Linear and geometrically non-linear frequencies and mode shapes of beams carrying a point mass at various locations. An analytical approch and a parametric study

• Autorzy: Adri A. , Benamar R.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, the frequencies and mode shapes of a clamped beam carrying a point mass, located at different positions, are investigated analytically and a parametric study is performed. The dynamic equation is written at two intervals of the beam span with the appropriate end and continuity conditions. After the necessary algebraic transformations, the generalised transcendental frequency equation is solved iteratively using the Newton Raphson method. Once the corresponding program is implemented, investigations are made of the changes in the beam frequencies and mode shapes for many values of the mass and mass location. Numerical results and plots are given for the clamped beam first and second frequencies and mode shapes corresponding to various added mass positions. The effect of the geometrical non-linearity is then examined using a single mode approach in order to obtain the corresponding backbone curves giving the amplitude dependent non-linear frequencies.

Słowa kluczowe

EN

non-linear vibration; Hamilton’s principle; Newton-Raphson method; backbone curve; second formulation

PL

drgania nieliniowe; zasada Hamiltona; metoda Newtona-Raphsona; analiza modalna

• Wydawca: Polskie Towarzystwo Diagnostyki Technicznej
• Czasopismo: Diagnostyka
• Rocznik: 2017
• Tom: Vol. 18, No. 2
• Strony: 13--21
• Opis fizyczny: Bibliogr. 29 poz., rys., tab., wykr.

Twórcy

autor

Adri A.

• Laboratoire de Mécanique Productique & Génie Industriel (LMPGI) École Supérieure de Technologie Hassan II University in Casablanca

autor

Benamar R.

• Equipe des Etudes et Recherches en Simulation et Instrumentation Ecole Mohammadia des Ingénieurs; Mohammed V University in Rabat

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