Free vibration of piles embedded in soil having different modulus of subgrade reaction

Yeşilce, Yusuf; Çatal, Hikmet Hüseyin

doi:10.1016/j.apm.2007.02.015

Cited by 34 publications

(19 citation statements)

References 8 publications

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“…Esmailzadeh and Ohadi investigated vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads [16]. Yesilce and Catal calculated normalized natural frequencies of Timoshenko pile due to the different values of axial force using transfer matrix and considering rotatory inertia [17].…”

Section: Introductionmentioning

confidence: 99%

Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method

Yeşilce

Çatal

2010

Arch Appl Mech

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The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko beams under various supporting conditions is plenty, but the free vibration analysis of Reddy-Bickford beams with variable cross-section on elastic soil with/without axial force effect using the Differential Transform Method (DTM) has not been investigated by any of the studies in open literature so far. In this study, the free vibration analysis of axially loaded and semi-rigid connected Reddy-Bickford beam with variable cross-section on elastic soil is carried out by using DTM. The model has 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 in this study. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle and considering rotatory inertia. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. At first, the terms are found directly from the analytical solutions of the differential equations that describe the deformations of the cross-section according to the highorder theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The calculated natural frequencies of semi-rigid connected Reddy-Bickford beam with variable cross-section on elastic soil using DTM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed.

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Section: Introductionmentioning

confidence: 99%

Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method

Yeşilce

Çatal

2010

Arch Appl Mech

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“…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. Catal (2006b) calculated frequency factors of a beam on elastic soil using differential transform method.…”

Section: Introductionmentioning

confidence: 99%

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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“…Ç atal and Ç atal (2006) analyzed a partially embedded pile in elastic soil using differential transform method. Yeşilce and Ç atal (2008) obtained the natural circular frequencies of piles embedded in the soil having different subgrade reaction. Çalım and Akkurt (2010) studied on the free vibration and static response of straight and circular beams on elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation

Hızal¹,

Çatal²

2016

Structural Engineering and Mechanics

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Abstract. Vibration analysis of the beams on elastic foundation has gained the great interest of many researchers. In the literature, there are many studies that focus on the free vibration analysis of the beams on one or two parameter elastic foundations. On the other hand, there are no sufficient studies especially focus on the comparison of dynamic response including the bending moment and shear force of the beams resting on Winkler and two parameter foundations. In this study, dynamic response of the axially loaded Timoshenko beams resting on modified Vlasov type elastic soil was investigated by using the separation of variables method. Governing equations were obtained by assuming that the material had linear elastic behaviour and mass of the beam was distributed along its length. Numerical analysis were provided and presented in figures to find out the differences between the modified Vlasov model and conventional Winkler type foundation. Furthermore, the effect of shear deformation of elastic soil on the dynamic response of the beam was investigated.

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Free vibration of piles embedded in soil having different modulus of subgrade reaction

Cited by 34 publications

References 8 publications

Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method

Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method

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

Comparative dynamic analysis of axially loaded beams on modified Vlasov foundation

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