کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
785319 1465401 2007 8 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the sensitivity of non-generic bifurcation of non-linear normal modes
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
On the sensitivity of non-generic bifurcation of non-linear normal modes
چکیده انگلیسی

It is shown that a non-generic bifurcation of non-linear normal modes may occur if the ratio of linear natural frequencies is near r  -to-one, r=1,3,5,…r=1,3,5,… . Non-generic bifurcations are explicitly obtained in the systems having certain symmetry, as observed frequently in literatures. It is found that there are two kinds of non-generic bifurcations, super-critical and sub-critical. The normal mode generated by the former kind is extended to large amplitude, but that by the latter kind is limited to small amplitude which depends on the difference between two linear natural frequencies and disappears when two frequencies are equal. Since a non-generic bifurcation is not generic, it is expected generically that if a system having a non-generic bifurcation is perturbed then the non-generic bifurcation disappears, and generic bifurcation appears in the perturbed system. Examples are given to verify the change in bifurcations and to obtain the stability behavior of normal modes. It is found that if a system having a super-critical non-generic bifurcation is perturbed, then two new normal modes are generated, one is stable, but the other unstable, implying a saddle-node bifurcation. If the system having a sub-critical non-generic bifurcation is perturbed, then no new normal mode is generated, but there is an interval of instability on a normal mode, implying two saddle-node bifurcations on the mode. Application of this study is discussed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Non-Linear Mechanics - Volume 42, Issue 7, September 2007, Pages 973–980
نویسندگان
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