Free vibration/buckling analyses of noncylindrical initially compressed helical composite springs

Kaçar, İlyas; Yıldırım, Vebil

doi:10.1080/15397734.2015.1066687

Cited by 23 publications

(14 citation statements)

References 72 publications

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“…1 . It may be noted that this procedure may be extended to the solution of higher-order differential equations with variable coefficients as done in some studies [35][36][37][38][39].…”

Section: Derivation Of the Governing Equationmentioning

confidence: 99%

Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs

Yıldırım

2018

J Braz. Soc. Mech. Sci. Eng.

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A substantial elastic analysis of uniform rotating discs made of radially functionally graded (FG) polar orthotropic materials is managed with both analytical and numerical methods by imposing possible boundary conditions and frequently used material grading rules such as a simple power and an exponential patterns. The complementary functions method (CFM) is originally chosen as a numerical technique to solve the governing equation having variable coefficients. Before applying CFM on the current two-point boundary value problem, the governing equation derived by the transformed onaxis in-plane stiffness terms is transformed into the initial value problem. To show the effectiveness of the method, as an additional study, some closed-form formulas are obtained to cover the rotating uniform discs made of functionally simple power-law graded polar orthotropic materials under the same constraints. It was shown that both analytical and numerical results display a perfect harmony. An extensive parametric study which considers physically or hypothetically exist different material types, several inhomogeneity indexes, anisotropy degrees varying in a wide range of 0.3-5, three types of boundary conditions, is conducted with the help of both analytical formulas and numerical solutions. To the best of the author's knowledge, although especially the anisotropy effects have been worked through for ordinary polar orthotropic materials, investigations on the anisotropy degrees on the elastic behaviour of discs made of an advanced material having varying properties along the desired directions such as a FG anisotropic material is still so limited and requires vast knowledge. Since different transformed stiffness terms through the radial direction may be developed by considering different fibre orientations, present results comprising anisotropy effects may also be interpreted as the results of such discs made of specially orthotropic materials such as cross-ply or balanced symmetrical laminates. It is mainly concluded that the use of a radially FG anisotropic material having an anisotropy degree less than the unit proposes admissible circumferential stresses along with the effective properties which continuously radially increase from the inner surface towards the outer under centrifugal forces. On the other hand, anisotropy degrees greater than the unit with increasing material properties from the inner surface to the outer mitigates the radial stresses. Negative inhomogeneity indexes with smaller anisotropy degrees are preferable to get smaller radial displacements.

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“…1 . It may be noted that this procedure may be extended to the solution of higher-order differential equations with variable coefficients as done in some studies [35][36][37][38][39].…”

Section: Derivation Of the Governing Equationmentioning

confidence: 99%

Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs

Yıldırım

2018

J Braz. Soc. Mech. Sci. Eng.

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“…Crescenzo et al [11] investigated the two-dimensional buckling behavior of uni-form helical springs using lumped stiffness. Kacar et al [12] utilized the stiffness matrices to obtain natural frequencies and buckling loads of non-uniform helical springs made of composite materials, based on first-order shear deformation theory. A geometrically exact beam theory is applied to model the dynamics of helical springs by Zhang et al [13].…”

Section: Introductionmentioning

confidence: 99%

A numerical model for investigation of dynamic behavior and free vibration of functionally graded cylindrical helical springs

Bahri

Ebrahimi

Atibeh

2021

jcc

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“…Taktak et al [5,6] also used this same finite element for the calculation of the natural frequencies and the dynamic response of a simple or assembled helical spring. Other researchers [7][8][9][10][11] have used theoretical and numerical methods for the dynamic behavior study as well as the buck-ling of coil springs. However, most of these studies are limited to the linear elastic case.…”

Section: Introductionmentioning

confidence: 99%

Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures

Boussaoui

Lahmam

Braikat

2021

Modelling and Simulation in Engineering

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In this work, we propose a high-order algorithm based on the asymptotic numerical method (ANM) for the nonlinear elastic computation of helical structures without neglecting any nonlinear term. The nonlinearity considered in the following study will be a geometric type, and the kinematics adopted in this numerical modeling takes into account the hypotheses of Timoshenko and de Saint-Venant. The finite element used in the discretization of the middle line of this structure is curvilinear with twelve degrees of freedom. Using a simple example, we show the efficiency of the algorithm which was carried out in this context and which resides in the reduction of the number of inversions of the tangent matrix compared to the incremental iterative algorithm of Newton-Raphson.

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Free vibration/buckling analyses of noncylindrical initially compressed helical composite springs

Cited by 23 publications

References 72 publications

Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs

Numerical/analytical solutions to the elastic response of arbitrarily functionally graded polar orthotropic rotating discs

A numerical model for investigation of dynamic behavior and free vibration of functionally graded cylindrical helical springs

Numerical High-Order Model for the Nonlinear Elastic Computation of Helical Structures

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