کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
782974 1465078 2007 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Non-linear free vibrations of Kelvin–Voigt visco-elastic beams
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Non-linear free vibrations of Kelvin–Voigt visco-elastic beams
چکیده انگلیسی

A full visco-elastic non-linear beam with cubic non-linearities is considered, and the governing equations of motion of the system for large amplitude vibrations are derived. By using the method of multiple scales, the non-linear mode shapes and natural frequencies of the beam are then analytically formulated. The resulting formulations for amplitude, non-linear natural frequencies and mode shapes can be used for any type of boundary conditions. Next, method of Galerkin is used to separate the time and space variables. The equations of motion show the presence of a non-linear damping term in addition to the ones with non-linear inertia and geometry. As it is known, the presence of non-linear inertia and the geometric terms make the non-linear natural frequencies to be dependent on constant amplitude of vibration. But, when damping non-linearities are present, it is seen that the amplitude is exponentially time-dependent, and so, the non-linear natural frequencies will be logarithmically time-dependent. Additionally, it is shown that the mode shapes will be dependent on the third power of time-dependent amplitude. The analytical results are applied to hinged–hinged and hinged–clamped boundary conditions and the results are compared with numerical simulations. The results match very closely for both cases specially for the case of hinged–hinged beam.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: International Journal of Mechanical Sciences - Volume 49, Issue 6, June 2007, Pages 722–732
نویسندگان
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