TY - JOUR
T1 - Free vibrations with large amplitude of axially loaded beams on an elastic foundation using the Adomian modified decomposition method
AU - Adair, Desmond
AU - Ibrayev, Askar
AU - Tazabekova, Alima
AU - Kim, Jong R.
N1 - Funding Information:
This investigation was supported by Nazarbayev University Small Competitive Grant no. 090118FD5317 and ORAU Grant no. SOE2017003.
Funding Information:
)is investigation was supported by Nazarbayev University Small Competitive Grant no. 090118FD5317 and ORAU Grant no. SOE2017003.
Publisher Copyright:
© 2019 Desmond Adair et al.
PY - 2019
Y1 - 2019
N2 - Analytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation to become a recursive algebraic equation, and, after some additional simple mathematical operations, the equations can be cast as an eigenvector problem whose solution results in the calculation of natural frequencies and corresponding closed-form series solution of the mode shapes. Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. In addition to the calculation of natural frequencies and mode shapes, investigations are made of the effects on the free vibrations of the Winkler parameter and of increasing the axial loading.
AB - Analytical solutions describing free transverse vibrations with large amplitude of axially loaded Euler–Bernoulli beams for various end restrains resting on a Winkler one-parameter foundation are obtained using the Adomian modified decomposition method (AMDM). The AMDM allows the governing equation to become a recursive algebraic equation, and, after some additional simple mathematical operations, the equations can be cast as an eigenvector problem whose solution results in the calculation of natural frequencies and corresponding closed-form series solution of the mode shapes. Important to the use of the Adomian modified decomposition method is the treatment of the nonlinear Fredholm integral coefficient, which forms part of the governing equation. In addition to the calculation of natural frequencies and mode shapes, investigations are made of the effects on the free vibrations of the Winkler parameter and of increasing the axial loading.
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U2 - 10.1155/2019/3405075
DO - 10.1155/2019/3405075
M3 - Article
AN - SCOPUS:85062861436
SN - 1070-9622
VL - 2019
JO - Shock and Vibration
JF - Shock and Vibration
M1 - 3405075
ER -