کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
784954 1465332 2014 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Analysis of motion of inverted pendulum with vibrating suspension axis at low-frequency excitation as an illustration of a new approach for solving equations without explicit small parameter
ترجمه فارسی عنوان
تجزیه و تحلیل حرکت آونگ معکوس با محور ارتعاش ارتعاشی در تحریک فرکانس پایین به عنوان یک تصویر از یک رویکرد جدید برای حل معادلات بدون پارامتر کوچک صریح
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی


• A new approach for solving equations without explicit small parameter is proposed.
• Inverted pendulum with vibrating axis is studied at low-frequency excitation.
• Not only the effective stiffness of the system changes, but also its effective mass.
• Stable solutions of the Mathieu equation without small parameter are derived.

In the classical papers (see, e.g. P.L. Kapitsa, Pendulum with vibrating axis of suspension. Usp. Fiz. Nauk 44 1 (1954) 7–20 (in Russian)) motion of pendulum with vibrating suspension axis was considered in the case when frequency of external loading is much higher than the natural frequency of the pendulum in the absence of this loading. The present paper is concerned with the analysis of inverted pendulum׳s motion at unconventional values of parameters. Case when frequency of external loading and the natural frequency of the pendulum in the absence of this loading are of the same order is studied. Vibration intensity is assumed to be relatively low. A new modification of the method of direct separation of motions (MDSM) is proposed to study the corresponding equation which in the considered case does not contain a small parameter explicitly. The aim is to obtain solutions of this equation in the stability domain. It is revealed that in the considered range of parameters not only the effective stiffness of the system changes due to the external loading, but also its effective mass. Applicability of the proposed approach for solving non-linear equations without small parameter is demonstrated; as an illustration, a damped Duffing equation is considered.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Non-Linear Mechanics - Volume 63, July 2014, Pages 1–9
نویسندگان
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