Resonance subharmonic vibrations of beam with breathing fatigue crack

• Дата: 2016
• Автори: Аврамов, К. В., Раимбердиев, Т. П., Шехватова, E. М.
• Формат: Стаття
• Мова: Russian
• Опубліковано: Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2016
• Теми: vibrations of beam with breathing crack; Galerkin method; finite degree of freedom dynamical system; multiple scales method; principle resonance; УДК 621.565; уравнение колебаний балки с дышащей трещиной; метод Бубнова–Галеркина; динамическая модель с конечным числом степеней свободы; метод многих масштабов; основной резонанс; рівняння коливань балки з дихаючою тріщиною; метод Гальоркіна; динамічна модель зі скінченним числом ступенів вільності; метод багатьох масштабів; основний резонанс
• Онлайн доступ: https://journals.uran.ua/jme/article/view/71857
• Назва журналу: Energy Technologies & Resource Saving

The vibrations of the beam with breathing crack are described by the partial differential equation with contact parameter. The quasi linear dynamical system with finite degrees of freedom is obtained to analyze the beam vibrations. In order to obtain this dynamical system the solution is expanded by eigenmodes. The Galerkin method is applied to the partial differential equation, which is described the beam vibration. It is shown, when the stiffness matrix of the beam with crack is symmetric and when it is asymmetric. The multiple scales method is used to analyze the quasilinear dynamical system. The considered dynamical system contains the internal resonance. The second main resonance is analyzed. The system of four autonomous differential equations is obtained. The characteristic exponents of the linearized modulation equations are calculated to analyze stability of the periodic motions. The frequency response at the second principal resonance is obtained. This frequency response describes the system subharmonic vibrations