Nonlinear vibration of a cantilever beam with tip mass under random base excitation

2001 ◽  
Author(s):  
Guangfeng Cheng ◽  
Chuh Mei ◽  
Raymond Lee
Keyword(s):  
Nonlinear Vibration ◽  
Cantilever Beam ◽  
Base Excitation ◽  
Tip Mass

EFFECT OF ADDED TIP MASS ON THE NONLINEAR FLAPWISE AND CHORDWISE VIBRATION OF CANTILEVER COMPOSITE BEAM UNDER BASE EXCITATION

2012 ◽  
Vol 12 (02) ◽  
pp. 285-310 ◽  
Author(s):  
M. EFTEKHARI ◽  
M. MAHZOON ◽  
S. ZIAEI-RAD
Keyword(s):  
Cantilever Beam ◽  
Multiple Scales ◽  
Equilibrium Points ◽  
Laminated Composite ◽  
Base Excitation ◽  
System A ◽  
Autoparametric Resonance ◽  
The Stability ◽  
Tip Mass ◽  
Made In

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.

Large Amplitude Vibration of a Cantilever Beam with Tip Mass under Random Base Excitation

2002 ◽  
Vol 4 (4) ◽  
pp. 203-210 ◽  
Author(s):  
Guangfeng Cheng ◽  
Chuh Mei ◽  
Raymond Y. Y. Lee
Keyword(s):  
Cantilever Beam ◽  
Large Amplitude ◽  
Beam Theory ◽  
Single Mode ◽  
Rotary Inertia ◽  
System Response ◽  
Base Excitation ◽  
Random Response ◽  
Lumped Mass ◽  
Tip Mass

Nonlinear large amplitude random vibration of cantilever beam with lumped mass and rotary inertia under zero mean, stationary, Gaussian random base excitation is studied, using the inextensional beam theory. Single-mode approximation is employed to discretize the Lagrange's equation. The resulting nonlinear governing modal equation of motion is solved with application of the stochastic linearization method. Two examples, a cantilever beam with/without tip mass, are analyzed as application of the developed methodology. Effects of mass and rotary inertia variation on system response are investigated in detail. Results showed that increasing rotary inertia could reduce the random response of the beam structure and the random response of the structure is quite sensitive to the tip mass variation. The nonlinearities of the inextensional beam vibration result in a spring hardening system.

scholarly journals Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Wang Hongjin ◽  
Meng Qingfeng ◽  
Feng Wuwei
Keyword(s):  
Cantilever Beam ◽  
Analytical Methods ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Inertial Force ◽  
Mode Shapes ◽  
Base Excitation ◽  
Inertial Moment ◽  
Tip Mass ◽  
Improved Methods

Two improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in detail by replacing the tip-mass with an equivalent inertial force and inertial moment acting at the free end of the cantilever based on D’Alembert’s principle. The concentrated equivalent inertial force and inertial moment are further represented as distributed loads using Dirac Delta Function. In this case, some typical natural frequencies and mode shapes of the cantilever model are calculated by the improved and unimproved analytical methods. The comparing results show that, after improvement, these two methods are in extremely good agreement with each other even the offset distance between the gravity center of the tip-mass and the attachment point is large. As further verification, the transient and steady displacement responses of the cantilever system under a sine base excitation are presented in which two improved methods are separately utilized. Finally, an experimental cantilever system is fabricated and the theoretical displacement responses are validated by the experimental measurements successfully.

Dynamic Response of Spiral Cantilever Undergoing Magnetic Coupling

2014 ◽  
Vol 14 (08) ◽  
pp. 1440021
Author(s):  
Xiaoling Bai ◽  
Yumei Wen ◽  
Ping Li ◽  
Jin Yang ◽  
Xiao Peng ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Cantilever Beam ◽  
Magnetic Force ◽  
Coupling Effect ◽  
Magnetic Coupling ◽  
Resonant Frequencies ◽  
Energy Harvesters ◽  
Magnetic Transducer ◽  
Underlying Mechanisms ◽  
Tip Mass

Cantilever beams have found intensive and extensive uses as underlying mechanisms for energy transduction in sensors as well as in energy harvesters. In magnetoelectric (ME) transduction, the underlying cantilever beam usually will undergo magnetic coupling effect. As the beam itself is either banded with magnetic transducer or magnets, the dynamic motion of the cantilever can be modified due to the magnetic force between the magnets and ME sensors. In this study, the dynamic response of a typical spiral cantilever beam with magnetic coupling is investigated. The spiral cantilever acts as the resonator of an energy harvester with a tip mass in the form of magnets, and a ME transducer is positioned in the air gap and interacts with the magnets. It is expected that this spiral configuration is capable of performing multiple vibration modes over a small frequency range and the response frequencies can be magnetically tunable. The experimental results show that the magnetic coupling between the magnets and the transducer plays a favorable role in achieving tunable resonant frequencies and reducing the frequency spacings. This will benefits the expansion of the response band of a device and is especially useful in energy harvesting.

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