در تحقیق حاضر تحلیل ارتعاشات غیرخطی و پایداری نانورزوناتور پیزوالکتریک (PENR) با در نظر گرفتن اثرات کنترل کننده های غیرکلاسیک مانند تئوری غیر موضعی (NLT)، تئوری گرادیان کرنش (SGT) و تئوری های سطح/رابط گورتین-مرداک (GMSIT) در مقایسه با نظریه کلاسیک (CT)ارائه شده است. نانورزوناتور مورد مطالعه تحت تحریک الکترواستاتیک غیرخطی با ولتاژ مستقیم (DC) و متناوب (AC) و همچنین محیط ویسکو پاسترناک قرار دارد. برای این تحلیل از اصل همیلتون و روش گالرکین به ترتیب برای به دست آوردن معادلات حاکم و شرایط مرزی و همچنین برای حل معادله حرکت استفاده شده است. برای بررسی پاسخ فرکانسی غیرخطی و تحلیل پایداری PENR از روش میانگین‌گیری مختلط همراه با روش پیمایش طول قوس استفاده می‌شود. نتایج نشان می‌دهند که نادیده گرفتن اثرات سطح/رابط در مقیاس کوچک، پیش‌بینی نادرستی از پاسخ ارتعاشی PENR را نشان می‌دهد. همچنین در شرایط مرزی مختلف، مقیاس طول ماده و پارامترهای غیرمحلی به ترتیب منجر به کاهش و افزایش سفتی PENR می‌شوند و دامنه نوسان و دامنه ناپایداری نظریه‌های غیر کلاسیک NLT و SGT نسبت به حالت کلاسیک بیشتر می باشد. همچنین تغییر پارامترهای سطح/رابط منجر به کاهش یا افزایش فرکانس تشدید، دامنه تشدید، رفتار غیرخطی و ناپایداری سیستم PENR می گردد.
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