The Dynamic Stiffness Matrix Method in Forced Vibration Analysis of Multiple-Cracked Beam

Khiem, Nguyen Tien; Lien, Tran Van

doi:10.1006/jsvi.2001.4109

Cited by 41 publications

(17 citation statements)

References 17 publications

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“…This elegant concept has led to the so -called dynamic stiffness method (DSM) (N.T. Khiem, T.V.Lien 2002;H.Su, J.R. Banerjee 2015;N.T.Khiem, N.D.Kien, N.N. Huyen 2014;T.V.…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 17mentioning

confidence: 99%

Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

Tran

Ngo²,

Khiem

2017

Lat. Am. j. solids struct.

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In this paper, authors present the study of free vibration of bending multiple cracked functionally graded material (FGM) beam. Vibration equations of multiple cracked FGM beam were established by using the rotational spring model of cracks, dynamic stiffness method (DSM) and actual position of neutral plane. The frequency equation obtained was in a simple form, that provides an effective approach to study not only free vibration of the beams but also inverse problems like identification of material and crack parameters in structure. The obtained numerical results show good agreement with other previous published results. Thence, numerical computation has been carried out to investigate the effect of each crack, the number of cracks, material and geometric parameters on the natural frequencies of multiple cracked Timoshenko FGM beams.

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“…This elegant concept has led to the so -called dynamic stiffness method (DSM) (N.T. Khiem, T.V.Lien 2002;H.Su, J.R. Banerjee 2015;N.T.Khiem, N.D.Kien, N.N. Huyen 2014;T.V.…”

Section: Latin American Journal Of Solids and Structures 14 (2017) 17mentioning

confidence: 99%

Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

Tran

Ngo²,

Khiem

2017

Lat. Am. j. solids struct.

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“…In this case, using the transfer matrix procedure given in references [8,9], one can obtain the local dynamic stiffness matrix of a multiple cracked 3D element denoted by K c e in the same form as given by the equations (8)-(10), but with the following matrices …”

Section: Dynamic Stiffness Model Of Cracked Structuresmentioning

confidence: 99%

Crack detection for structure based on the dynamic stiffness model and the inverse problem of vibration

Khiem

2006

Inverse Problems in Science and Engineering

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Detecting cracks in structures is a problem of great importance and difficulty in engineering. This work concerns the problem of crack detection for structure using its dynamical characteristics. First, a dynamic stiffness model of framed structure with multi-cracked 3D beam elements has been conducted as a basic instrument for analysis of framed structure with cracked members. Then, the crack detection problem for structures based on the conducted model is formulated in the form of a parameter estimation problem and solved by using the nonlinear programming method. The theory has been illustrated by some numerical results.

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“…The dynamic behavior of cracked structures has been a topic of active research over the last few decades. A large number of studies on the free and forced vibration of cracked structures, using analytical or numerical methods or both, are available in open literature [1][2][3][4][5][6][7][8]. For Timoshenko beams in which the effect of transverse shear deformation is nonnegligible, Kisa et al [9] analyzed the free vibration of cracked Timoshenko beam using a combination of finite element and mode synthesis method.…”

Section: Introductionmentioning

confidence: 98%

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

2011

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This paper investigates the nonlinear flexural dynamic behavior of a clamped Timoshenko beam made of functionally graded materials (FGMs) with an open edge crack under an axial parametric excitation which is a combination of a static compressive force and a harmonic excitation force. Theoretical formulations are based on Timoshenko shear deformable beam theory, von Karman type geometric nonlinearity, and rotational spring model. Hamilton's principle is used to derive the nonlinear partial differential equations which are transformed into nonlinear ordinary differential equation by using the Least Squares method and Galerkin technique. The nonlinear natural frequencies, steady state response, and excitation frequencyamplitude response curves are obtained by employing the Runge-Kutta method and multiple scale method, respectively. A parametric study is conducted to study the effects of material property distribution, crack depth, crack location, excitation frequency, and slenderness ratio on the nonlinear dynamic characteristics of parametrically excited, cracked FGM Timoshenko beams.

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The Dynamic Stiffness Matrix Method in Forced Vibration Analysis of Multiple-Cracked Beam

Cited by 41 publications

References 17 publications

Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko Beams

Crack detection for structure based on the dynamic stiffness model and the inverse problem of vibration

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

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