- Tytuł:
- 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. - Powiązania:
- https://bibliotekanauki.pl/articles/329670.pdf
- Data publikacji:
- 2017
- Wydawca:
- Polska Akademia Nauk. Polskie Towarzystwo Diagnostyki Technicznej PAN
- Tematy:
-
non-linear vibration
Hamilton’s principle
Newton-Raphson method
backbone curve
second formulation
drgania nieliniowe
zasada Hamiltona
metoda Newtona-Raphsona
analiza modalna - Opis:
- 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.
- Źródło:
-
Diagnostyka; 2017, 18, 2; 13-21
1641-6414
2449-5220 - Pojawia się w:
- Diagnostyka
- Dostawca treści:
- Biblioteka Nauki
Artykuł