• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.65-77
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• 2017

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• International Journal of Precision Engineering and Manufacturing
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• v.7 no.1
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• pp.24-29
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• 2006

In this paper, the effect of open crack on the dynamic behavior of simply supported Timoshenko beam with a moving mass was studied. The influences of the depth and the position of the crack on the beam were studied on the dynamic behavior of the simply supported beam system by numerical methods. The equation of motion is derived by using Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces on the crack section and is derived by applying fundamental fracture mechanics theory. As the depth of the crack increases, the mid-span deflection of the Timoshenko beam with a moving mass is increased.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.1-13
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• 2012

In this paper the dynamic behavior of a viscoelastic Timoshenko beam subjected to a concentrated moving load are studied analytically and numerically. The viscoelastic properties of the beam obey the linear standard model in shear and incompressible in bulk. The governing equation for Timoshenko beam theory is obtained in viscoelastic form using the correspondence principle. The analytical solution is based on the Fourier series and the numerical solution is performed with finite element method. The effects of the material properties and the load velocity are investigated on the responses by numerical and analytical methods. In addition, the results are compared with the Euler beam results.

• Journal of KSNVE
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• v.9 no.5
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• pp.1012-1018
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• 1999

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

• Smart Structures and Systems
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• v.1 no.3
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• pp.283-308
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• 2005

This paper features about the modeling and design of a fast output sampling feedback controller for a smart Timoshenko beam system for a SISO case by considering the first 3 vibratory modes. The beam structure is modeled in state space form using FEM technique and the Timoshenko beam theory by dividing the beam into 4 finite elements and placing the piezoelectric sensor/actuator at one location as a collocated pair, i.e., as surface mounted sensor/actuator, say, at FE position 2. State space models are developed for various aspect ratios by considering the shear effects and the axial displacements. The effects of changing the aspect ratio on the master structure is observed and the performance of the designed FOS controller on the beam system is evaluated for vibration control.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.6
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• pp.99-107
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• 2008

In this paper, the stability of a cracked cantilever Timoshenko beam with a tip mass subjected to follower force is investigated. In addition, an analysis of the flutter instability(flutter critical follower force) and a critical natural frequency of a cracked cantilever Euler / Timoshenko beam with a tip mass subjected to a follower force is presented. The vibration analysis on such cracked beam is conducted to identify the critical follower force for flutter instability based on the variation of the first two resonant frequencies of the beam. Therefore, the effect of the crack's intensity, location and a tip mass on the flutter follower force is studied. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.12
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• pp.1547-1557
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• 2013

A forced vibration model of a rail system was established using the Timoshenko beam theory to determine the dynamic response of a rail under time-varying load considering the damping effect and stiffness of the elastic foundation. By using a Fourier series and a numerical method, the critical velocity and dynamic response of the rail were obtained. The forced vibration model was verified by using FEM and Euler beam theory. The permanent deformation of the rail was predicted based on the forced vibration model. The permanent deformation and wear were observed through the experiment. Parametric studies were then conducted to investigate the effect of five design factors, i.e., rail cross-section shape, rail material density, rail material stiffness, containment stiffness, and damping coefficient between rail and containment, on four performance indices of the rail, i.e., critical velocity, maximum deflection, maximum longitudinal stress, and maximum shear stress.

• Journal of Korean Society of Steel Construction
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• v.18 no.3
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• pp.349-359
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• 2006

This paper presents a new block stiffness matrix for the analysis an orthogonal Cartesian coordinate system. The displacement fields are defined using the first order shear deformable beam theory. The longitudinal displacement can be expressed as the sum of the projected plane deformation of the cross-section due to Timoshenko's beam theory and axial warping deformation due to modified Vlasov's thin-waled beam theory. The derived element takes into account flexural shear deformation and torsional warping deformation. Three different types of beam elements, namely, the two-noded, three-noded, and four-noded beam elements, are developed. The quadratic and cubic elements are found to be very efficient for the flexural analysis of laminated composite beams. The versatility and accuracy of the new element are demonstrated by comparing the numerical results available in the literature.

• Steel and Composite Structures
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• v.25 no.4
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• pp.415-426
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• 2017

The thermo-mechanical vibration behavior of two dimensional functionally graded (2D-FG) porous nanobeam is reported in this paper. The material properties of the nanobeam are variable along thickness and length of the nanobeam according to the power law function. The nanobeam is modeled within the framework of Timoshenko beam theory. Eringen's nonlocal elasticity theory is used to develop the governing equations. Using the generalized differential quadrature method (GDQM) the governing equations are solved. The effect of porosity, temperature distribution, nonlocal value, L/h, FG power indexes along thickness and length and are investigated using parametric studies.