Periodic behavior of a cantilever beam with end mass subjected to harmonic base excitation

1998 ◽  
Vol 33 (4) ◽  
pp. 567-577 ◽  
Author(s):  
E. Esmailzadeh ◽  
G. Nakhaie-Jazar
2012 ◽  
Vol 12 (02) ◽  
pp. 285-310 ◽  
Author(s):  
M. EFTEKHARI ◽  
M. MAHZOON ◽  
S. ZIAEI-RAD

In this paper, a comparative study is performed for a symmetrically laminated composite cantilever beam with and without a tip mass under harmonic base excitation. The base is subjected to both flapwise and chordwise excitations tuned to the primary resonances of the two directions and conditions of 2:1 autoparametric resonance. In the literature, the governing nonlinear equations of the same problem without tip mass have been derived using the extended Hamilton's principle. Extension is made in this study to include the effect of a tip mass on the response of the beam. The natural frequencies are obtained numerically using the diversity guided evolutionary algorithm (DGEA). Next, the multiple scales method is applied to determine the nonlinear response and stability of the system. A set of four first-order differential equations describing the modulation of the amplitudes and phases of interacting modes are derived for the perturbation analysis. For verification, the above equations are reduced to the special case of the cantilever beam without tip mass for comparison with existing results. Finally, the effect of the tip mass on the stability of the fixed points and on the amplitude of oscillation about the equilibrium points in both the frequency and force modulation responses is examined.


Author(s):  
Pezhman A. Hassanpour ◽  
Andrea J. Helmns

This paper presents the investigation of operational deflection shapes of vibration of a cantilever beam using a low-cost digital video camera, and by application of image processing techniques. The beam is uniform and under base excitation. The analytical model of the system is developed using dimensionless formulation. The analytical ODS’s are derived, and then compared with those found from experiment. The significance of this research is that it provides the researchers an inexpensive alternative tool for investigating the behavior of systems with low-frequency dynamics.


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