| Autor: |
Ike, C. |
| Předmět: |
|
| Zdroj: |
Nigerian Journal of Technology; Sep2024, Vol. 43 Issue 3, p421-427, 7p |
| Abstrakt: |
This study presents analytical solutions using the finite sine transformation methodology (FSTM) for the natural dynamic solutions of thick beams. The Euler-Bernoulli beam theory (EBBT) disregards the contributions of transverse shear strains due to the Euler-Bernoulli-Navier orthogonality hypothesis used in its formulation and is unsuitable for thick beams. It derived a variational formulation of flexural vibration equations of sinusoidal shear deformable beams using first principles approach. The governing equation is formulated for transverse dynamic loading and in-plane compressive force as a non-homogeneous partial differential equation (PDE). The PDE did not need shear correction factors. The formulation yielded a cosine function shaped transverse shear strain and stress distribution which was maximum at the neutral axis and vanished at the beam surfaces. The PDE was solved for free flexural vibration where it became homogeneous due to the absence of forcing excitation forces. The FSTM was used for solving simply supported beams since sinusoidal kernel complies with end conditions. The problem simplifies for harmonic excitation to an algebraic eigenvalue problem solvable using algebraic methods. The roots are utilized to compute modal vibrations and the resonant vibration frequency at the first mode, (n = 1). The resonant frequencies obtained are identical with past results that used theory of elasticity technique. The results for the first five vibration modes are also close to previous results obtained thick beam models for all modes and aspect ratios considered. The effectiveness of the FSTM and its accuracy has been demonstrated for simply supported thick beam vibration problems. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
