PSI - Issue 71

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ScienceDirect

Procedia Structural Integrity 71 (2025) 477–483

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of SICE 2024 organizers In the formulation, the Rayleigh-Ritz method is applied with admissible shape functions. The complication of taper is treated as a perturbation parameter over the uniform straight cantilever beam. Based on the perturbation theory and the Rayleigh-Ritz method, a closed-form formula is derived. The formula is derived as a correction due to taper over a uniform, non-rotating, straight cantilever beam. The accuracy of the formula is validated against literature and FEM simulations. Additionally, a web application is developed for practicing engineers. 1. Introduction The natural frequency of a beam is a critical parameter in structural engineering and mechanics, as it determines the frequency at which a structure or component naturally vibrates when subjected to an external force or disturbance. Understanding and analyzing the natural frequency of a beam is important for several reasons, including structural integrity and safety, dynamic analysis, vibration control and mitigation, avoiding resonance, performance optimization, and applications in aerospace and mechanical engineering. Resonance is a particularly important phenomenon, as it can lead to dynamic amplification, where small forces applied at the natural frequency of a structure can result in much larger displacements. By designing structures with 5 th International Structural Integrity Conference & Exhibition (SICE 2024) Natural Frequency of Turbomachinery Blade by Perturbation Method Ishaan Tapas, Ajinkya Baxy Department of Mechanical Engineering, Visvesvaraya National Institute of Technology Nagpur, 440033, INDIA Abstract The present work focuses on deriving a perturbation formula for determining the natural frequencies of turbo-machinery blades. The blades are modelled as tapered cantilever beams. Cantilever beams are structural elements fixed at one end and free at the other, widely used in engineering applications, including turbine blades. Accurate prediction of natural frequencies is essential for the design and analysis of these structures, as it helps in understanding their dynamic behaviour and avoiding resonance-related failures. The formulation is done using the Lagrangian approach with use of Euler-Bernoulli beam theory. The complication due to taper is the varying cross-sectional area, which is captured in potential energy and kinetic energy. Keywords: Perturbation method, Rayleigh-Ritz method, Tapered beam, Dynamics, Lagrangian formulation

* Corresponding author: ishaan.tapas1310@gmail.com

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of SICE 2024 organizers 10.1016/j.prostr.2025.08.064