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Journal articles on the topic 'Tapered cantilever beam'

Author: Grafiati
Published: 3 June 2025
Last updated: 1 August 2025

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1

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 (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 re
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2

Anand, Ashutosh, and Manish Kumar. "Tapered substrate thickness to enhance the performance of piezoelectric energy harvester." Nanomaterials and Energy 11, no. 3-4 (2022): 1–11. http://dx.doi.org/10.1680/jnaen.22.00038.

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In this paper, the improvement of the performance of the piezoelectric (PZ) cantilever beam using the non-uniform substrate thickness has been presented. This reduces the resonant frequency, improves stress distribution and generates more output voltage and power. Both analytical and finite element method (FEM) analyses have been performed to investigate the effect of tapered substrate thickness on the PZ cantilever beam. The tapered substrate thickness has been used in rectangular and trapezoidal cantilever structures. All the designed cantilever structures have the same fabrication area, and
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3

Keshmiri, Alireza, Nan Wu, and Quan Wang. "Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method." International Journal of Structural Stability and Dynamics 18, no. 07 (2018): 1850101. http://dx.doi.org/10.1142/s0219455418501018.

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In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accur
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4

Wang, Zhongmin, and Rongrong Li. "Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section." Shock and Vibration 2018 (2018): 1–14. http://dx.doi.org/10.1155/2018/1056397.

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Problems related to the transverse vibration of a rotating tapered cantilever beam with hollow circular cross-section are addressed, in which the inner radius of cross-section is constant and the outer radius changes linearly along the beam axis. First, considering the geometry parameters of the varying cross-sectional beam, rotary inertia, and the secondary coupling deformation term, the differential equation of motion for the transverse vibration of rotating tapered beam with solid and hollow circular cross-section is derived by Hamilton variational principle, which includes some complex var
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5

Messaoud, Bouamra, Fellah Ahmed, Saimi Ahmed, and Bouzidi Imane. "Free vibration analysis of bidirectional functionally graded double-tapered beam using the p-version of the finite element method." South Florida Journal of Development 5, no. 12 (2024): e4824. https://doi.org/10.46932/sfjdv5n12-049.

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In this paper, we conducted a frequency analysis of bidirectional functionally graded double-tapered beam (BDFG beam) using the p-version of the finite element method, the beam was modeled by the Euler Bernoulli beam theory, the global matrices of the equation of motion are determined by applying the Lagrange equation on the kinetic and deformation energies. The material properties are assumed to vary along the thickness and width directions according the power-law distribution. The numerical results are obtained by a developed Matlab code and compared with Ansys Workbench and Solidworks for a
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6

Raju, S. Srinivasulu, M. Umapathy, and G. Uma. "High-output piezoelectric energy harvester using tapered beam with cavity." Journal of Intelligent Material Systems and Structures 29, no. 5 (2017): 800–815. http://dx.doi.org/10.1177/1045389x17721044.

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Energy harvesting using cantilever-based piezoelectric structure is most popular for harvesting electrical energy from ambient vibrations. Efforts are also made to maximize the harvester power by means of tailoring the structural parameters of the cantilever beam. This article proposes a method to maximize the harvester voltage from the cantilever-based piezoelectric energy harvester by means of tailoring the structure of the cantilever, to have a tapering in width, thickness and in both width and thickness (double taper). It is also proposed to introduce rectangular and trapezoidal cavities i
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7

Yoshizawa, Katsuhito, and Kikuo Ikarashi. "Elastic Local Buckling Strength of Tapered H-Shaped Cantilever Beams." Applied Mechanics and Materials 166-169 (May 2012): 1033–39. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1033.

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The purpose of this paper is to investigate the elastic local buckling strength and the behavior of tapered H-shaped beams under stress condition of cantilever beam. The analyses were conducted by separating H-shaped beam into two plate elements (web and flanges). From the results of analyses, authors evaluate elastic local buckling strength of each plate element, and clarify the several effects of tapered shape by comparing buckling strength and the behavior of tapered H-shaped beam with uniform H-shaped beam. In addition, authors examine coupled buckling of the two plate elements and confirm
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8

Chen, Z., H. T. Zhao, J. Chen, Z. T. Zhang, and D. P. Duan. "Deformation Analysis of the Tapered Inflatable Beam." Journal of Mechanics 34, no. 4 (2017): 453–59. http://dx.doi.org/10.1017/jmech.2017.17.

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AbstractIn the theory research and engineering practice, more basic inflatable models are essential for the mechanical property analysis of inflatable structures. Firstly, this paper presents a model of the tapered inflatable cantilever beam based on Timoshenko's theory and analyzes its deformation under a concentrated force. Moreover, the following forces resulting from internal pressure and taper ratio are introduced into the equilibrium equations of the deformed configuration. Thus, the model is optimized compared to the existing one for a straight beam. To verify the effectiveness and the
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9

Ufe, M. M., S. N. Apebo, and A. Y. Iorliam. "Derivation and optimization of deflection equations for tapered cantilever beams using the finite element method." Nigerian Journal of Technology 39, no. 2 (2020): 351–62. http://dx.doi.org/10.4314/njt.v39i2.5.

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This study derived analytical solutions for the deflection of a rectangular cross sectional uniformly tapered cantilever beam with varying configurations of width and breadth acting under an end point load. The deflection equations were derived using a numerical analysis method known as the finite element method. The verification of these analytical solutions was done by deterministic optimisation of the equations using the ModelCenter reliability analysis software and the Abaqus finite element modelling and optimisation software. The results obtained show that the best element type for the fi
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10

Chalah, Farid, Salah Eddine Djellab, Kamel Falek, Lila Chalah-Rezgui, and Abderrahim Bali. "Tapered Beam Fundamental Natural Frequency Based on Rayleigh Quotient." Applied Mechanics and Materials 330 (June 2013): 526–30. http://dx.doi.org/10.4028/www.scientific.net/amm.330.526.

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Different continuous variations in the inertia are considered in achieving cantilever tapered beams to match functional design and resistance requirements. In this investigation, the expressions of linear and cubic variations in the inertia are associated to a linear mass distribution. An exact solution of the fourth order differential equation, with none constant coefficients governing the studied tapered beam element equilibrium, is obtained for each case. These displacements functions are normalized and introduced in the well known Rayleigh quotient formula for calculating the fundamental n
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11

Morgan, J. "Analysis of beams subjected to large deflections." Aeronautical Journal 93, no. 929 (1989): 356–60. http://dx.doi.org/10.1017/s0001924000017292.

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SynopsisThe transfer matrix method of structural analysis is applied to the problem of beams subjected to large deflections by dividing the beam into a large number of uniform sections and applying elementary bending theory to each section. The solution using this method is compared with the theoretical solution of Bisshopp and Drucker for large deflections in uniform cantilever beams. The method has also been applied to uniform and tapered cantilever beams at various angles to the horizontal under vertical point loading and the results compared with experimental data obtained from laboratory
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12

Deepak, Kute*1 &. Hredeya Mishra2. "TWO CRACK DETECTION IN TAPERED CANTILEVER BEAM USING NATURAL FREQUENCY AS BASIC CRITERION." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 7 (2018): 228–33. https://doi.org/10.5281/zenodo.1311656.

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Crack in a vibrating component changes the physical characteristics of a structure which in turn alter its dynamic response characteristics. Crack depth and crack location are main parameters for analysis. In this project a method has been proposed for the detection of open cracks based on frequency measurements on tapered cantilever beams. The present method enables one to detect a crack in a beam without the help of the massless rotational spring model. Both forward and inverse problems are solved and results are presented.In forward problem,the natural frequencies are determined by FEA soft
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13

Wong, Foek Tjong, Junius Gunawan, Kevin Agusta, Herryanto Herryanto, and Levin Sergio Tanaya. "On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam." Civil Engineering Dimension 21, no. 2 (2019): 89–96. http://dx.doi.org/10.9744/ced.21.2.89-96.

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A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the b
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14

Cekus, Dawid. "Free vibration of a cantilever tapered Timoshenko beam." Scientific Research of the Institute of Mathematics and Computer Science 11, no. 4 (2012): 11–17. http://dx.doi.org/10.17512/jamcm.2012.4.02.

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15

Russo, Edwin P., and Gregory Garic. "Shear‐Stress Distribution in Symmetrically Tapered Cantilever Beam." Journal of Structural Engineering 118, no. 11 (1992): 3243–49. http://dx.doi.org/10.1061/(asce)0733-9445(1992)118:11(3243).

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16

Nageswara Rao, B., and G. Venkateswara Rao. "Large amplitude vibrations of a tapered cantilever beam." Journal of Sound and Vibration 127, no. 1 (1988): 173–78. http://dx.doi.org/10.1016/0022-460x(88)90357-4.

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17

Sadeghi, A., and H. Zohoor. "A fresh insight into the non-linear vibration of double-tapered atomic force microscope cantilevers by considering the Hertzian contact theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 1 (2010): 233–47. http://dx.doi.org/10.1243/09544062jmes2184.

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The non-linear flexural vibration for a double-tapered atomic force microscope cantilever has been investigated by using the Timoshenko beam theory. In this article, the normal and tangential tip—sample interaction forces are found from the Hertzian contact model, and the effects of the contact position, normal and lateral contact stiffness, height of the tip, thickness of the beam, angle between the cantilever and the sample surface, and breadth and height taper ratios on the non-linear frequency to linear frequency ratio have been studied. The differential quadrature method is employed to so
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18

Wang, Lingzhi, Ting Tan, Zhimiao Yan, and Zhitao Yan. "Tapered galloping energy harvester for power enhancement and vibration reduction." Journal of Intelligent Material Systems and Structures 30, no. 18-19 (2019): 2853–69. http://dx.doi.org/10.1177/1045389x19873409.

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The cantilever beam was commonly designed with uniform cross-section for the galloping energy harvesters. To improve its performance, two tapered galloping energy harvesters are proposed in this work. In the first tapered design, the beam’s thickness is linearly changed with constant width. In the second tapered design, both the beam’s thickness and width are linearly varied. A generalized fluid–structure–electricity coupled distributed-parameter model is established by the Hamilton principle and Gauss law for the tapered galloping energy harvesters. By means of the properties of the Bessel fu
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19

Ahmed, Sohail, and Sanam Ayub. "Failure Analysis of Composite Thin Walled Multi-Cell Closed Cross Section Beams with Multi-Tapered Configuration." Applied Mechanics and Materials 789-790 (September 2015): 382–88. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.382.

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This paper explicitly highlights the failure analysis and study of thin walled composite beams (multi-cell and multi-tapered) in cantilever configurations when subjected to constrained torsional load, using MSC Patran / Nastran finite element package. Initially, the verification of the model was done with the analytical results in order to ensure the model accuracy. All the multi-tapered beams under examination are composed of closed section and three cell configuration with twisting moment applied at the free end. There is a vivid description of all the effects of different composite material
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20

Atiyah, Qasim Abbas, Ammar Saleem Hameed, and Baqer Jabbar Assi. "Vibration Analysis of Uniform and Tapered Composite Beams with Embedded Shape Memory Alloy." Journal of University of Babylon for Engineering Sciences 27, no. 1 (2019): 82–93. http://dx.doi.org/10.29196/jubes.v27i1.1972.

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In this study, laminated composite materials were hybridized with E-glass fiber and Nitinol (Nickel-Titanium) wires. Hand lay-up technique was used to prepare the samples, epoxy resin type (Sikadur 52 N) was used as matrix reinforced by one fiber from E-glass fiber woven roving with embedded nitinol wires with a diameter 0.5 mm for samples and number of wires such as 0, 1, 3, 5 and 9 to find the effect of the number of wires on the natural frequency. The samples were fixed as a cantilever beam. The effects of increasing the number of nitinol wires, the diameter of nitinol wires, the length of
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21

Lee, Jong-Won. "Fault Detection Method of Tapered Cantilever Pipe-type Beam." Journal of the Architectural Institute of Korea Structure & Construction 31, no. 2 (2015): 13–20. http://dx.doi.org/10.5659/jaik_sc.2015.31.2.13.

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22

A., AL-QAISIA, and ABDEL-JABER S. "NON-LINEAR FORCED VIBRATION OF A TAPERED CANTILEVER BEAM." International Conference on Applied Mechanics and Mechanical Engineering 13, no. 13 (2008): 1–11. http://dx.doi.org/10.21608/amme.2008.38988.

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23

Lu, Shi-kun, Deng-xin Hua, Yan Li, Fang-yuan Cui, and Peng-yang Li. "Stiffness Calculation Model of Thread Connection Considering Friction Factors." Mathematical Problems in Engineering 2019 (January 23, 2019): 1–19. http://dx.doi.org/10.1155/2019/8424283.

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In order to design a reasonable thread connection structure, it is necessary to understand the axial force distribution of threaded connections. For the application of bolted connection in mechanical design, it is necessary to estimate the stiffness of threaded connections. A calculation model for the distribution of axial force and stiffness considering the friction factor of the threaded connection is established in this paper. The method regards the thread as a tapered cantilever beam. Under the action of the thread axial force, in the consideration of friction, the two cantilever beams int
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24

Hajheidari, Peyman, Ion Stiharu, and Rama Bhat. "Performance of tapered cantilever piezoelectric energy harvester based on Euler–Bernoulli and Timoshenko Beam theories." Journal of Intelligent Material Systems and Structures 31, no. 4 (2019): 487–502. http://dx.doi.org/10.1177/1045389x19891526.

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The cantilever beam configuration plays an important role in the power extracted from the vibration-based piezoelectric energy harvesters. Although it has already been proven that triangular and trapezoidal shapes optimize and improve the electrical output of the piezoelectric energy harvesters, the impact of other shapes has not been considered. It is necessary to figure out which shape can provide the maximum amount of power and efficiency, as well. In this article, a complete study regarding the influence of non-uniform theories using both Timoshenko and Euler–Bernoulli beams for both unimo
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25

H. Al-Raheimy, Nawal, and Lekaa Hammed. "FREE TRANSVERSE VIBRATIONS OF CANTILEVER BEAM FOR TAPERED THICKNESS PREPARED FROM VARIANT FIBERS REINFORCED POLYESTER." Journal of the Serbian Society for Computational Mechanics 16, no. 2 (2022): 1–12. http://dx.doi.org/10.24874/jsscm.2022.16.02.01.

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The natural frequency of the cantilever beam for the tapered thickness in the current paper is estimated using a Raleigh-Ritz approach. The study explores the effect of different parameters on the behavior of the beam such as the length of beam “L”, thickness at clamped end “hc”, width “b”, the ratio of thickness at free end to thickness at clamped end “hf/hc”, types of fibers and the concentration of fibers “f” in the resin of unsaturated polyester representing the matrix. The resin can be reinforced by aligned long fibers such as E-fibers glass, Kevlar-49 and carbon fiber
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26

Lee, Jong Won, Sang Ryul Kim, and Bong Ki Kim. "Modal Property Estimation of Tapered Cantilever Pipe-type Cracked Beam." Journal of the Computational Structural Engineering Institute of Korea 27, no. 5 (2014): 361–68. http://dx.doi.org/10.7734/coseik.2014.27.5.361.

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27

Akbarzade, M., and A. Farshidianfar. "Nonlinear dynamic analysis of an elastically restrained cantilever tapered beam." Journal of Applied Mechanics and Technical Physics 58, no. 3 (2017): 556–65. http://dx.doi.org/10.1134/s002189441703021x.

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28

Huo, Yinlei, and Zhongmin Wang. "Dynamic analysis of a rotating double-tapered cantilever Timoshenko beam." Archive of Applied Mechanics 86, no. 6 (2015): 1147–61. http://dx.doi.org/10.1007/s00419-015-1084-6.

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29

Nageswara Rao, B., and G. Venkateswara Rao. "Large deflections of a spring-hinged tapered cantilever beam with a rotational distributed loading." Aeronautical Journal 91, no. 909 (1987): 429–37. http://dx.doi.org/10.1017/s0001924000021667.

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SummaryLarge deflection problem of a spring loaded hinged nonuniform cantilever beam subjected to a rotational distributed loading is formulated by means of a second-order non-linear integro-differential equation. The problem is examined by considering the beam of rectangular cross-section with linear depth taper subjected to a uniform rotational distributed load. The elastic curves of a beam for this special case are presented.
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30

Deepak, Kute*1 &. Hredeya Mishra2. "TWO REVIEW OF NATURAL FREQUENCY CRITERION FOR CRACK DETECTION IN TAPERED CANTILEVER BEAM." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 7 (2018): 234–38. https://doi.org/10.5281/zenodo.1311658.

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Tapered cantilever beams are widely used as machine elements and structural elements in mechanical, naval, civil, aeronautical engineering. There are unexpected sudden failures on machine elements. In order to attain maximum reliability of machine and structure, so the best way is to monitoring the health of susceptible critical component.Cracks are the most encountered damage types in the structures due to fatigue or manufacturing defects. Cracks found in structural elements may fail the whole system. Natural frequencies of structures are measured most easily and accurately. Experimental Moda
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31

Ibrahim, S. M., Y. A. Al-Salloum, and H. Abbas. "Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory." Advanced Materials Research 919-921 (April 2014): 79–82. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.79.

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Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the str
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32

Bui Thi Thu Hoai, Le Cong Ich, and Nguyen Dinh Kien. "Size-dependent nonlinear bending of tapered cantilever microbeam based on modified couple stress theory." Vietnam Journal of Science and Technology 62, no. 6 (2024): 1196–209. https://doi.org/10.15625/2525-2518/19281.

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The Euler-Bernoulli beam theory is adopted in conjunction with modified couple stress theory (MCST) in this paper to formulate a beam element for size-dependent nonlinear bending analysis of a tapered cantilever microbeam subjected to end force/moment. The microbeam is considered to be linearly tapered in both the width and height directions. The element is derived in the context of the co-rotational approach in which the internal force vector and the tangent stiffness matrix are firstly derived in an element attached coordinate system and then transferred to the global one by the transformati
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33

Maulana, Taufiq Ilham, Bagus Soebandono, and Aris Susanti. "STRESS AND DEFORMATION STUDY ON CASTELLATED STEEL BEAM WITH TAPERED SHAPE AND HEXAGONAL OPENINGS." SINERGI 23, no. 1 (2019): 61. http://dx.doi.org/10.22441/sinergi.2019.1.009.

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Castellated steel beam is a beam with a regular section cut into half with a particular pattern and regrouped with welding to increase its height compared to the original. This structure element has been developed in building constructions since many years ago. However, its uniform section along the span will make the modification no longer effective in cantilever structure, unless it has additional adaptation. Therefore, in this study, it is proposed to use a castellated steel beam with a tapered shape to be applied as cantilever structures. A steel beam with IWF section 150x75x5x7 is the pri
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N. Tamil Selvam et al.,, N. Tamil Selvam et al ,. "Analysis of Fracture Toughness Mode–I of Tapered Double Cantilever Beam." International Journal of Mechanical and Production Engineering Research and Development 8, no. 4 (2018): 897–904. http://dx.doi.org/10.24247/ijmperdaug201893.

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35

Zhao, Xing Wei, Zhen Dong Hu, and Gert H. M. van der Heijden. "Dynamic analysis of a tapered cantilever beam under a travelling mass." Meccanica 50, no. 6 (2015): 1419–29. http://dx.doi.org/10.1007/s11012-015-0112-5.

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36

Barton, Bryce L., Mahesh S. Shetty, Victor Birman, and Lokeswarappa R. Dharani. "Tapered cylindrical cantilever beam retrofitted with steel reinforced polymer or grout." Composites Part B: Engineering 42, no. 2 (2011): 207–16. http://dx.doi.org/10.1016/j.compositesb.2010.10.006.

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37

Craver, W. L., and P. Jampala. "Transverse Vibrations of a Linearly Tapered Cantilever Beam With Constraining Springs." Journal of Sound and Vibration 166, no. 3 (1993): 521–29. http://dx.doi.org/10.1006/jsvi.1993.1310.

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38

Luo, Yumei, Yundong Li, Linyan Li, and Zhongxiang Li. "Mathematical Model of the Tapered Cantilever Beam Based on the Geometrically Exact Beam Theory." Journal of Applied Mathematics and Physics 13, no. 02 (2025): 490–505. https://doi.org/10.4236/jamp.2025.132027.

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39

K.S., VIVEK, and RAM K.S. SAI. "Stability of Web and Flange Tapered Steel Cantilever Thin-Walled Beams and Beam-Columns." i-manager's Journal on Structural Engineering 6, no. 2 (2017): 20. http://dx.doi.org/10.26634/jste.6.2.13636.

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40

Teixeira, JMD, RDSG Campilho, and FJG da Silva. "Numerical assessment of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for the GIC determination of adhesive layers." Journal of Adhesion 94, no. 11 (2018): 951–73. http://dx.doi.org/10.1080/00218464.2017.1383905.

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41

Maulana, Taufiq Ilham, Bagus Soebandono, Beta Satria Jagad, and Hakas Prayuda. "Stress and deformation analysis of tapered cantilever castellated beam using numerical method." IOP Conference Series: Materials Science and Engineering 352 (May 2018): 012029. http://dx.doi.org/10.1088/1757-899x/352/1/012029.

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42

Grabois, Thiago Melo, Jan Neggers, Laurent Ponson, François Hild, and Romildo Dias Toledo Filho. "On the validation of integrated DIC with tapered double cantilever beam tests." Engineering Fracture Mechanics 191 (March 2018): 311–23. http://dx.doi.org/10.1016/j.engfracmech.2017.12.015.

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43

Lee, Jong-Won. "Crack identification method for tapered cantilever pipe-type beam using natural frequencies." International Journal of Steel Structures 16, no. 2 (2016): 467–76. http://dx.doi.org/10.1007/s13296-016-6017-x.

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44

Le Blanc, M., R. M. Measures, M. M. Ohn, and S. Y. Huang. "Tunable chirping of a fibre Bragg grating using a tapered cantilever beam." Electronics Letters 30, no. 25 (1994): 2163–65. http://dx.doi.org/10.1049/el:19941476.

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45

Mehraeen, S., S. Jagannathan, and K. A. Corzine. "Energy Harvesting From Vibration With Alternate Scavenging Circuitry and Tapered Cantilever Beam." IEEE Transactions on Industrial Electronics 57, no. 3 (2010): 820–30. http://dx.doi.org/10.1109/tie.2009.2037652.

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46

Lee, Jong-Won. "Crack Detection Method of Tapered Cantilever Pipe-type Beam with a Tip Mass." Journal of the Architectural Institute of Korea Structure & Construction 32, no. 4 (2016): 3–10. http://dx.doi.org/10.5659/jaik_sc.2016.32.4.3.

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47

Gao, Teng, J. U. Cho, and Seong S. Cheon. "Experiment and Analysis on Impact of Tapered Double Cantilever Beam with Aluminum Alloy." Composites Research 27, no. 2 (2014): 72–76. http://dx.doi.org/10.7234/composres.2014.27.2.072.

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48

Davalos, J. F., P. Madabhusi-Raman, P. Z. Qiao, and M. P. Wolcott. "Compliance rate change of tapered double cantilever beam specimen with hybrid interface bonds." Theoretical and Applied Fracture Mechanics 29, no. 2 (1998): 125–39. http://dx.doi.org/10.1016/s0167-8442(98)00024-x.

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Chen, Der-Wei, and Tsung-Lung Liu. "Free and forced vibrations of a tapered cantilever beam carrying multiple point masses." Structural Engineering and Mechanics 23, no. 2 (2006): 209–16. http://dx.doi.org/10.12989/sem.2006.23.2.209.

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Biswal, Alok Ranjan, Tarapada Roy, and Rabindra Kumar Behera. "Genetic algorithm- and finite element-based design and analysis of nonprismatic piezolaminated beam for optimal vibration energy harvesting." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 14 (2015): 2532–48. http://dx.doi.org/10.1177/0954406215595253.

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Abstract:
The current article deals with finite element (FE)- and genetic algorithm (GA)-based vibration energy harvesting from a tapered piezolaminated cantilever beam. Euler–Bernoulli beam theory is used for modeling the various cross sections of the beam. The governing equation of motion is derived by using the Hamilton's principle. Two noded beam elements with two degrees of freedom at each node have been considered in order to solve the governing equation. The effect of structural damping has also been incorporated in the FE model. An electric interface is assumed to be connected to measure the vol
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