Nonlinear vibration analysis of cantilever beams: Analytical, numerical and experimental perspectives

Qamar Abbas; Rab Nawaz; Haseeb Yaqoob; Hafiz Muhammad Ali; Muhammad Musaddiq Jamil

doi:10.1016/j.padiff.2025.101115

Nonlinear vibration analysis of cantilever beams: Analytical, numerical and experimental perspectives

Qamar Abbas
, Rab Nawaz
, Haseeb Yaqoob
, Hafiz Muhammad Ali^*
, Muhammad Musaddiq Jamil

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

This study investigates the vibrational behavior of a mild steel cantilever beam with and without an attached end mass using experimental, numerical, analytical, and computational methods. Vibrational frequencies were determined using LABVIEW, MATLAB, and SOLIDWORKS, with analytical results derived from Euler-Bernoulli beam (EBB) theory. Experimental results closely matched MATLAB simulations, with an average percentage error of 1.44%, but showed a 14.44% deviation from analytical results due to neglected accelerometer mass. Findings highlight the importance of precise modeling, accounting for factors like damping and mass effects, to achieve accurate results. The study underscores the significance of resonant frequency identification in mitigating vibration failures in engineering systems.

Original language	English
Article number	101115
Journal	Partial Differential Equations in Applied Mathematics
Volume	13
DOIs	https://doi.org/10.1016/j.padiff.2025.101115
State	Published - Mar 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Keywords

Analytical
Cantilever beams
Experimental
Nonlinear vibration analysis
Numerical

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.padiff.2025.101115

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@article{58f95a9842cd484ba308faa3ff0e7be5,

title = "Nonlinear vibration analysis of cantilever beams: Analytical, numerical and experimental perspectives",

abstract = "This study investigates the vibrational behavior of a mild steel cantilever beam with and without an attached end mass using experimental, numerical, analytical, and computational methods. Vibrational frequencies were determined using LABVIEW, MATLAB, and SOLIDWORKS, with analytical results derived from Euler-Bernoulli beam (EBB) theory. Experimental results closely matched MATLAB simulations, with an average percentage error of 1.44\%, but showed a 14.44\% deviation from analytical results due to neglected accelerometer mass. Findings highlight the importance of precise modeling, accounting for factors like damping and mass effects, to achieve accurate results. The study underscores the significance of resonant frequency identification in mitigating vibration failures in engineering systems.",

keywords = "Analytical, Cantilever beams, Experimental, Nonlinear vibration analysis, Numerical",

author = "Qamar Abbas and Rab Nawaz and Haseeb Yaqoob and Ali, \{Hafiz Muhammad\} and Jamil, \{Muhammad Musaddiq\}",

note = "Publisher Copyright: {\textcopyright} 2025 The Author(s)",

year = "2025",

month = mar,

doi = "10.1016/j.padiff.2025.101115",

language = "English",

volume = "13",

journal = "Partial Differential Equations in Applied Mathematics",

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publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Nonlinear vibration analysis of cantilever beams

T2 - Analytical, numerical and experimental perspectives

AU - Abbas, Qamar

AU - Nawaz, Rab

AU - Yaqoob, Haseeb

AU - Ali, Hafiz Muhammad

AU - Jamil, Muhammad Musaddiq

PY - 2025/3

Y1 - 2025/3

N2 - This study investigates the vibrational behavior of a mild steel cantilever beam with and without an attached end mass using experimental, numerical, analytical, and computational methods. Vibrational frequencies were determined using LABVIEW, MATLAB, and SOLIDWORKS, with analytical results derived from Euler-Bernoulli beam (EBB) theory. Experimental results closely matched MATLAB simulations, with an average percentage error of 1.44%, but showed a 14.44% deviation from analytical results due to neglected accelerometer mass. Findings highlight the importance of precise modeling, accounting for factors like damping and mass effects, to achieve accurate results. The study underscores the significance of resonant frequency identification in mitigating vibration failures in engineering systems.

AB - This study investigates the vibrational behavior of a mild steel cantilever beam with and without an attached end mass using experimental, numerical, analytical, and computational methods. Vibrational frequencies were determined using LABVIEW, MATLAB, and SOLIDWORKS, with analytical results derived from Euler-Bernoulli beam (EBB) theory. Experimental results closely matched MATLAB simulations, with an average percentage error of 1.44%, but showed a 14.44% deviation from analytical results due to neglected accelerometer mass. Findings highlight the importance of precise modeling, accounting for factors like damping and mass effects, to achieve accurate results. The study underscores the significance of resonant frequency identification in mitigating vibration failures in engineering systems.

KW - Analytical

KW - Cantilever beams

KW - Experimental

KW - Nonlinear vibration analysis

KW - Numerical

UR - https://www.scopus.com/pages/publications/85217040636

U2 - 10.1016/j.padiff.2025.101115

DO - 10.1016/j.padiff.2025.101115

M3 - Article

AN - SCOPUS:85217040636

SN - 2666-8181

VL - 13

JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

M1 - 101115

ER -

Nonlinear vibration analysis of cantilever beams: Analytical, numerical and experimental perspectives

Abstract

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Keywords

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