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How to cite this paper
APA: Kazemi, A., Nadi, A., Moradi, M., Tahmoorian, F & Beiranvand, P. (2024). RETRACTED: Using the method of differential equations by quadratic to solve the free vibrations of columns under the effect of axial load and column weight. Engineering Solid Mechanics, 12(3), 269-282.
Chicago/Turabian: Kazemi, A., Nadi, A., Moradi, M., Tahmoorian, F & Beiranvand, P. 2024. "RETRACTED: Using the method of differential equations by quadratic to solve the free vibrations of columns under the effect of axial load and column weight." Engineering Solid Mechanics 12, no. 3 (2024): 269-282.
AMA: Kazemi, A., Nadi, A., Moradi, M., Tahmoorian, F & Beiranvand, P. RETRACTED: Using the method of differential equations by quadratic to solve the free vibrations of columns under the effect of axial load and column weight. Engineering Solid Mechanics. 2024;12(3):269-282.
References
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Hosseini, M., Ashrafi, H. R., Beiranvand, P., & Omidi, M. (2014). Comparing numerical methods in solving differential equations of columns buckling for determining critical load and concluding in analysis accuracy. International Journal of Scientific Research in Knowledge, 2(Special Issue), 88-93.
Lee, J., & Schultz, W. W. (2004). Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudo spectral method. Journal of Sound and Vibration, 269(3-5), 609-621.
Mahmoud, A. A., Awadalla, R., & Nassar, M. M. (2011). Free vibration of non-uniform column using DQM. Mechanics Research Communications, 38(6), 443-448.
Motaghian, S. E., Mofid, M., & Akin, J. E. (2018). A new Fourier series solution for free vibration of non-uniform beams, resting on variable elastic foundation. Scientia Iranica, 25(6), 2967-2979.
Okay, F., Atay, M. T., & Coskun, S. B. (2010). Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 11(10), 851-857.
Taha, M., & Essam, M. (2013). Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method. Ain Shams Engineering Journal, 4(3), 515-521.
Torabi, K & Afshari, H. (2017). Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness. Engineering Solid Mechanics, 5(1), 71-92.
Wen, H. B., Zeng, T., & Hu, G. Z. (2017). Application of Laplace Transform to the free vibration of continuous beams. Archives of Civil Engineering, 63(1), 163-180.
Yagci, B., Filiz, S., Romero, L. L., & Ozdoganlar, O. B. (2009). A spectral-Tchebychev technique for solving linear and nonlinear beam equations. Journal of Sound and Vibration, 321(1-2), 375-404.
Yokoyama, T. (1990). Vibrations of a hanging Timoshenko beam under gravity. Journal of Sound and Vibration, 141(2), 245-258.
Hosseini, M., Ashrafi, H. R., Beiranvand, P., & Omidi, M. (2014). Comparing numerical methods in solving differential equations of columns buckling for determining critical load and concluding in analysis accuracy. International Journal of Scientific Research in Knowledge, 2(Special Issue), 88-93.
Lee, J., & Schultz, W. W. (2004). Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudo spectral method. Journal of Sound and Vibration, 269(3-5), 609-621.
Mahmoud, A. A., Awadalla, R., & Nassar, M. M. (2011). Free vibration of non-uniform column using DQM. Mechanics Research Communications, 38(6), 443-448.
Motaghian, S. E., Mofid, M., & Akin, J. E. (2018). A new Fourier series solution for free vibration of non-uniform beams, resting on variable elastic foundation. Scientia Iranica, 25(6), 2967-2979.
Okay, F., Atay, M. T., & Coskun, S. B. (2010). Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method. International Journal of Nonlinear Sciences and Numerical Simulation, 11(10), 851-857.
Taha, M., & Essam, M. (2013). Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method. Ain Shams Engineering Journal, 4(3), 515-521.
Torabi, K & Afshari, H. (2017). Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness. Engineering Solid Mechanics, 5(1), 71-92.
Wen, H. B., Zeng, T., & Hu, G. Z. (2017). Application of Laplace Transform to the free vibration of continuous beams. Archives of Civil Engineering, 63(1), 163-180.
Yagci, B., Filiz, S., Romero, L. L., & Ozdoganlar, O. B. (2009). A spectral-Tchebychev technique for solving linear and nonlinear beam equations. Journal of Sound and Vibration, 321(1-2), 375-404.
Yokoyama, T. (1990). Vibrations of a hanging Timoshenko beam under gravity. Journal of Sound and Vibration, 141(2), 245-258.