Academic literature on the topic 'Cantilever Euler-Bernoulli beam'
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Journal articles on the topic "Cantilever Euler-Bernoulli beam"
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Siva Sankara Rao, Yemineni, Kutchibotla Mallikarjuna Rao, and V. V. Subba Rao. "Estimation of damping in riveted short cantilever beams." Journal of Vibration and Control 26, no. 23-24 (March 20, 2020): 2163–73. http://dx.doi.org/10.1177/1077546320915313.
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In layered and riveted structures, vibration damping happens because of a micro slip that occurs because of a relative motion at the common interfaces of the respective jointed layers. Other parameters that influence the damping mechanism in layered and riveted beams are the amplitude of initial excitation, overall length of the beam, rivet diameter, overall beam thickness, and many layers. In this investigation, using the analytical models such as the Euler–Bernoulli beam theory and Timoshenko beam theory and half-power bandwidth method, the free transverse vibration analysis of layered and riveted short cantilever beams is carried out for observing the damping mechanism by estimating the damping ratio, and the obtained results from the Euler–Bernoulli beam theory and Timoshenko beam theory analytical models are validated by the half-power bandwidth method. Although the Euler–Bernoulli beam model overestimates the damping ratio value by a very less fraction, both the models can be used to evaluate damping for short riveted cantilever beams along with the half-power bandwidth method.
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Adair, Desmond, and Martin Jaeger. "A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams." Journal of Vibration and Control 24, no. 17 (June 14, 2017): 3855–64. http://dx.doi.org/10.1177/1077546317714183.
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A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.
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Ključanin, Dino, and Abaz Manđuka. "The cantilever beams analysis by the means of the first-order shear deformation and the Euler-Bernoulli theory." Tehnički glasnik 13, no. 1 (March 23, 2019): 63–67. http://dx.doi.org/10.31803/tg-20180802210608.
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The effect of the Timoshenko theory and the Euler-Bernoulli theory are investigated in this paper through numerical and analytical analyses. The investigation was required to obtain the optimized position of the pipes support. The Timoshenko beam theory or the first order shear deformation theory was used regarding thick beams where the shearing effect of the beam is considered. The study of the thin beams was performed with the Euler-Bernoulli theory. The analysis was done for stainless steel AISI-440C beams with the rectangular cross-section. The steel beams were a cantilever and stressed under varying point-centred load.
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Savarimuthu, Kirubaveni, Radha Sankararajan, Gulam Nabi Alsath M., and Ani Melfa Roji M. "Design and analysis of cantilever based piezoelectric vibration energy harvester." Circuit World 44, no. 2 (May 8, 2018): 78–86. http://dx.doi.org/10.1108/cw-11-2017-0067.
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Purpose This paper aims to present the design of a cantilever beam with various kinds of geometries for application in energy harvesting devices with a view to enhance the harvested power. The cantilever beams in rectangular, triangular and trapezoidal geometries are simulated, designed and evaluated experimentally. A power conditioning circuit is designed and fabricated for rectification and regulation. Design/methodology/approach The analytical model based on Euler–Bernoulli beam theory is analyzed for various cantilever geometries. The aluminum beam with Lead Zirconate Titanate (PZT) 5H strip is used for performing frequency, displacement, strain distribution, stress and potential analysis. A comparative analysis is done based on the estimated performance of the cantilevers with different topologies of 4,500 mm3 volume. Findings The analysis shows the trapezoidal cantilever yielding a maximum voltage of 66.13 V at 30 Hz. It exhibits maximum power density of 171.29 W/mm3 at optimal resistive load of 330 kΩ. The generated power of 770.8 µW is used to power up a C-mote wireless sensor network. Originality/value This study provides a complete structural analysis and implementation of the cantilever for energy harvesting application, integration of power conditioning circuit with the energy harvester and evaluation of the designed cantilevers under various performance metrics.
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Daneshmehr, Ali Reza, Majid Akbarzadeh Khorshidi, and Delara Soltani. "Dynamic Analysis of a Micro-Cantilever Subjected to Harmonic Base Excitation via RVIM." Applied Mechanics and Materials 332 (July 2013): 545–50. http://dx.doi.org/10.4028/www.scientific.net/amm.332.545.
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In this paper, dynamic analysis of a cantilever beam with micro-scale dimensions is presented. The micro-cantilever is subjected to harmonic base excitation and constant force at micro-cantilever tip. By Euler-Bernoulli beam theory assumptions, the mathematical formulation of vibrating micro-cantilever beam is derived using extended Hamilton principle. The governing partial-diffrential equation is solved by reconstruction of variational iteration method (RVIM), with possession of its boundary conditions. The RVIM is an approximate method of solving that answers easy and quick and has high accuracy.
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Jalali, Mohammad Hadi, and Geoff Rideout. "Analytical and experimental investigation of cable–beam system dynamics." Journal of Vibration and Control 25, no. 19-20 (August 2019): 2678–91. http://dx.doi.org/10.1177/1077546319867171.
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Interactions between cables and structures affect the design and nondestructive testing of electricity transmission lines, guyed towers, and bridges. An analytical model for an electricity pole beam–cable system is presented, which can be extended to other applications. A cantilever beam is connected to two stranded cables. The cables are modeled as tensioned Euler–Bernoulli beams, considering the sag due to self-weight. The pole is also modeled as a cantilever Euler–Bernoulli beam and the equations of motion are derived using Hamilton’s principle. The model was validated with a reduced-scale system in the laboratory and a setup was designed to accurately measure the bending stiffness of the stranded cable under tension. It is concluded that the bending stiffness and sag of the cable have a significant effect on the dynamics of beam–cable structures. By adding the cable to the pole structure, some hybrid modes emerge in the eigenvalue solution of the system. Modes with antisymmetric cable motion are sag-independent and the modes with symmetric cable motion are dependent on the cable sag. The effect of sag on the natural frequencies is more significant when the bending stiffness of the cables is higher.
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Mishra, Manish Kumar, P. M. Mishra, and Vikas Dubey. "Deflection Modelling of MEMS Cantilever Beam Through Collocation Method Taking B-Splinesas Approximating Functions." International Journal of Social Ecology and Sustainable Development 13, no. 3 (May 2022): 1–15. http://dx.doi.org/10.4018/ijsesd.290007.
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The Mathematical Modeling and Analysis of cantilever beam adhesion problem, under the action of electrostatic attraction force iscarried out. The model uses Euler-Bernoulli beam theory for one end fixed and other end free type beams for small deflection. A MATLAB code has prepared to predict and plot the deflection profile of MEMS cantilever beam during the action of stiction force on application of applied voltage as snap down occurs. The model predicts the cantilever behavior on occurrence of snap downvoltage. To envisage the deflection profile, A collocation method employing B-Spline as approximating functions & Gaussian quadrature point as collocation points has been utilized for solving the governing equation by keeping the four end boundary conditions of cantilever beam in mind. The numerical results reveal the deflection profile of the MEMS cantilever Beam, which are validated with the previous data & deflection profile available by numerous published research papers
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Zhang, Kai, De Shi Wang, and Qi Zheng Zhou. "Study on the Electromechanical Coupling Performance of Bimorph Piezoelectric Cantilever." Applied Mechanics and Materials 302 (February 2013): 447–51. http://dx.doi.org/10.4028/www.scientific.net/amm.302.447.
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In order to accurately predict the electromechanical coupling performance of bimorph piezoelectric cantilever structure. Based on Euler-Bernoulli beam assumption, the expression of output voltage response of the bimorph piezoelectric cantilever is written, the output voltage curve of unit acceleration excitation are obtained, the law of the output voltage influenced by the structure parameters of the cantilever beam length, width and thickness of the metal beam and the piezoelectric layer are analyzed, the results will play an important theoretical and engineering significance in the development of high efficient piezoelectric energy harvesting device.
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Nikolić, Aleksandar, and Slaviša Šalinić. "A rigid multibody method for free vibration analysis of beams with variable axial parameters." Journal of Vibration and Control 23, no. 1 (August 8, 2016): 131–46. http://dx.doi.org/10.1177/1077546315575818.
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This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler–Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.
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Shterev, Kiril, and Emil Manoach. "Geometrically Non-Linear Vibration of a Cantilever Interacting with Rarefied Gas Flow." Cybernetics and Information Technologies 20, no. 6 (December 1, 2020): 126–39. http://dx.doi.org/10.2478/cait-2020-0067.
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Abstract The work is devoted to study 2D pressure driven rarefied gas flow in a microchannel having an elastic obstacle. The elastic obstacle is clamped at the bottom channel wall and its length is half of the channel height. The gas flow is simulated by Direct Simulation Monte Carlo (DSMC) method applying the advanced Simplified Bernoulli Trial (SBT) collision scheme. The elastic obstacle is modelled as geometrically nonlinear Euler Bernoulli beam. A reduced 3 modes reduction model of the beam is created. The influence of the gas flow on the beam vibration is studied, considering the linear and nonlinear beam theories.
Dissertations / Theses on the topic "Cantilever Euler-Bernoulli beam"
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Kundu, Bidisha. "On the analysis of axially loaded Euler-Bernoulli beam using Galerkin, Fourier transform, and Lie symmetry approach." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/5244.
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The beam with axial load is one of the fundamental models in the field of physics and
engineering. The applications of this model span from a guitar string to the rotating blade
of a helicopter. It has an important role in vibration theory and structural mechanics.
Also, it establishes a relationship between the mathematical continuum concept and
continuum mechanics as it is the most basic example of a continuum physical model.
For the long and slender beams, the Euler-Bernoulli beam theory is used. In this thesis,
Euler-Bernoulli beam with axial load is studied. For the wide application in industry,
an accurate and simple closed form solution for the general problem is highly desirable.
Here, general problem implies a beam with variable stiffness, variable mass, and variable
axial load. The governing equation of motion is a partial differential equation of order
four in the spatial variable and of order two in the temporal variable.
However, there is a deficiency in the research on exact solutions of the above mentioned
model. The modern numerical methods such as finite element methods can give
an approximate solution but it requires huge computer time and sometimes extensive
coding. In this thesis, we look at some basic methods such as the Galerkin method and
Fourier transform method. We also apply Lie symmetry method to extract the closed
form solution. There are three parts in the thesis. In Part I, the Galerkin method is
written; in Part II, the Fourier transform method is discussed and finally, in Part III,
the Lie method is given
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Sarkar, Korak. "Inverse Problems in Free Vibration Analysis of Rotating and Non-Rotating Beams and its Application to Random Eigenvalue Characterization." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/3139.
Full textAbstract:
Rotating and non-rotating beams are widely used to model important engineering struc-tures. Hence, the vibration analyses of these beams are an important problem from a structural dynamics point of view. Depending on the beam dimensions, they are mod-eled using different beam theories. In most cases, the governing differential equations of these types of beams do not yield any simple closed-form solutions; hence we look for the inverse problem approach in determining the beam property variations given certain solutions.
The long and slender beams are generally modeled using the Euler-Bernoulli beam theory. Under the premise of this theory, we study (i) the second mode tailoring of non-rotating beams having six different boundary conditions, (ii) closed-form solutions for free vibration analysis of free-free beams, (iii) closed-form solutions for free vibration analysis for gravity-loaded cantilever beams, (iv) closed-form solutions for free vibration analysis of rotating cantilever and pinned-free beams and (v) beams with shared eigen-pair. Short and thick beams are generally modeled using the Timoshenko beam theory. Here, we provide analytical closed-form solutions for the free vibration analysis of ro-tating non-homogeneous Timoshenko beams. The Rayleigh beam provides a marginal improvement over the Euler-Bernoulli beam theory without venturing into the math-ematical complexities of the Timoshenko beam theory. Under this theory, we provide closed-form solutions for the free vibration analysis of cantilever Rayleigh beams under three different axial loading conditions - uniform loading, gravity-loading and centrifu-gally loaded.
We assume simple polynomial mode shapes which satisfy the different boundary conditions of a particular beam, and derive the corresponding beam property variations. In case of the shared eigenpair, we use the mode shape of a uniform beam which has a closed-form solution and use it to derive the stiffness distribution of a corresponding axially loaded beam having same length, mass variation and boundary condition. For the Timoshenko beam, we assume polynomial functions for the bending displacement and the rotation due to bending. The derived properties are demonstrated as benchmark analytical solutions for approximate and numerical methods used for the free vibration analysis of beams. They can also aid in designing actual beams for a pre-specified frequency or nodal locations in some cases. The effect of different parameters in the derived property variations and the bounds on the pre-specified frequencies and nodal locations are also studied for certain cases.
The derived analytical solutions can also serve as a benchmark solution for different statistical simulation tools to find the probabilistic nature of the derived stiffness distri-bution for known probability distributions of the pre-specified frequencies. In presence of uncertainty, this flexural stiffness is treated as a spatial random field. For known probability distributions of the natural frequencies, the corresponding distribution of this field is determined analytically for the rotating cantilever Euler-Bernoulli beams. The derived analytical solutions are also used to derive the coefficient of variation of the stiffness distribution, which is further used to optimize the beam profile to maximize the allowable tolerances during manufacturing.
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Sarkar, Korak. "Inverse Problems in Free Vibration Analysis of Rotating and Non-Rotating Beams and its Application to Random Eigenvalue Characterization." Thesis, 2016. http://hdl.handle.net/2005/3139.
Full textAbstract:
Rotating and non-rotating beams are widely used to model important engineering struc-tures. Hence, the vibration analyses of these beams are an important problem from a structural dynamics point of view. Depending on the beam dimensions, they are mod-eled using different beam theories. In most cases, the governing differential equations of these types of beams do not yield any simple closed-form solutions; hence we look for the inverse problem approach in determining the beam property variations given certain solutions.
The long and slender beams are generally modeled using the Euler-Bernoulli beam theory. Under the premise of this theory, we study (i) the second mode tailoring of non-rotating beams having six different boundary conditions, (ii) closed-form solutions for free vibration analysis of free-free beams, (iii) closed-form solutions for free vibration analysis for gravity-loaded cantilever beams, (iv) closed-form solutions for free vibration analysis of rotating cantilever and pinned-free beams and (v) beams with shared eigen-pair. Short and thick beams are generally modeled using the Timoshenko beam theory. Here, we provide analytical closed-form solutions for the free vibration analysis of ro-tating non-homogeneous Timoshenko beams. The Rayleigh beam provides a marginal improvement over the Euler-Bernoulli beam theory without venturing into the math-ematical complexities of the Timoshenko beam theory. Under this theory, we provide closed-form solutions for the free vibration analysis of cantilever Rayleigh beams under three different axial loading conditions - uniform loading, gravity-loading and centrifu-gally loaded.
We assume simple polynomial mode shapes which satisfy the different boundary conditions of a particular beam, and derive the corresponding beam property variations. In case of the shared eigenpair, we use the mode shape of a uniform beam which has a closed-form solution and use it to derive the stiffness distribution of a corresponding axially loaded beam having same length, mass variation and boundary condition. For the Timoshenko beam, we assume polynomial functions for the bending displacement and the rotation due to bending. The derived properties are demonstrated as benchmark analytical solutions for approximate and numerical methods used for the free vibration analysis of beams. They can also aid in designing actual beams for a pre-specified frequency or nodal locations in some cases. The effect of different parameters in the derived property variations and the bounds on the pre-specified frequencies and nodal locations are also studied for certain cases.
The derived analytical solutions can also serve as a benchmark solution for different statistical simulation tools to find the probabilistic nature of the derived stiffness distri-bution for known probability distributions of the pre-specified frequencies. In presence of uncertainty, this flexural stiffness is treated as a spatial random field. For known probability distributions of the natural frequencies, the corresponding distribution of this field is determined analytically for the rotating cantilever Euler-Bernoulli beams. The derived analytical solutions are also used to derive the coefficient of variation of the stiffness distribution, which is further used to optimize the beam profile to maximize the allowable tolerances during manufacturing.
Conference papers on the topic "Cantilever Euler-Bernoulli beam"
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Kahrobaiyan, M. H., M. Zanaty, and S. Henein. "An Analytical Model for Beam Flexure Modules Based on the Timoshenko Beam Theory." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67512.
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Short beams are the key building blocks in many compliant mechanisms. Hence, deriving a simple yet accurate model of their elastokinematics is an important issue. Since the Euler-Bernoulli beam theory fails to accurately model these beams, we use the Timoshenko beam theory to derive our new analytical framework in order to model the elastokinematics of short beams under axial loads. We provide exact closed-form solutions for the governing equations of a cantilever beam under axial load modeled by the Timoshenko beam theory. We apply the Taylor series expansions to our exact solutions in order to capture the first and second order effects of axial load on stiffness and axial shortening. We show that our model for beam flexures approaches the model based on the Euler-Bernoulli beam theory when the slenderness ratio of the beams increases. We employ our model to derive the stiffness matrix and axial shortening of a beam with an intermediate rigid part, a common element in the compliant mechanisms with localized compliance. We derive the lateral and axial stiffness of a parallelogram flexure mechanism with localized compliance and compare them to those derived by the Euler-Bernoulli beam theory. Our results show that the Euler-Bernoulli beam theory predicts higher stiffness. In addition, we show that decrease in slenderness ratio of beams leads to more deviation from the model based on the Euler-Bernoulli beam theory.
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Tondo, Gledson Rodrigo, Sebastian Rau, Igor Kavrakov, and Guido Morgenthal. "Physics-informed Gaussian process model for Euler-Bernoulli beam elements." In IABSE Symposium, Prague 2022: Challenges for Existing and Oncoming Structures. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE), 2022. http://dx.doi.org/10.2749/prague.2022.0445.
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<p>A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the structure’s bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed model is applied on a numerically simulated cantilever beam, where the regressed bending stiffness is evaluated and the influence measurement noise on the prediction quality is investigated. Further, the regressed probabilistic stiffness distribution is used in a structural health monitoring context, where the Mahalanobis distance is employed to reason about the possible location and extent of damage in the structural system. To validate the developed framework, an experiment is conducted and measured heterogeneous datasets are used to update the assumed analytical structural model.</p>
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Aldraihem, Osama J., Robert C. Wetherhold, and Tarunraj Singh. "A Comparison of the Timoshenko Theory and the Euler-Bernoulli Theory for Control of Laminated Beams." In ASME 1996 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/imece1996-0655.
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Abstract In this paper, the governing equations and boundary conditions of laminated beam smart structures are presented. Sensor and actuator layers are included in the beam so as to facilitate vibration supression. Two mathematical models are presented: the shear-deformable (Timoshenko) model and the shear-indeformable (Euler-Bernoulli) model. The differential equations for a continuous beam are approximated by utilizing finite element techniques for both models. A cantilever laminated beam with and without a tip mass is investigated to assess the validity and the accuracy of the two models when used for vibration supression. Comparison between the two models is presented to show the advantages and the limitations of each of the models. Since the Timoshenko beam theory is higher order than the Euler-Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio. It is shown that use of an Euler-Bernoulli model to represent beam dynamics can lead to the design of an unstable controller.
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Sharghi, Hesam, and Onur Bilgen. "A Multi-Point Loaded Piezocomposite Beam: Modeling of Vibration Energy Harvesting." In ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/smasis2018-7947.
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Energy harvesting from ambient vibrations and mechanical deformations using piezoelectric materials has received significant attention over the last decade. These types of energy harvesters find applications in structural health monitoring, wireless sensor networks, etc. In this paper, vibration energy harvesting from piezocomposite beams with unconventional boundary conditions is investigated. The so-called inertial four-point boundary condition is useful in applications where the cantilevered beam setup leads to non-uniform stress-strain distribution along the beam domain. In this paper, the Euler-Bernoulli beam theory is used to model the beam. The voltage output, maximum power output, and the tip velocity are investigated. The efficiency of the four-point loaded beam is compared to a cantilever beam.
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Minas, Sophie, Michael Paidoussis, and Farhang Daneshmand. "Experimental and Analytical Investigation of Hanging Tubular Cantilevers With Discharging Axial and Radial Flow." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70466.
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The fluid-elastic instability of hanging cantilevered pipes subject to internal and external flows is studied. Flow-induced vibrations cause these flexible tubular cantilevers to experience dynamic divergence (flutter) as well as static divergence (buckling) at high enough flow velocities. Specifically, the system studied consists of a flexible tubular hanging cantilever, which hangs concentrically within an outer rigid tube. Fluid flows internally from the clamped end of the cantilever to the free end and flows in the opposite direction in the annular region between the cantilever and the outer tube. For the system investigated, flow discharges radially from the free-end of the cantilever through the use of an end-piece. A linear model is derived in which series solutions are employed using Euler-Bernoulli beam comparison functions and is compared with experimental results. The effects of end-piece mass, confinement, pipe length, and comparisons between radial and axial flow have also been studied.
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Sado, Danuta. "Dynamics of a Cantilever Beam With Attached Pendulum." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17157.
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Abstract This work draws attention to the to the analysis of dynamics of a nonlinear coupled cantilever beam-pendulum oscillator. Dynamical systems of this type have important technical applications, because many mechanical components consist of linear or weakly nonlinear continuos substructures such as beam coupled to nonlinear oscillators. The present paper is a continuation of the author’s previous work where in applying the Galerkin method the modal series was truncated at the first mode. In this work it is assumed that the cantilever beam behaves like an Euler-Bernoulli beam and to its end pendulum is attached. The integro-differential equations are transformed into an ordinary differential equations with the use of Galerkin procedure with beam functions. In this study, in applying the Galerkin method the modal series was truncated at the second mode. Next these equations were solved numerically and there was studied the effect of the internal friction on energy transfer in a coupled structure that consist of a linear viscoelastic beam supporting at its tip a nonlinear pendulum.
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Zhu, Bin, Christopher D. Rahn, and Charles E. Bakis. "Tunable Vibration Absorption of a Cantilever Beam Utilizing Fluidic Flexible Matrix Composites." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12580.
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Bonding a fluidic flexible matrix composite (F2MC) tube to a cantilever beam can create a lightly damped tuned vibration absorber. The beam transverse vibration couples with the F2MC tube strain to generate flow into an external accumulator via a flow port. The fluid inertia is analogous to the vibration absorbing mass in a conventional tuned vibration absorber. The large F2MC tube pressure accelerates the fluid so that the developed inertia forces cancel most of the vibration loads. An analytical model is developed based on Euler-Bernoulli beam theory and Lekhnitskii’s solution for anisotropic layered tubes. The analysis results show that the cantilever beam vibration can be reduced by more than 99% by designing the F2MC fiber angle, the tube attachment points, and the flow port geometry.
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Pasic, H., K. Alam, and D. Garg. "Dynamics of a Cantilever Electrode Beam on a Vibrating Base." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10281.
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Vibration of a simple uniform Bernoulli-Euler cantilever beam attached to a rigid base vibrating in a direction perpendicular to the beam is studied both analytically and experimentally. The objective is to study electrode deflection in electrostatic precipitators, with emphasis on the interaction of the vibrating electrode with the ambient fluid. The analytical solution can be used to find reliable estimates of the maximum vibration amplitude of the electrodes, which is a primary cause of detrimental sparking of the electrodes. An experimental system was built to validate the analytical results and to investigate the importance of the beam interaction with the ambient air/fluid medium — which is often overlooked in most of the existing analytical models. The results demonstrate that the drag effect of the ambient air can change the characteristics of the vibration significantly, thereby limiting the applicability of the analytical or numerical results.
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Naguleswaran, S. "Out-of-Plane Vibrations of a Stepped Euler-Bernoulli Beam Clamped to a Rotating Hub." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21568.
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Abstract This paper is concerned with the vibrations of an Euler-Bernoulli stepped cantilever, clamped to a hub rotating at a constant speed. The system parameters are: the speed of rotation of the hub, the position of the step, the ratio of the mass per unit length of the two portions of the beam and the ratio of the flexural rigidity. Analytical solution of the mode shape differential equations for out-of-plane vibrations (normal to the plane of rotation) is developed. The frequency equation is expressed as a 4th order determinant equated to zero. A scheme is presented to derive the natural frequencies. The first three frequencies are tabulated for various combinations of the system parameters. Published results (which were obtained via finite element procedure) are compared with the analytical results.
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Dey, Somnath, and V. Kartik. "Intermittent Contact Dynamics of a Micro-Cantilever in High Speed Contact Mode Scanning Probe Microscopy." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52367.
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The intermittent contact dynamics of a scanning probe microscopy (SPM) micro-cantilever are investigated in the context of high speed imaging in contact mode. At high scan speeds the cantilever can completely detach from the sample surface, and this lowers the achievable image resolution and limits the imaging speed. An analysis is performed, modeling the micro-cantilever as an Euler-Bernoulli beam and approximating the effect of the tip’s contact with the surface by an attached spring with an end mass that is subjected to attractive/repulsive interaction force. At low scan speeds, the cantilever follows the surface profile, while the frequency spectra exhibit a number of side-bands, while at higher speeds, the contact is intermittent. The sensitivity of the cantilever’s deflection varies along the length and hence the image resolution strongly depends on the point selected for optical laser deflection.