Vibration analysis of rotating Timoshenko beams by means of the differential quadrature method

Abstract

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering.The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

Free Vibration Analysis of Centrifugally Stiffened Non Uniform Timoshenko Beams

“…(Bambill et al, 2010). The finite element model employed in the analysis has 3000 beam elements of two nodes in the longitudinal direction (Rossi, 2007).…”

“…Not so many studies have tackled the problem of rotating beams taking into account rotary inertia, shear deformation and their combined effects, hub radius and ends elastically restrained, (Bambill et al, 2010). In applications where the rotary inertia and the shear deformation effects are not significant, an analysis based on the Euler-Bernoulli beam theory can be used.…”

Forced vibration analysis of damped beam structures with composite cross-section using Timoshenko beam element

“…On the other hand, Fig. 1(b) shows an equivalent single-layer finite element model for the current study, which is based upon the Timoshenko beam theory (Timoshenko 1955, Bambill et al 2010. Where, the reference axis and the superscript (•) * indicate the neutral axis of the damped structure and the complex values respectively, and the elastic constants ρ, G * and are the equivalent Fig.…”

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.…”