Free vibration of partially supported piles with the effects of bending moment, axial and shear force

Çatal, Hikmet Hüseyin

doi:10.1016/s0141-0296(02)00113-x

Cited by 34 publications

(9 citation statements)

References 4 publications

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“…The equation of motion for a Timoshenko beam can be written as (Catal 2002, Benaroya 2004, Catal 2006a, Yesilce & Catal 2008:…”

Section: The Mathematical Model and Formulationmentioning

confidence: 99%

“…The solution of differential equation (1) can be obtained by the method of separation of variables (Doyle & Pavlovic 1982, Catal 2002, Catal 2006a.…”

Section: The Mathematical Model and Formulationmentioning

confidence: 99%

“…Doyle & Pavlovic (1982) solved the partial differential equation for free vibration of beams partially attached to elastic foundation using separation of variable method and neglecting shear effect. Catal (2002Catal ( , 2006a) calculated natural circular frequencies and relative stiffness of the pile due to the values of axial forces acting on the pile and the shape factors. Yesilce & Catal (2008) calculated normalized natural frequencies of the pile using carry-over matrix and considering rotatory inertia.…”

Section: Introductionmentioning

confidence: 99%

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Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Yeşilce

Demirdağ

Catal

2008

Sadhana

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Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1-4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.

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“…The equation of motion for a Timoshenko beam can be written as (Catal 2002, Benaroya 2004, Catal 2006a, Yesilce & Catal 2008:…”

Section: The Mathematical Model and Formulationmentioning

confidence: 99%

“…The solution of differential equation (1) can be obtained by the method of separation of variables (Doyle & Pavlovic 1982, Catal 2002, Catal 2006a.…”

Section: The Mathematical Model and Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Yeşilce

Demirdağ

Catal

2008

Sadhana

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“…Doyle and Pavlovic [18] solved the partial differential equation for free vibration of beams partially attached to elastic foundation using separation of variable method and neglecting shear effect. Catal [19,20] calculated natural frequencies and relative stiffness of the pile due to the values of axial forces acting on the pile and the shape factors. Yesilce and Catal [21] calculated normalized natural frequencies of the pile due to the different values of axial force using carry-over matrix and considering rotatory inertia.…”

Section: Introductionmentioning

confidence: 99%

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

Yeşilce

Demirdağ

2008

International Journal of Mechanical Sciences

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“…Esmailzadeh & Ohadi (2000) investigated vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads. Catal (2002) calculated natural frequencies and relative stiffness of the pile for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported by using Timoshenko beam theory and transfer matrix. Further, he proceeded to determine the natural frequencies of Timoshenko piles partially embedded in the soil, but semi-rigidly connected at the upper ends, using the method of initial values (Catal 2006).…”

Section: Introductionmentioning

confidence: 99%

Free vibration of semi-rigid connected Reddy-Bickford piles embedded in elastic soil

Yeşilce

Çatal

2008

Sadhana

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The literature on free vibration analysis of Bernoulli-Euler and Timoshenko piles embedded in elastic soil is plenty, but that of Reddy-Bickford piles partially embedded in elastic soil with/without axial force effect is fewer. The soil that the pile partially embedded in is idealized by Winkler model and is assumed to be two-layered. The pile part above the soil is called the first region and the parts embedded in the soil are called the second and the third region, respectively. It is assumed that the behaviour of the material is linear-elastic, that axial force along the pile length to be constant and the upper end of the pile that is semi-rigid supported against rotation is modelled by an elastic spring. The governing differential equations of motion of the rectangular pile in free vibration are derived using Hamilton's principle and Winkler hypothesis. The terms are found directly from the solutions of the differential equations that describe the deformations of the cross-section according to the high-order theory. The models have six degrees of freedom at the two ends, one transverse displacement and two rotations, and the end forces are a shear force and two end moments. Natural frequencies of the pile are calculated using transfer matrix and the secant method for non-trivial solution of linear homogeneous system of equations obtained due to values of axial forces acting on the pile, total and embedded lengths of the pile, the linear-elastic rotational restraining stiffness at the upper end of the pile and to the boundary conditions of the pile. Two different boundary conditions are considered in the study. For the first boundary condition, the pile's end at the first region is semi-rigid connected and not restricted for horizontal displacement and the end at the third region is free and for the second boundary condition, the pile's end at the first region is semi-rigid connected and restricted for horizontal displacement and the end at the third region is fixed supported. The calculated natural frequencies of semi-rigid connected Reddy-Bickford pile embedded in elastic soil are given in tables and compared with results of Timoshenko pile model.

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Free vibration of partially supported piles with the effects of bending moment, axial and shear force

Cited by 34 publications

References 4 publications

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

Free vibration of semi-rigid connected Reddy-Bickford piles embedded in elastic soil

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