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<p>Tapered beams are widely employed in aerospace, marine, and other transportation structures due to their superior high-frequency damping characteristics. Accurate analysis of their high-frequency dynamic response is crucial for effective structural design. Energy finite element analysis (EFEA) has been proven to be a powerful tool for predicting high-frequency dynamic responses. However, the existing EFEA models for tapered beams (Euler-EFEA) are predominantly based on Euler–Bernoulli beam theory, which neglects shear deformation, and their accuracy can be decreased for structures with a small slenderness ratio under high-frequency excitation. This study develops an enhanced EFEA model for tapered beams based on Timoshenko beam theory (Timoshenko-EFEA), which accounts for both bending and shear effects. The governing equations are formulated using energy density as the primary variable and are solved through the FEA. To validate the proposed model, the dynamic response of a tapered beam with a small slenderness ratio subjected to high-frequency excitation is computed using both the Timoshenko-EFEA formulation and conventional FEA with dense meshes. The close agreement confirms the accuracy and reliability of the Timoshenko-EFEA model. Furthermore, to identify the suitable application fields of Euler–EFEA and Timoshenko models, comparative analyses are performed between the Timoshenko-EFEA and Euler-EFEA models under various excitation conditions, slenderness ratios, and taper parameter&#xa0;<i>m</i>. The findings underscore the critical role of shear deformation in high-frequency dynamic modeling of tapered beams.</p>

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Timoshenko-EFEA model for tapered beams and its application

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Miaoxia Xie,
  • Hongtao Ou,
  • Jiaqi Sun,
  • Shihao Zhang,
  • Ling Li,
  • Lixia Li

摘要

Tapered beams are widely employed in aerospace, marine, and other transportation structures due to their superior high-frequency damping characteristics. Accurate analysis of their high-frequency dynamic response is crucial for effective structural design. Energy finite element analysis (EFEA) has been proven to be a powerful tool for predicting high-frequency dynamic responses. However, the existing EFEA models for tapered beams (Euler-EFEA) are predominantly based on Euler–Bernoulli beam theory, which neglects shear deformation, and their accuracy can be decreased for structures with a small slenderness ratio under high-frequency excitation. This study develops an enhanced EFEA model for tapered beams based on Timoshenko beam theory (Timoshenko-EFEA), which accounts for both bending and shear effects. The governing equations are formulated using energy density as the primary variable and are solved through the FEA. To validate the proposed model, the dynamic response of a tapered beam with a small slenderness ratio subjected to high-frequency excitation is computed using both the Timoshenko-EFEA formulation and conventional FEA with dense meshes. The close agreement confirms the accuracy and reliability of the Timoshenko-EFEA model. Furthermore, to identify the suitable application fields of Euler–EFEA and Timoshenko models, comparative analyses are performed between the Timoshenko-EFEA and Euler-EFEA models under various excitation conditions, slenderness ratios, and taper parameter m. The findings underscore the critical role of shear deformation in high-frequency dynamic modeling of tapered beams.