Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation

Alper Oğulcan Söylemez; Bekir Akgöz

doi:10.24107/ijeas.1654819

Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation

Abstract

This paper deals with the investigation of the vibrational behavior of aluminum cantilever beams for various slenderness ratios. Analytical solutions based on the Bernoulli-Euler beam theory are compared with the results from SOLIDWORKS. The first three natural frequencies are analyzed, highlighting the influence of beam length and mode number. The results demonstrate that the Bernoulli-Euler beam theory provides accurate results for high slenderness ratios and lower modes, while SOLIDWORKS offers reliable results for practical applications. The findings contribute valuable insights into the design and analysis of structural elements, particularly for nanomechanics studies. This study presents a rare and comprehensive dataset, systematically comparing analytical theory with finite element method simulations performed on beams with varying slenderness ratios.

Keywords

References

Donnel, L. H., Beams Plates and Shells. (Engineering Societies Monographs), McGraw-Hill Inc., 1976.
Gere, J. M., Timoshenko S.P., Mechanics of Materials, PWS Publishing Company, 1997.
Bozyiğit, B., Çatal, S., Çatal, H.H., Timoshenko Kirişlerinin Serbest Titreşim Analizinin Diferansiyel Transformasyon Metodu ile İncelenmesi, 3. Turkish Earthquake Engineering and Seismology Conference, İzmir, Turkey, 2015.
Thomson, W. T., Theory of Vibration with Applications, Prentice Hall; 2nd Edition, 1981.
Meirovitch, L., Fundamentals of Vibrations, McGraw-Hill Inc., 2001.
Magrab, E., Vibrations of Elastic Systems: With Applications to MEMS and NEMS, Springer, 2012.
Rayleigh, J. W. S., Theory of Sound Volume 1, Cambridge University Press; 1st Edition, 1877.
Beyçimen, S., Vibration Analysis of Restrained Beams, Master’s Thesis, Bursa Uludağ University; Graduate School of Natural and Applied Sciences, 2019.

Scott, R., In the Wake of Tacoma: Suspension Bridges and the Quest for Aerodynamic Stability, Amer Society of Civil Engineers, 2001.
Çatal, S., Basit Mesnetli Kirişin Diferansiyel Transform Metoduyla Serbest Titreşim Analizi, 3rd International Symposium on Innovative Approaches in Scientific Studies (Section: Engineering and Natural Sciences), Ankara, Turkey, 2019.
Chopra, A., Dynamics of Structures, Prentice Hall; 2nd Edition, 2004.
Clough, R. W., Penzien, J., Dynamics of Structures, McGraw-Hill Inc.; 2nd Edition, 1993.
Celep, Z., Kumbasar, N., Yapı Dinamiği, Beta Dağıtım, 2001.
Wang. J., Vibration of Stepped Beams on Elastic Foundations, Journal of Sound and Vibration, 149 (2), 315-322, 1991.
Kukla, S., Free Vibration of a Beam Supported on a Stepped Elastic Foundation, Journal of Sound and Vibration, 149 (2), 259-265, 1991.
Naguleswaran, S., Vibration of an Euler-Bernoulli Beam on Elastic End Supports and With Up to Three Step Changes in Cross-Section. International Journal of Mechanical Sciences, 44, 2541-2555, 2002.
Naguleswaran, S., Natural Frequencies, Sensitivity and Mode Shape Details of an Euler-Bernoulli Beam with One Step Change in Cross-Section and With Ends on Classical Supports, Journal of Sound and Vibration, 252 (4), 751-767, 2002
Naguleswaran, S., Transverse Vibration of an Euler-Bernoulli Beam on up to Five Resilient Supports Including Ends, Journal of Sound and Vibration, 261, 372-384, 2003
Coşkun, S. B., Atay, M. T., Ozturk, B., Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques, Advances in Vibration Analysis Research, 1, 1-22, 2011
Ece, M. C., Aydogdu, M., Taskin, V., Vibration of a Variable Cross-Section Beam, Mechanics Research Communications, 34, 78-84, 2007.
Timoshenko, S. P., On the Transverse Vibrations of Bars of Uniform Cross-Section, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 43 (253), 125-131, 1922.
Timoshenko, S. P., Vibration Problems in Engineering, D. Van Nostrand Company Inc.; 2nd Edition, 1937.
Kocatürk, K., Şimşek, M., Free Vibration Analysis of Timoshenko Beams Under Various Boundary Conditions, Journal of Engineering and Natural Sciences, 2005/1, 30-44, 2005.
Koç, Y., Examining free vibration of simply-supported beam with using Euler-Bernolli and Timoshenko beam theories, Master’s Thesis, Bursa Uludağ University; Graduate School of Natural and Applied Sciences, 2006.
Huang, T. C., The Effect of Rotatory Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams with Simple End Conditions, Journal of Applied Mechanics, 28 (4), 579-584, 1961.
Şimşek, M., Analysis of behaviour of beams subjected to an eccentric compressive force under effect of a moving harmonic load, PhD’s Thesis, Yıldız Teknik University, Graduate School of Natural and Applied Sciences, 2005.
Prokic, A., Besevic, M., Lukic, D., A Numerical Method for Free Vibration Analysis of Beams, Latin American Journal of Solids and Structures, 11, 1432-1444, 2014.
Han, S. M., Benaroya, H., Wei, T., Dynamics of Transversely Vibrating Beam Using Four Engineering Theories, Journal of Sound and Vibration, 225 (5), 935-988, 1999.
Avcar, M., Free Vibration Analysis of Beams Considering Different Geometric Characteristics and Boundary Conditions, International Journal of Mechanics and Applications, 4 (3), 94-100, 2014.
Şimşek, M., Free Vibration Analysis of Beams Subjected to Axial Load Under Various Boundary Conditions, Sigma Journal of Engineering and Natural Sciences, 23(3), 1-10, 2005.
Zhou, D., Cheung, Y. K., The Free Vibration of a Type of Tapered Beams, Computer Method in Applied Mechanics and Engineering, 188, 203-216, 2000.
Bulut, B., Effect of Taper Ratio on Parametric Stability of a Rotating Tapered Beam, European Journal of Mechanics A/Solids, 37, 344-350, 2013.
Banerjee, J. R., Jackson, D. R., Free Vibration of a Rotating Tapered Rayleigh Beam: A Dynamic Stiffness Method of Solution, Computers & Structures, 124, 11-20, 2013
Baghani, M., Mazaheri, H., Salarieh, H., Analysis of Large Amplitude Free Vibrations of Clamped Tapered Beams on a Nonlinear Elastic Foundation, Applied Mathematical Modelling, 38, 1176-1186, 2014
Lee, J. W., Lee, J. Y., Free Vibration Analysis using Transfer-Matrix Method on a Tapered Beam, Computers & Structures, 164, 75-82, 2016.
Çalım, F. F., Değişken Kesitli Timoshenko Kirişinin Serbest Titreşim Analizi, Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 6 (1), 76-82, 2017.
Çalım, F. F., Free and Forced Vibrations of Non-Uniform Composite Beams, Composite Structures, 413-423, 2009.
Cranch, E. T., Adler, A. A., Bending Vibration of Variable Section Beams, Journal of Applied Mechanics, 23 (1), 103-108, 1956.
Meirovitch, L., Analytical Methods in Vibrations, Macmillan Publications Co., Inc., 1967.
Gorman, D. J., Free Vibration Analysis of Beams and Shafts, Wiley: New York, 1975.
Rao, S. S., Mechanical Vibrations, Addison-Wesley Publishing Company: 3rd Edition, 1995.
Lee, J., Free Vibration Analysis of Beams with Non-Ideal Clamped Boundary Conditions, Journal of Mechanical Science and Technology, 27, 297-303, 2013.
Jategaonkar, R., Chehil, D. S., Natural Frequencies of a Beam with Varying Section Properties, Journal of Sound and Vibration, 133 (2), 303-322, 1989.
Li, X. F., Wang, B. L., Vibrational Modes of Timoshenko Beams at Small Scales, Applied Physics Letters, 94, 94-95, 2009.
Thomas, D. L., Wilson, J. M., Wilson, R. R., Timoshenko Beam Finite Elements, Journal of Sound and Vibration, 31(3), 315-330, 1973.
Dirilmiş, M., Experimental and Numerical Vibration Analysis of a Flexible Beam with Complex Cross Section Under Different Payloads, Harran University Journal of Engineering, 6(1), 55-63, 2021.
Singh, S., Singh, A., Free Vibration Analysis on Cantilever Beam – A Review, International Research Journal of Engineering and Technology, 4(2), 1449-1452, 2008.
Repetto, C., Roatta, A., Welti, R., Forced Vibrations of a Cantilever Beam, European Journal of Physics, 33, 1187-1195, 2012.
Ali, M. S., Vibration Analysis and Modelling of a Cantilever Beam, University of Engineering and Technology, 74 (3), 505-522, 2024.
Civalek, Ö., Akgöz, B., Free Vibration Analysis of Axially Functionally Graded Tapered Bernoulli–Euler Microbeams Based on the Modified Couple Stress Theory, Composite Structures, 98, 314-322, 2013.
Civalek, Ö., Demir, Ç., Akgöz, B., Free Vibration and Bending Analyses of Cantilever Microtubules Based on Nonlocal Continuum Model, Mathematical and Computational Applications, 15 (2), 3289-298, 2010.
Akgöz, B., Civalek, Ö., Ersoy, H., Numanoğlu, H. M., A New Eigenvalue Problem Solver for Thermo-Mechanical Vibration of Timoshenko Nanobeams by an Innovative Nonlocal Finite Element Method, Mathematical Methods in the Applied Sciences, 45 (5), 2592-2614, 2022.
Civalek, Ö., Akgöz, B., Free Vibration Analysis of Microtubules as Cytoskeleton Components: Nonlocal Euler-Bernoulli Beam Modeling, Scientia Iranica, 17 (5), 367-375, 2010.
Civalek, Ö., Akbaş, Ş. D., Akgöz, B., Dasjterdi, S., Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes, Nanomaterials, 11(3), 571, 2010.
Demir, C., Akgöz, B., Erdinc, M. C., Mercan, K., Civalek, Ö., Free Vibration Analysis of Graphene Sheets on Elastic Matrix, Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (2), 551-562, 2017.
Akgöz, B., Civalek, Ö., Investigation of Size Effects on Static Response of Single-Walled Carbon Nanotubes Based on Strain Gradient Elasticity, International Journal of Computational Methods, 9 (2), 1240032, 2012.
Dastjerdi, S., Malikan, M., Akgöz, B., Civalek, Ö., Wiczenbach, T., Eremeyev, VA., On the Deformation and Frequency Analyses of SARS-CoV-2 at Nanoscale, International Journal of Engineering Science, 170, 103604, 2022.
Dastjerdi, S., Akgöz, B., Civalek, Ö., On the Shell Model for Human Eye in Glaucoma Disease, International Journal of Engineering Science, 158, 103414, 2021.
Abouelregal, A.E., Akgöz, B., Civalek, Ö., Nonlocal Thermoelastic Vibration of a Solid Medium Subjected to a Pulsed Heat Flux via Caputo-Fabrizio Fractional Derivative Heat Conduction, Applied Physics A, 128 (8), 660, 2022.
Ramesh, M. N. V., Free Vibration Analysis of Rotating Functionally-Graded Cantilever Beams, International Journal of Acoustics and Vibration, 19 (1), 31-41, 2014.
Zannon, M., Free Vibration of Thin Film Cantilever Beam, International Journal of Engineering and Technical Research, 2 (11), 304-316, 2014.
Sinha, S. K., Combined Torsional-Bending-Axial Dynamics of a Twisted Rotating Cantilever Timoshenko Beam with Contact-Impact Loads at the Free End, Journal of Applied Mechanics, 74 (3), 505-522, 2007.
Cunedioğlu, Y., Devecioğlu, B., Free Vibration Analaysis of Cracked Cantilever Sandwich Beams, Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 11 (4), 1138-1145, 2022.
Arshad, U., Vibration Analysis and Modelling of a Cantilever Beam – A Complex Engineering Problem, University of Engineering and Technology Lahore; Mechanical Engineering, 2020.
Demirtaş, A., Bayraktar, M., Free Vibration Analysis of an Aircraft Wing by Considering as a Cantilever Beam, Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi, 7 (1), 12-21, 2019.
Xiaolin, C., Liu, Y., Finite Element Modeling and Simulation with ANSYS Workbench, CRC Press, 2014.
Akgöz, B., Söylemez, A.O., Deflections of Cantilever Beams Subjected to A Point Load At the Free End, International Journal of Engineering & Applied Sciences, 16 (3), 141-152, 2024.

Details

Primary Language

English

Subjects

Structural Dynamics

Journal Section

Research Article

Authors

Alper Oğulcan Söylemez
0009-0000-5352-4316
Türkiye

Bekir Akgöz ^*
0000-0003-2097-2555
Türkiye

Early Pub Date

November 26, 2025

Publication Date

November 30, 2025

Submission Date

March 11, 2025

Acceptance Date

June 30, 2025

Published in Issue

Year 2025 Volume: 17 Number: 3

DOI

https://doi.org/10.24107/ijeas.1654819

IZ

https://izlik.org/JA83UA53CM

Cite

RIS / Bibtex

APA

Söylemez, A. O., & Akgöz, B. (2025). Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation. International Journal of Engineering and Applied Sciences, 17(3), 141-157. https://doi.org/10.24107/ijeas.1654819

AMA

1.Söylemez AO, Akgöz B. Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation. IJEAS. 2025;17(3):141-157. doi:10.24107/ijeas.1654819

Chicago

Söylemez, Alper Oğulcan, and Bekir Akgöz. 2025. “Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation”. International Journal of Engineering and Applied Sciences 17 (3): 141-57. https://doi.org/10.24107/ijeas.1654819.

EndNote

Söylemez AO, Akgöz B (November 1, 2025) Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation. International Journal of Engineering and Applied Sciences 17 3 141–157.

IEEE

[1]A. O. Söylemez and B. Akgöz, “Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation”, IJEAS, vol. 17, no. 3, pp. 141–157, Nov. 2025, doi: 10.24107/ijeas.1654819.

ISNAD

Söylemez, Alper Oğulcan - Akgöz, Bekir. “Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation”. International Journal of Engineering and Applied Sciences 17/3 (November 1, 2025): 141-157. https://doi.org/10.24107/ijeas.1654819.

JAMA

1.Söylemez AO, Akgöz B. Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation. IJEAS. 2025;17:141–157.

MLA

Söylemez, Alper Oğulcan, and Bekir Akgöz. “Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation”. International Journal of Engineering and Applied Sciences, vol. 17, no. 3, Nov. 2025, pp. 141-57, doi:10.24107/ijeas.1654819.

Vancouver

1.Alper Oğulcan Söylemez, Bekir Akgöz. Free Vibration Response of Cantilever Beams by Using SolidWorks Simulation. IJEAS. 2025 Nov. 1;17(3):141-57. doi:10.24107/ijeas.1654819