On the representation of a cantilevered beam carrying a tip mass by an equivalent spring–mass system

2005 ◽  
Vol 282 (1-2) ◽  
pp. 538-542 ◽  
Author(s):  
M. Gürgöze
Keyword(s):  
Mass System ◽  
Cantilevered Beam ◽  
Tip Mass

A Multi-Point Loaded Piezocomposite Beam: Experiments on Sensing and Vibration Energy Harvesting

2018 ◽  
Author(s):  
Patrick S. Heaney ◽  
Onur Bilgen
Keyword(s):  
Unit Length ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Beam Curvature ◽  
Cantilevered Beam ◽  
Potential Applications ◽  
Tip Mass ◽  
Patch Length ◽  
Piezoelectric Vibration

A common configuration for a piezoelectric vibration energy harvester is the cantilevered beam with the piezoelectric device located near the beam root to maximize energy transduction. The beam curvature in this configuration is monotonically decreasing from root to tip, so the transduction per unit length of piezoelectric material decreases with increasing patch length. As an alternative to such conventional configuration, this paper proposes a so-called inertial four-point loading for beam-like structures. The effects of support location and tip mass on the beam curvature shapes are analyzed for four-point loaded cases to demonstrate the effect of these configurations on the total strain induced on the piezoelectric patch. These configurations are tested experimentally using several different support locations and compared with results from a baseline cantilevered beam. Performance comparisons of their power ratios are made, which indicate improvement in the transduction per unit strain of the four-point loading cases over the cantilevered configuration. The paper concludes with a discussion of potential applications of the inertial four-point loaded configuration.

Full Beam Formulation of a Rotating Beam-Mass System

1994 ◽  
Vol 116 (1) ◽  
pp. 93-99 ◽  
Author(s):  
B. Fallahi ◽  
S. H.-Y. Lai ◽  
R. Gupta
Keyword(s):  
Nonlinear Term ◽  
Cross Coupling ◽  
Automatic Generation ◽  
Shape Functions ◽  
Rotating Beam ◽  
Mass System ◽  
Computational Implementation ◽  
Geometric Stiffening ◽  
Rigid Body Motions ◽  
Tip Mass

In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.

Non-Linear Piezoelectric Vibration Energy Harvesting From a Vertical Cantilever Beam With Tip Mass

2013 ◽  
Author(s):  
Onur Bilgen ◽  
S. Faruque Ali ◽  
Michael I. Friswell ◽  
Grzegorz Litak ◽  
Marc de Angelis
Keyword(s):  
Energy Harvester ◽  
Harmonic Component ◽  
Vibration Energy ◽  
Base Excitation ◽  
Vibration Energy Harvesting ◽  
Vibration Energy Harvester ◽  
Potential Wells ◽  
Non Linear ◽  
Cantilevered Beam ◽  
Tip Mass

An inverted cantilevered beam vibration energy harvester with a tip mass is evaluated for its electromechanical efficiency and power output capacity in the presence of pure harmonic, pure random and various combinations of harmonic and random base excitation cases. The energy harvester employs a composite piezoelectric material device that is bonded near the root of the beam. The tip mass is used to introduce non-linearity to the system by inducing buckling in some configurations and avoiding it in others. The system dynamics include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. This configuration exploits the non-linear properties of the system using base excitation in conjunction with the tip mass at the end of the beam. Such nonlinear device has the potential to work well when the input excitation does not have a dominant harmonic component at a fixed frequency. The paper presents an extensive experimental analysis, results and interesting conclusions derived directly from the experiments supported by numerical simulations.

Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

2018 ◽  
Vol 25 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Vamsi C. Meesala ◽  
Muhammad R. Hajj
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Governing Equations ◽  
Mass System ◽  
Tip Mass

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

Tuning of a Piezoelectric Harvester by Means of a Cantilever Spring-Mass System

2018 ◽  
Author(s):  
Alberto Doria ◽  
Cristian Medè ◽  
Giulio Fanti ◽  
Daniele Desideri ◽  
Alvise Maschio ◽  
...  
Keyword(s):  
High Frequency ◽  
Natural Frequencies ◽  
Coupled System ◽  
Vibration Absorber ◽  
Main Resonance ◽  
Dynamic Vibration Absorber ◽  
Mass System ◽  
High Frequency Resonance ◽  
Tip Mass ◽  
Piezoelectric Harvester

The possibility of improving the performance of a piezoelectric harvester by means of a cantilever dynamic vibration absorber (CDVA) is investigated. The CDVA cancels the original mode of vibration of the harvester and generates two new modes. Some prototypes are developed using a mathematical model for predicting the natural frequencies of the coupled system. Impulsive tests were performed on prototypes. Experimental results show that a small CDVA can lower the main resonance frequency of an harvester of the same extent as a larger tip mass. The measured voltage shows also an high frequency resonance peak, which can be exploited for collecting energy. A multi-physics numerical model is developed for performing modal analysis and stress analysis. Numerical results show that the stress inside the piezoelectric material of the harvester with CDVA results smaller than the stress inside the harvester with a tip mass tuned to the same frequency.

Dynamic analysis of the flexible hub-beam system based on rigid-flexible coupling mechanism

2020 ◽  
Vol 234 (3) ◽  
pp. 536-545
Author(s):  
Xiaowei Guo ◽  
Xin Yang ◽  
Fuqiang Liu ◽  
Zhangfang Liu ◽  
Xiaolin Tang
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Flexible Beam ◽  
Coupling Mechanism ◽  
Mass System ◽  
Typical Structure ◽  
Concentrated Load ◽  
Flexible Coupling ◽  
Beam System ◽  
Tip Mass

The flexible hub-beam system is a typical structure of the rigid-flexible coupling dynamic system. In this paper, the dynamic property of the flexible hub-beam system is investigated. First, based on the dynamic analysis of the flexible beam in the flexible hub-beam system, the dynamic model of a flexible hub-beam-tip mass system is established and researched. Second, the dynamic response of the flexible beam under different external loads, including end concentrated load, end sinusoidal load, and uniform load, is analyzed and calculated. Finally, the influence of magnitude, direction, and type of load on the dynamic response of the flexible beam is also discussed. This research can provide a novel strategy for controlling the maximum stress of the structural components to be lower than the yield stress of the material, and flexible components remain in the linear elastic range even under the condition of high-speed rotation.

Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Masoud Ansari ◽  
Ebrahim Esmailzadeh ◽  
Nader Jalili
Keyword(s):  
Frequency Analysis ◽  
Time Domain ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Bending Vibrations ◽  
Resonant Condition ◽  
Mass System ◽  
Coupled Equations ◽  
Tip Mass ◽  
Gyroscopic Systems

An exact frequency analysis of a rotating beam with an attached tip mass is addressed in this paper while the beam undergoes coupled torsional-bending vibrations. The governing coupled equations of motion and the corresponding boundary condition are derived in detail using the extended Hamilton principle. It has been shown that the source of coupling in the equations of motion is the rotation and that the equations are linked through the angular velocity of the base. Since the beam-tip-mass system at hand serves as the building block of many vibrating gyroscopic systems, which require high precision, a closed-form frequency equation of the system should be derived to determine its natural frequencies. The frequency analysis is the basis of the time domain analysis, and hence, the exact frequency derivation would lead to accurate time domain results, too. Control strategies of the aforementioned gyroscopic systems are mostly based on their resonant condition, and hence, acquiring knowledge about their exact natural frequencies could lead to a better control of the system. The parameter sensitivity analysis has been carried out to determine the effects of various system parameters on the natural frequencies. It has been shown that even the undamped systems undergoing base rotation will have complex eigenvalues, which demonstrate a damping-type behavior.

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