Free vibration analysis of an embarked rotating composite shaft using the hp-version of the FEM

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This paper presents the vibratory behavior of a spinning composite shaft with curvilinear fibers on rigid bearings in the case of free vibrations. A p-version of finite element is used to define the model. A theoretical study allows the establishment of the kinetic energy and the strain energy of the shaft, necessary to the result of the equations of motion. In this model the transverse shear deformation, rotary inertia and gyroscopic effects have been incorporated. A hierarchical beam finite element with six degrees of freedom per node is developed and employed to find the natural frequencies of a spinning composite shaft with variable stiffness (curvilinear fibers). A computer code is elaborate for calculating the natural-frequencies for various rotating speeds of the composite shafts with curvilinear fibers. In the absence of publications of vibration analysis of rotating composite shafts with curvilinear fibers, the formulation is verified by comparisons with published data on rotating composite shafts reinforced by straight fibers. The influence of the physical, geometrical parameters, the boundary conditions and the curvilinear fiber paths on the first natural frequencies of the spinning composite shafts is studied by plotting various Campbell diagrams.

“…It is noted, if ratio L/D increases the first natural frequencies decreases and vice versa. For more details you can see our publication (Boukhalfa and Hadjoui, 2010).…”

Section: Influence Of the Stacking Sequence On The Natural Frequenciesmentioning

confidence: 99%

Campbell Diagrams of a Spinning Composite Shaft with Curvilinear Fibers

Boukhalfa

2017

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“…To study their behavior it is therefore important to design methods for the numerical solutions of these partial differential equations. In this respect, recently some approximate analytical techniques (see for instance, Bayat et al, 2010;Baghari et al, 2014;Jafari et al, 2014;Bayat et al, 2011;, Ganji, 2012;He, 1999;He, 2006;Khan et al, 2012;Liu and Gurram, 2009;Mirgolbabaei et al, 2010;Sfahani et al, 2011) as well as numerical methods by Lai et al (2008) (see also, Boukhalfa et al, 2010 Ganji et al, 2011) and references therein, have been proposed to investigate the nonlinear vibrations of beams for designing and fabrication purpose.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

Khan

Kaneez

2017

In this paper, we present a new numerical method for nonlinear vibrational analysis of Euler-Bernoulli beams. Our approach is based on the continuous Galerkin-Petrov time discretization method. The Euler-Bernoulli beam equation which governs its vibrations is transformed into set of ordinary differential equations and the presented method is employed in order to investigate the vibrational response. A comparison is made between present method and different other methods available in literature. It is observed that the obtained results are in strong agreement with other results in literature. We conclude that the present method has a great potential to deal with nonlinear vibration analysis problems of beams and related structures like rods and shafts.

“…The vibration problems of uniform Euler-Bernoulli beams can be solved by analytical or approximate approaches. In this respect, several methods have been developed recently for finding approximate solutions to nonlinear problems; see (Boukhalfa and Hadjoui, 2010;Da Silva et al, 2009;He, 2006;Ganji et al, 2011;Ganji, 2012;Bayat et al, 2011;Khan et al, 2012;Nikkar et al, 2012;Ghasempoor et al, 2102;Ghotbi et al, 2012;Fereidoon et al, 2010) and the references therein. Lai et al (2008) utilized Adomian Decomposition Method to obtain the natural frequencies and mode shapes for the Euler-Bernoulli beam under various supporting conditions.…”

Section: Introductionmentioning

confidence: 99%

Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

Bagheri

Nikkar

Ghaffarzadeh

2014

In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He's Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.