Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method

Adair, Desmond; Jaeger, Martin

doi:10.1016/j.apm.2015.09.097

Cited by 33 publications

(16 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…e terms in equation (23) are linear except for the nonlinear Fredholm integral coefficient shown in equation (24). Before continuing with the main solution method, the nonlinear term will be treated first through the use of appropriate Cauchy products.…”

Section: Nonlinear Fredholm Integral Coefficientmentioning

confidence: 99%

“…In the present work, the adomian modified decomposition method [21,22] is utilized to calculate free transverse vibration characteristics of axially loaded Euler-Bernoulli beams with various end restrains, resting on a Winkler one-parameter foundation. e method is chosen as it has proved efficient and accurate [23,24] for solving linear and nonlinear differential equations, and it has the advantage of computational simplicity. In addition, it does not involve linearization, discretization, perturbation, or a priori assumptions, which may alter the physics of the problem considered [21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method

Adair

Ibrayev

Tazabekova

et al. 2019

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Nonlinear Fredholm Integral Coefficientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method

Adair

Ibrayev

Tazabekova

et al. 2019

Shock and Vibration

Self Cite

View full text Add to dashboard Cite

show abstract

“…Also, the dynamics of rotating tapered hollow beams is of practical significant, for example, rotating tank gun barrel (hollow circular cross-section). As pointed out in [1], in dynamical analysis, a rotating beam differs from a nonrotating beam because it also possesses centrifugal stiffness and Coriolis effects that influence its dynamical characteristics. Besides the above effects, there are some complicated factors, including the secondary coupling deformation term, coupling effect, and the variable coefficient differential equation.…”

Section: Introductionmentioning

confidence: 99%

“…Ghafari and Rezaeepazhand [20] presented free vibration analysis of rotating composite beams with arbitrary cross-section using dimensional reduction method. Adair and Jaeger [1] used the computational approach of AMDM to analyze the free vibration of nonuniform Euler-Bernoulli beams under various boundary conditions, rotation speeds, and hub radii and simultaneously obtained the natural frequencies and corresponding closed-form series solution of the mode shape. Panchore and Ganguli [21] studied the free vibration problem of a rotating Rayleigh beam using the quadratic B-spline finite element method.…”

Section: Introductionmentioning

confidence: 99%

Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross‐Section

Wang

2018

Shock and Vibration

View full text Add to dashboard Cite

Problems related to the transverse vibration of a rotating tapered cantilever beam with hollow circular cross-section are addressed, in which the inner radius of cross-section is constant and the outer radius changes linearly along the beam axis. First, considering the geometry parameters of the varying cross-sectional beam, rotary inertia, and the secondary coupling deformation term, the differential equation of motion for the transverse vibration of rotating tapered beam with solid and hollow circular cross-section is derived by Hamilton variational principle, which includes some complex variable coefficient terms. Next, dimensionless parameters and variables are introduced for the differential equation and boundary conditions, and the differential quadrature method (DQM) is employed to solve this differential equation with variable coefficients. Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. Finally, for rotating solid tapered beams, comparisons with previously reported results demonstrate that the results obtained by the present method are in close agreement; for rotating tapered hollow beams, the effects of the hub dimensionless angular speed, ratios of hub radius to beam length, the slenderness ratio, the ratio of inner radius to the root radius, and taper ratio of cross-section on the first three-order dimensionless natural frequencies are more further depicted.

show abstract

“…Specific to this work, the Adomain decomposition and Adomian modified decomposition method have been used by several groups [14,15] for uniform and non-uniform beams, starting with either the Euler-Bernoulli or Timoshenko formulations. Mao [14] applied the AMDM to rotating uniform beams and included a centrifugal stiffening term while Adair and Jaeger [15] applied the AMDM to rotating non-uniform beams which also included a centrifugal stiffening term. Yaman [16] has used the Adomian decomposition method to investigate the influence of the orientation effect on the natural frequency of a cantilever beam carrying a tip mass.…”

mentioning

confidence: 99%

Simulation of the vibrations of a non-uniform beam loaded with both a transversely and axially eccentric tip mass

Adair¹,

Jaeger²

2017

Int. J. CMEM

Self Cite

View full text Add to dashboard Cite

The main purpose of this work is to employ the Adomian modified decomposition method (AMDM) to calculate free transverse vibrations of non-uniform cantilever beams carrying a transversely and axially eccentric tip mass. The effects of the variable axial force are taken into account here, and Hamilton's principle and Timoshenko beam theory are used to obtain a single governing non-linear partial differential equation of the system as well as the appropriate boundary conditions. Two product non-linearities result from the analysis and the respective Cauchy products are computed using Adomian polynomials. The use of AMDM to make calculations for such a cantilever beam/tip mass arrangement has not, to the authors' knowledge, been used before. The obtained analytical results are compared with numerical calculations reported in the literature and good agreement is observed. The qualitative and quantitative knowledge gained from this research is expected to enable the study of the effects of an eccentric tip mass and beam non-uniformity on the vibration of beams for improved dynamic performance.

show abstract

Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method

Cited by 33 publications

References 33 publications

Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method

Free Vibrations with Large Amplitude of Axially Loaded Beams on an Elastic Foundation Using the Adomian Modified Decomposition Method

Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross‐Section

Simulation of the vibrations of a non-uniform beam loaded with both a transversely and axially eccentric tip mass

Contact Info

Product

Resources

About