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Authors

Muhammad Mubashir*
Sarfraz Shoukat
Anas Asim
Ahmed Kadhim Zarzoor
Rayyan Qaisar
Naji Ullah
Abdul Ghaffar
Muhammad Shoaib-Ur-Rehman

Abstract

The study of dynamic response of structural members is of great importance in aerospace design where the structural members such as wing spars should not resonate for ensuring the flight safety and structural integrity. Although a lot of research has been conducted on vibration of beams, a comprehensive comparison between metallic and composite cantilever beam and its application to aerospace-related cross-sections has so far not been done. The proposed study is focused on analytical formulations, Rayleigh-Ritz variational approach and finite element analysis (FEA) to systematically evaluate and compare modal characteristics of Aluminum and graphite-epoxy cantilever beam with three geometries T-shape, I-shape and rectangular shape. The closed-form Euler-Bernoulli beam equations and Rayleigh-Ritz approximations was implemented with the help of MATLAB and ANSYS mode-shape contours for the first three bending modes were used for visual validation of the numerical work. The results show very good consistency in the determination of the first bending mode among three implemented methods but for higher order modes variational method show the deviation of 12% in frequency magnitude as compared to analytical and FEA techniques. Among the three tested configurations (I-shape, Rectangular and T-shape), I-shape beam shows higher frequency because of its greater bending stiffness (I/A) as compared to other shapes. Material comparison further highlighted that composite beam shows higher frequency as compare to metallic because of its higher specific modulus (E⁄ρ). Overall, even some minor variations were observed among the results for three methods, but still all three approaches predicted the same trends for frequency, which proves that the applied methodology and MATLAB codes developed for current research work can be implemented as an application of frequency estimation for aerospace structural components.

Keywords:
Rayleigh-Ritz method, modal analysis, aerospace spars, graphite-epoxy composites, T-beam vibration

Article Details

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