The influence of rotatory inertia, tip mass, and damping on the stability of a cantilever beam on an elastic foundation

1975 ◽  
Vol 43 (3) ◽  
pp. 543-552 ◽  
Author(s):  
G.L. Anderson
Keyword(s):  
Elastic Foundation ◽  
Cantilever Beam ◽  
Rotatory Inertia ◽  
The Stability ◽  
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.

Stability of a Beam on an Elastic Foundation Subjected to a Nonconservative Load

1980 ◽  
Vol 47 (1) ◽  
pp. 116-120 ◽  
Author(s):  
Z. Celep
Keyword(s):  
Approximate Solution ◽  
Numerical Calculation ◽  
Elastic Foundation ◽  
Cantilever Beam ◽  
Numerical Study ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
The Common ◽  
The Stability

In this investigation, the influence of a Winkler type of elastic foundation on the stability of the cantilever beam subjected to a nonconservative load which consists of a vertical and a follower components is studied. In addition to the common transverse foundation modulus, a rotatory foundation modulus is considered. Approximate solution is obtained by using Galerkin’s method. Numerical calculation are reported and displayed for various combinations of the nonconservativeness parameter, transverse and rotatory modulus of the foundation, distance of the point of application of the load and that of the transverse spring. As a result of the numerical study unexpected feature of stability of the cantilever beam in contrast to the behavior of the column is identified.

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.

Multimodal Energy Harvesting System: Piezoelectric and Electromagnetic

2008 ◽  
Vol 20 (5) ◽  
pp. 625-632 ◽  
Author(s):  
Yonas Tadesse ◽  
Shujun Zhang ◽  
Shashank Priya
Keyword(s):  
Energy Harvesting ◽  
Resonance Frequency ◽  
Permanent Magnet ◽  
Cantilever Beam ◽  
Piezoelectric Energy Harvesting ◽  
Prototype System ◽  
Finite Element Software ◽  
Piezoelectric Energy ◽  
Energy Harvesting System ◽  
Tip Mass

In this study, we report a multimodal energy harvesting device that combines electromagnetic and piezoelectric energy harvesting mechanism. The device consists of piezoelectric crystals bonded to a cantilever beam. The tip of the cantilever beam has an attached permanent magnet which, oscillates within a stationary coil fixed to the top of the package. The permanent magnet serves two purpose (i) acts as a tip mass for the cantilever beam and lowers the resonance frequency, and (ii) acts as a core which oscillates between the inductive coils resulting in electric current generation through Faraday's effect. Thus, this design combines the energy harvesting from two different mechanisms, piezoelectric and electromagnetic, on the same platform. The prototype system was optimized using the finite element software, ANSYS, to find the resonance frequency and stress distribution. The power generated from the fabricated prototype was found to be 0.25 W using the electromagnetic mechanism and 0.25 mW using the piezoelectric mechanism at 35 g acceleration and 20 Hz frequency.

Characteristics of an Eigensystem Describing the Elastic Stability of a Thin Cantilever Beam

1962 ◽  
Vol 66 (623) ◽  
pp. 722-724 ◽  
Author(s):  
B. Saravanos
Keyword(s):  
Equilibrium Problem ◽  
Cantilever Beam ◽  
Elastic Stability ◽  
Additional Component ◽  
Connecting Rod ◽  
The Stability

The stability of a uniform cantilever beam subjected to an articulated tip load has been analysed as an equilibrium problem of static elastic stability. It was found there that the articulation of the connecting rod applying the tip load introduced additional component forces during the process of beam deformation.

Free and Forced Vibration of a Kinked Cantilever Beam

1999 ◽  
Author(s):  
B. S. Reddy ◽  
K. R. Y. Simha ◽  
A. Ghosal
Keyword(s):  
Cantilever Beam ◽  
Mode Shape ◽  
Forced Vibration ◽  
Equations Of Motion ◽  
Element Formulation ◽  
Kink Angle ◽  
Order Polynomial ◽  
Relationship Of ◽  
Tip Mass ◽  
Beam Mode

Abstract In this paper we use the assumed modes method to derive an analytical model of a kinked cantilever beam of unit mass carrying a kink mass (mk) and a tip mass (mt). The model is used to study the free and forced vibration of such a beam. For the free vibration, we obtain the mode shape of the complete beam by solving an eight order polynomial whose coefficients are functions of the kink mass, kink angle and tip mass. A relationship of the form f(mk,mt,δ)=mk+mt(4+103cosδ+23cos2δ)=constant appears to give the same fundamental frequency for a given kink angle, δ, and different combinations of kink mass and tip mass. To derive the dynamic equations of motion, the complete kinked beam mode shape is used in a Lagrangian formulation. The equations of motion are numerically integrated with a torque applied at the base and the tip response for various kink angles are presented. The results match those obtained from a traditional finite element formulation.

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