Free Vibrations of Spinning Beams Under Nonclassical Boundary Conditions Using Adomian Modified Decomposition Method

Abstract

This study employs the Adomian modi¯ed decomposition method (AMDM) for the dynamic analysis of Euler-Bernoulli beams spinning about their longitudinal axes under various boundary conditions. Based on the AMDM, the governing di®erential equations for the spinning beam become a recursive algebraic equation system. By using the boundary condition equations, the natural frequencies can be readily obtained. The computed results under di®erent classical and nonclassical boundary conditions as well as spinning speeds are presented. The accuracy is assured from comparison with published results. It is shown that the AMDM o®ers an accurate and straightforward method of free vibration analysis of spinning beams with arbitrary boundary conditions.

Vibration characteristics of rotating functionally graded porous beams reinforced by graphene platelets

“…The earliest study on vibration characteristics of the rotating beam was reported by Southwell and Gough [1]. After that, many related works [2][3][4][5][6][7][8][9][10] in a variety of methods were published.…”

Free vibration analysis of a rotating double tapered beam with flexible root via differential quadrature method

“…One of the extensively studied topics is free vibration analysis or the computation of dynamic characteristics, which is a critical design and performance evaluation criteria designating the life of structure, operating limits and stability. Therefore, numerous numerical methods such as Adomian decomposition (Adair and Jaeger, 2018a, 2018b; Mao, 2014), differential transformation (Mei, 2008; Nourifar et al , 2018; Kaya, 2006; Kumar et al , 2019; Kurt and Kaya, 2019; Ozdemir and Kaya, 2006a, 2006b; Rajasekaran, 2013), differential quadrature (Bambill et al , 2010; Choi et al , 1999), dynamic stiffness (Banerjee et al , 2006; Banerjee and Kennedy, 2014), finite element (Abbas, 1986; Chung and Yoo, 2002; Hoa, 1979; Hodges and Rutkowski, 1981; Wang and Werely, 2004), Fourier series (Chen and Du, 2019), mesh free Galerkin (Panchore et al , 2018), power series (Adair and Jaeger, 2018a, 2018b; Huang et al , 2010), Rayleigh-Ritz (Oh and Yoo, 2016; Ramesh and Rao, 2014; Roy and Meguid, 2018), Ritz (Navazi et al , 2017), transfer matrix (Lee and Lee, 2018, 2020; Rui et al , 2018) and variational iteration (Chen et al , 2016) have been used to avoid possible resonance cases by computing the dynamic characteristics of rotating-beam structures more accurately.…”

Free vibration analysis of partially connected parallel beams with elastically restrained ends

“…Therefore, many techniques applied by researchers for this purpose, such as finite element method, 12,13 differential quadrature method, 14,15 discrete singular convolution method, 16,17 and so on. 18–23 Among these methods, the differential transform method (DTM) is a relatively new one. The DTM does not needs to domain discretizing and mode shape obtained by DTM is a continuous function and not discrete numerical values at knot point by mesh discrete technique.…”