PL EN
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
Adri Ahmed 1  
,   Benamar Rhali 2  
 
Więcej
Ukryj
1
Ecole Supérieure de Technologie
2
Ecole Mohammadia des Ingénieurs Rabat
AUTOR DO KORESPONDENCJI
Adri Ahmed   

Ecole Supérieure de Technologie, 7 route d'el jadida BP 8012 OASIS, 20000 Casablanca, Morocco
Data nadesłania: 13-04-2017
Data akceptacji: 29-05-2017
Data publikacji: 21-06-2017
 
Diagnostyka 2017;18(2):13–21
 
SŁOWA KLUCZOWE
DZIEDZINY
STRESZCZENIE
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.
eISSN:2449-5220
ISSN:1641-6414