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Tytuł artykułu

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. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
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
PL drgania nieliniowe   zasada Hamiltona   metoda Newtona-Raphsona   analiza modalna  
EN non-linear vibration   Hamilton’s principle   Newton-Raphson method   backbone curve   second formulation  
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.
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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