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تحلیل دینامیکی میکرو المان منعطف موازی با مدل قیدی تیر و تئوری گرادیان کرنشی اصلاح یافته | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 6، دوره 54، شماره 4، تیر 1401، صفحه 821-842 اصل مقاله (2.55 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2022.20518.7251 | ||
| نویسندگان | ||
| محمد ارحامی1؛ حمید معین فرد* 2 | ||
| 1دانشکده مهندسی، دانشگاه فردوسی مشهد، ایران | ||
| 2دانشکده مهندسی، دانشگاه فردوسی مشهد، ایران -قطب علمی رایانش نرم و پردازش هوشمند اطالعات، دانشگاه فردوسی مشهد، ایران | ||
| چکیده | ||
| در این پژوهش، رفتار دینامیکی میکرو المان منعطف موازی تحت بار انتهایی، مورد بررسی قرار می‌گیرد. ابتدا با تئوری گرادیان کرنشی اصلاح یافته و به کمک مدل قیدی تیر، انرژی کرنشی یک میکرو تیر منعطف، برحسب مؤلفه‌های جابجایی انتهای تیر به دست آمده، و از آن برای تعیین انرژی کرنشی المان منعطف موازی استفاده می‌شود. در ادامه، با روش لاگرانژ، مدل دینامیکی میکرو المان منعطف استخراج شده و حول نقطه تعادل، خطی‌سازی می‌گردد. سپس محدوده مجاز برای اعمال نیروهای استاتیکی به سکوی حرکتی، به نحوی که هم تئوری مورد استفاده از دقت کافی برخوردار باشد، و هم پایداری دینامیکی سیستم تحت اغتشاشات دینامیکی کوچک خدشه‌دار نشود، مشخص می‌گردد. نتایج بدست آمده حاکی از این است که تئوری الاستیسیته کلاسیک، سخت‌گیری بیش از حدی برای مشخص کردن دقیق ناحیه پایداری مکانیزم دارد. همچنین فرکانس‌های طبیعی سیستم نیز استخراج شده و اثر ابعاد و مؤلفه‌های استاتیکی نیرو بر آن‌ها، مورد مطالعه قرار گرفته است. مشاهده می‌شود که با کاهش ابعاد، فرکانس طبیعی بی‌بعد عرضیِ سیستم افزایش می‌یابد، اما فرکانس طبیعی بی‌بُعد طولی سیستم، به دلیل عدم وجود گرادیان کرنش در مُد طولی، ثابت می‌ماند. همچنین مشاهده شد که نیروی استاتیکی کششی باعث افزایش، و نیروی استاتیکی خمشی باعث کاهش فرکانس‌های طبیعی سیستم می‌شوند. با توجه به بی‌بعد بیان شدن روابط و نتایج ارائه شده در این پژوهش، می‌توانند به سادگی برای تحلیل دینامیکی مکانیزم‌های منعطف پیچیده‌تر، استفاده شوند. | ||
| کلیدواژه‌ها | ||
| المان منعطف موازی؛ مدل قیدی تیر؛ تحلیل دینامیکی؛ تئوری گرادیان کرنشی؛ تحلیل پایداری | ||
| عنوان مقاله [English] | ||
| Dynamic Analysis of Micro -Scale Parallelogram Flexures Using Beam Constraint Model and Modified Strain Gradient Theory | ||
| نویسندگان [English] | ||
| Mohammad Arhami1؛ Hamid Moeenfard2 | ||
| 1PhD Student, School of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Associate Professor, School of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Center of Excellence in Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran | ||
| چکیده [English] | ||
| In this paper, the dynamic behavior of a small-scale parallelogram (P) flexure is studied. First, using the beam constrain model and the modified strain gradient theory, the nonlinear strain energy of a small-scale beam is obtained in terms of its tip displacements. This energy expression is utilized to derive the strain energy of a P-flexure. Then the governing dynamic equations of motion are derived using Lagrange equations and are linearized around the operating equilibrium point. This linear model is employed to determine the allowable forces which do not lead to instability of the system. Moreover, the natural frequencies of the system are also extracted and the size effect as well as the static components of the applied loads on them are studied in detail. It is observed that by reducing the dimensions, the normalized transverse natural frequency of the system is increased. However, since there is no strain gradient in an axial mode, the axial normalized frequency is remained constant reducing the dimensions of the system. Moreover, it was observed that the tensile static forces lead to an increase, and transverse forces lead to a decrease in normalized natural frequency of the system. The procedure utilized for dynamic modeling of parallelogram flexures in this paper can be further extended for modeling more complex flexure systems. | ||
| کلیدواژه‌ها [English] | ||
| Parallelogram flexure, Beam constraint model, Dynamic analysis, Modified strain gradient theory, Stability analysis | ||
| مراجع | ||
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