کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
785200 1465362 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Residue harmonic balance approach to limit cycles of non-linear jerk equations
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Residue harmonic balance approach to limit cycles of non-linear jerk equations
چکیده انگلیسی

A residue harmonic balance is established for accurately determining limit cycles to parity- and time-reversal invariant general non-linear jerk equations with cubic non-linearities. The new technique incorporates the salient features of both methods of harmonic balance and parameter bookkeeping to minimize the total residue. The residue is separated into two parts in each step; one conforms to the present order of approximation and the remaining part for use in the next order. The corrections are governed by a set of linear ordinary differential equations that can be solved easily. Three specific cases of non-linear jerk equations are given to illustrate the validity and efficiency. The approximations to the angular frequency and the limit cycle are obtained and compared. The results show that the approximations obtained are in excellent agreement with the exact solutions for a wide range of initial velocities. The new technique is simple in principle and can be applied to other non-linear oscillating systems.


► The corrections are governed by a set of linear ordinary differential equations that can be easily solved.
► Three specific cases of non-linear jerk equations are given to illustrate the validity and efficiency.
► The approximations to the angular frequency and the limit cycle are obtained and compared.
► The new technique is simple in principle and can be applied to other non-linear oscillating systems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Non-Linear Mechanics - Volume 46, Issue 6, July 2011, Pages 898–906
نویسندگان
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