بررسی ارتعاشات آزاد ورق قطاعی تابعی مدرج دوبعدی کوپل با پیزوالکتریک مستقر بر بستر الاستیک دوپارامتری با استفاده از روش رایلی ریتز و تئوری مرتبه سوم تغییر شکل برشی

Abstract

<span lang="AR-SA" dir="RTL">در</span><span lang="AR-SA" dir="RTL">ا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ن</span><span lang="AR-SA" dir="RTL">مقاله</span><span lang="AR-SA" dir="RTL">ارتعاشات</span><span lang="AR-SA" dir="RTL">آزاد</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">قطاع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">تابع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مدرج</span><span lang="AR-SA" dir="RTL">دو</span><span lang="AR-SA" dir="RTL">بعد</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">کوپل</span><span lang="AR-SA" dir="RTL">با</span><span lang="AR-SA" dir="RTL">پ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">زوالکتر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ک</span><span lang="AR-SA" dir="RTL">بر</span><span lang="AR-SA" dir="RTL">مبنا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">تئور</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مرتبه</span><span lang="AR-SA" dir="RTL">سوم</span><span lang="AR-SA" dir="RTL">تغ</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ر شکل</span><span lang="AR-SA" dir="RTL">برش</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مستقر</span><span lang="AR-SA" dir="RTL">بر</span><span lang="AR-SA" dir="RTL">بستر</span><span lang="AR-SA" dir="RTL">الاست</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ک</span><span lang="AR-SA" dir="RTL">دو</span><span lang="AR-SA" dir="RTL">پارامتر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مورد</span><span lang="AR-SA" dir="RTL">بررس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">قرار</span><span lang="AR-SA" dir="RTL">گرفته</span><span lang="AR-SA" dir="RTL">است</span><span>. </span><span lang="AR-SA" dir="RTL">تئور</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مرتبه</span><span lang="AR-SA" dir="RTL">سوم</span><span lang="AR-SA" dir="RTL">تغ</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">شکل</span><span lang="AR-SA" dir="RTL">برش</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">با وجود</span><span lang="AR-SA" dir="RTL">داشتن</span><span lang="AR-SA" dir="RTL">معادلات</span><span lang="AR-SA" dir="RTL">پ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">چ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ده</span><span lang="AR-SA" dir="RTL">تر</span><span lang="AR-SA" dir="RTL">بدل</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ل</span><span lang="AR-SA" dir="RTL">در</span><span lang="AR-SA" dir="RTL">نظر</span><span lang="AR-SA" dir="RTL">گرفتن</span><span lang="AR-SA" dir="RTL">تاث</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">رات</span><span lang="AR-SA" dir="RTL">تغ</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">شکل</span><span lang="AR-SA" dir="RTL">برش</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">عرض</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">ا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">نرس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">دوران</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">منجر</span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">حصول</span><span lang="AR-SA" dir="RTL">نتا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ج دق</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ق</span><span lang="AR-SA" dir="RTL">تر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">م</span><span lang="AR-SA" dir="RTL">ی‌</span><span lang="AR-SA" dir="RTL">شود</span><span>. </span><span lang="AR-SA" dir="RTL">تغ</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">خواص</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">مدور</span><span lang="AR-SA" dir="RTL">تابع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">دو</span><span lang="AR-SA" dir="RTL">بعد</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">صورت</span><span lang="AR-SA" dir="RTL">پ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">وسته</span><span lang="AR-SA" dir="RTL">در</span><span lang="AR-SA" dir="RTL">دو</span><span lang="AR-SA" dir="RTL">راستا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ضخامت</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">مح</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ط</span><span lang="AR-SA" dir="RTL">در</span><span lang="AR-SA" dir="RTL">نظر</span><span lang="AR-SA" dir="RTL">گرفته</span><span lang="AR-SA" dir="RTL">شده است</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">برا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">مدل</span><span lang="AR-SA" dir="RTL">ساز</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">رفتار</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">تابع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">دو</span><span lang="AR-SA" dir="RTL">بعد</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">مدل</span><span lang="AR-SA" dir="RTL">قانون</span><span lang="AR-SA" dir="RTL">توان</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">کسر</span><span lang="AR-SA" dir="RTL">حجم</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">استفاده</span><span lang="AR-SA" dir="RTL">شده</span><span lang="AR-SA" dir="RTL">است</span><span>. </span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">منظور</span><span lang="AR-SA" dir="RTL">تع</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ن</span><span lang="AR-SA" dir="RTL">پتانس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ل الکتر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ک</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">لا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ه‌ها</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">پ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">زوالکتر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ک</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">توابع</span><span lang="AR-SA" dir="RTL">س</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">نوس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">استفاده</span><span lang="AR-SA" dir="RTL">شده</span><span lang="AR-SA" dir="RTL">است</span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">نحو</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">که</span><span lang="AR-SA" dir="RTL">معادله</span><span lang="AR-SA" dir="RTL">الکترواستات</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ک</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ماکسول</span><span lang="AR-SA" dir="RTL">بوس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">له</span><span lang="AR-SA" dir="RTL">ا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ن توابع</span><span lang="AR-SA" dir="RTL">ارضا</span><span lang="AR-SA" dir="RTL">م</span><span lang="AR-SA" dir="RTL">ی‌</span><span lang="AR-SA" dir="RTL">شود</span><span>. </span><span lang="AR-SA" dir="RTL">پس</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">تشک</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ل</span><span lang="AR-SA" dir="RTL">فانکشنال</span><span lang="AR-SA" dir="RTL">لاگرانژ</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ن</span><span lang="AR-SA" dir="RTL">بوس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">له</span><span lang="AR-SA" dir="RTL">تفاضل</span><span lang="AR-SA" dir="RTL">انرژ</span><span lang="AR-SA" dir="RTL">ی‌</span><span lang="AR-SA" dir="RTL">ها</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">جنبش</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">پتانس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ل</span><span lang="AR-SA" dir="RTL">ورق،</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">اصل</span><span lang="AR-SA" dir="RTL">هم</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">لتون</span><span lang="AR-SA" dir="RTL">و روش</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">تز</span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">منظور</span><span lang="AR-SA" dir="RTL">تع</span><span lang="AR-SA" dir="RTL">یی</span><span lang="AR-SA" dir="RTL">ن</span><span lang="AR-SA" dir="RTL">مقاد</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">فرکانس</span><span lang="AR-SA" dir="RTL">طب</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">استفاده</span><span lang="AR-SA" dir="RTL">شده</span><span lang="AR-SA" dir="RTL">است</span><span>. </span><span lang="AR-SA" dir="RTL">در</span><span lang="AR-SA" dir="RTL">ادامه</span><span lang="AR-SA" dir="RTL">پس</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">اعتبارسنج</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">نتا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ج</span><span lang="AR-SA" dir="RTL">با</span><span lang="AR-SA" dir="RTL">مراجع</span><span lang="AR-SA" dir="RTL">مختلف برا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">حالت‌ها</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">گوناگون،</span><span lang="AR-SA" dir="RTL">تاث</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ر</span><span lang="AR-SA" dir="RTL">پارامترها</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ورق</span><span lang="AR-SA" dir="RTL">از</span><span lang="AR-SA" dir="RTL">جمله</span><span lang="AR-SA" dir="RTL">زاو</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ه</span><span lang="AR-SA" dir="RTL">قطاع</span><span lang="AR-SA" dir="RTL">ورق،</span><span lang="AR-SA" dir="RTL">نسبت</span><span lang="AR-SA" dir="RTL">ضخامت</span><span lang="AR-SA" dir="RTL">به</span><span lang="AR-SA" dir="RTL">شعاع</span><span lang="AR-SA" dir="RTL">ورق،</span><span lang="AR-SA" dir="RTL">ضر</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ب</span><span lang="AR-SA" dir="RTL">توان</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">نسبت حجم</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">ضرا</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ب</span><span lang="AR-SA" dir="RTL">بستر</span><span lang="AR-SA" dir="RTL">بر</span><span lang="AR-SA" dir="RTL">رو</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">فرکانس</span><span lang="AR-SA" dir="RTL">طب</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">ع</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">سازه</span><span lang="AR-SA" dir="RTL">مورد</span><span lang="AR-SA" dir="RTL">بحث</span><span lang="AR-SA" dir="RTL">و</span><span lang="AR-SA" dir="RTL">بررس</span><span lang="AR-SA" dir="RTL">ی</span><span lang="AR-SA" dir="RTL">قرار</span><span lang="AR-SA" dir="RTL">گرفته</span><span lang="AR-SA" dir="RTL">است</span><span>.</span>