Free vibration analysis of a rotating double-tapered beam using the transfer matrix method

Lee, Jung Woo

doi:10.1007/s12206-020-0605-6

Cited by 12 publications

(9 citation statements)

References 41 publications

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“…Changing the formation of equation ( 17) to a matrix form, the transfer matrix of the massless flexible axle is then obtained as given in equation (18). On this basis, if the shearing stiffness of the axle is considered, equation ( 18) will be rewritten as equation ( 19):…”

Section: Transfer Matrix Of Flexible Axle Without Massmentioning

confidence: 99%

“…erefore, equations ( 14), ( 15), (18), and (19), respectively, represent the transfer matrices of the (a) Euler-Bernoulli beam, (b) Timoshenko beam, (c) elastic beam without mass and shearing stiffness, and (d) the massless elastic beam with shearing stiffness.…”

Section: Transfer Matrix Of Flexible Axle Without Massmentioning

confidence: 99%

“…H 2 and H 4 in equation ( 23) and H 4 and H 8 in equation ( 24) refer to the matrix H w in equation (22). e other matrices can be selected uniformly within equations ( 14), ( 15), (18), and ( 19) according to different elastic beam assumptions. It should be noted that, if the wheelset symmetries are taken into account, the computational efficiency is hopeful to be improved further.…”

Section: Wheelset Bending Vibration Model Based On Transfer Matrixmentioning

confidence: 99%

“…Also, the linear vibration theory was applied to establish the flexible wheelset model with concentrated mass and moment of inertia [16]. Recently, the transfer matrix method has been widely used to solve the vibrations of pipe structure [17], tapered beam [18], masonry walls [19], and even missile systems [20]. e relevant method for flexible body vibration simulation could be introduced into the railway vehicle system and even the vehicle-track coupled model [21] or train-track dynamic model [22].…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

Liu

2021

Shock and Vibration

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The elastic vibration of the wheelset is a potential factor inducing wheel-rail defects. It is important to understand the natural vibration characteristics of the flexible wheelset for slowing down the defect growth. To estimate the elastic free vibration of the railway wheelset with the multidiameter axle, the transfer matrix method (TMM) is applied. The transfer matrices of four types of elastic beam models are derived including the Euler–Bernoulli beam, Timoshenko beam, elastic beam without mass and shearing stiffness, and massless elastic beam with shearing stiffness. For each type, the simplified model and detailed models of the flexible wheelset are developed. Both bending and torsional modes are compared with that of the finite element (FE) model. For the wheelset bending modes, if the wheel axle is modelled as the Euler–Bernoulli beam and Timoshenko beam, the natural frequencies can be reflected accurately, especially for the latter one. Due to the lower solving accuracy, the massless beam models are not applicable for the analysis of natural characteristics of the wheelset. The increase of the dividing segment number of the flexible axle is helpful to improve the modal solving accuracy, while the computation effort is almost kept in the same level. For the torsional vibration mode, it mainly depends on the axle torsional stiffness and wheel inertia rather than axle torsional inertia.

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Section: Transfer Matrix Of Flexible Axle Without Massmentioning

confidence: 99%

Section: Transfer Matrix Of Flexible Axle Without Massmentioning

confidence: 99%

Section: Wheelset Bending Vibration Model Based On Transfer Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

Liu

2021

Shock and Vibration

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Yavuz

Özkol

2021

AEAT

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Purpose This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters. Design/methodology/approach Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time. Findings The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions. Originality/value The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

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Ultra compact 2D- PhC based sharp bend splitters for terahertz applications

Geerthana¹,

Sridarshini

Balaji

et al. 2023

Opt Quant Electron

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Free vibration analysis of a rotating double-tapered beam using the transfer matrix method

Cited by 12 publications

References 41 publications

Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

Estimation of Wheelset Natural Vibration Characteristics Based on Transfer Matrix Method with Various Elastic Beam Models

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

Ultra compact 2D- PhC based sharp bend splitters for terahertz applications

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