نیترید-بور 89

5-3-مدلسازی نانوسوییچ   90

5-3-1-راوابط کرنش-جابجایی.. 90

5-3-2-مواد پیزوالکتریک... 90

5-3-3-  نیروی‌های خارجی.. 91

5-3-4-تئوری پیزوالاستسیته غیرمحلی.. 92

5-4-معادلات حاکم  92

5-5-روش حل و نتایج عددی   95

5-5-1-روش مربع‌سازی دیفرانسیلی.. 95

5-5-2-نتایج عددی و بحث‌ها 97

6-فصل ششم : نتیجه‌گیری و پیشنهادها 101

6-1-نتیجه‌گیری   101

6-1-1-لزوم تحلیل و سازماندهی پژوهش    101

6-1-2-نتایج تحلیل و بررسی پژوهش    102

6-2-پیشنهادها برای کارهای بعدی   105

پیوست        106

الف- تعریف دستور روش bvp4c در متلب.. 106

مراجع     108

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