Stability of a Timoshenko beam resting on a Winkler elastic foundation

Lee, Sen-Yung; Kuo, Yau‐Hwang; Lin, Feng-Heui

doi:10.1016/s0022-460x(05)80001-x

Cited by 36 publications

(7 citation statements)

References 25 publications

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“…All six combinations of the classical end conditions are considered. The present paper complements many papers that have been written on this subject (Lee et al 1992, Wang and Stephens 1977, Naidu and Rao 1995, Shirima and Giger 1992, Rosa 1995and Razaqpor and Shah 1991, by giving a comprehensive and unified treatment of the aforementioned beam problems and by providing exact solutions in a canonical form. It is hoped that the paper will serve as a useful reference source of exact beam solutions to researchers and academicians working on Timoshenko beam problems that are of fundamental and practical importance.…”

Section: Introductionmentioning

confidence: 75%

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Green’s Functions for Timoshenko Beam Problems

Wang¹,

Lam²,

He³

1997

ASME 1997 Turbo Asia Conference

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In this paper, a unified formulation is given for the bending, buckling and vibration problems of uniform Timoshenko and Euler-Bernoulli beams resting on various models of elastic foundation. Canonical Green's functions have been derived for these beams which can be readily used to furnish exact solutions. In addition to elucidating the behaviour of the beams, the exact solutions serve as important benchmark results for checking the convergence and accuracy of various solutions obtained from numerical methods.

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Section: Introductionmentioning

confidence: 75%

“…1. The various models of elastic foundation considered are described below: • Winkler foundation (Lee et al 1992) having a modulus K,. • Pasternak foundation (Wang andStephens 1977 andNaidu andRao 1995) having the foundation moduli K, and K,.…”

Section: Problem Formulationmentioning

confidence: 99%

Green’s Functions for Timoshenko Beam Problems

Wang¹,

Lam²,

He³

1997

ASME 1997 Turbo Asia Conference

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“…The interaction of the beam with the stoppers is modelled as a contact interaction of the beam with a Winkler's foundation [18] with a spring constant k w , i.e. the reaction force which arise when the moving beam reaches a stopper is:…”

Section: Electro-mechanical Couplingmentioning

confidence: 99%

Vibration energy harvesting by a Timoshenko beam model and piezoelectric transducer

Stoykov

Litak

Manoach

2015

Eur. Phys. J. Spec. Top.

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Abstract. An electro-mechanical system of vibrational energy harvesting is studied. The beam is excited by external and kinematic periodic forces and damped by an electrical resistor through the coupled piezoelectric transducer. Nonlinearities are introduced by stoppers limiting the transverse displacements of the beam. The interaction between the beam and the stoppers is modeled as Winkler elastic foundation. The mechanical properties of the piezoelectric layer are taken into account and the beam is modeled as a composite structure. For the examined composite beam, the geometrically nonlinear version of the Timoshenko's beam theory is assumed. The equations of motion are derived by the principle of virtual work considering large deflections. An isogeometric approach is applied for space discretization and B-Splines are used as shape functions. Finally, the power output and the efficiency of the system due to harmonic excitations are discussed. The influence of the position of the stoppers and their length on the dynamics of the beam and consequently on the power output are analyzed and presented.

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“…Up to the present, considerable research efforts have been made for the dynamic stability problems under the non-conservative forces by using various approaches such as the Galerkin method (Leipholz, 1980;Elishakoff and Hollkamp, 1987;Levincon, 1966;Rao and Rao, 1975), the transfer matrix approach (Lee and Yang, 1994;Irie et al, 1980;Takahashi, 1999;Takahashi and Yoshioka, 1996), the integral equation formulation (Elfelsoufi and Azrar, 2005;2006), the finite difference method (Rao and Rao, 1990a;1990b;1988), the assumed mode method (Lee, 1996a;1996b;1995a;1995b), and many other forms of discretization methods (Lee et al, 1992;De Rosa and Franciosi, 1990). Amongst the analytical or numerical methods available for the dynamic stability problems, the finite element method seems to be undoubtedly the most versatile, accordingly a large amount of works (Lee et al, 2007;Ryu et al, 1998;Kim and Choo, 1998;Saje and Jelenic, 1994;Del Giudice et al, 1992) were devoted to the technical improvement of the finite elements.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability analysis for Beck’s type of inelastic Timoshenko steel columns

2015

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In this study, the dynamic stability analysis of a Beck's type of steel column subjected to a sub-tangential follower force is presented considering the effects of gradual yielding along the length of column, the shear deformation, and the rotary inertia. The nonlinear tangent modulus-stress, tangent modulus-slenderness ratio, and compressive stress-strain relationships of an inelastic column are derived from the column strength curve given in Korea Bridge Design Code (KBDC) based on the tangent modulus theory. The equations of motion of the Timoshenko inelastic column are derived from the Hamilton's principle. The finite element method using the Hermite cubic interpolation functions is employed to obtain the mass, inelastic stiffness, geometric stiffness, and load correction matrices, and the evaluation procedure for critical values of divergence and flutter of the non-conservative system is briefly described. The obtained results are compared with available results of other numerical or analytical methods. Finally, the effects of various structural parameters such as the material inelasticity, the shear deformation, the rotary inertia, the effective length factor, and the sub-tangentiality factor on the divergence and flutter behavior of non-conservative columns are parametrically investigated.

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Stability of a Timoshenko beam resting on a Winkler elastic foundation

Cited by 36 publications

References 25 publications

Green’s Functions for Timoshenko Beam Problems

Green’s Functions for Timoshenko Beam Problems

Vibration energy harvesting by a Timoshenko beam model and piezoelectric transducer

Dynamic stability analysis for Beck’s type of inelastic Timoshenko steel columns

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