• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.167-188
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• 2008

This study is concerned with the establishment of the characteristic equation of a combined system consisting of a cantilever beam with a tip mass and an in-span visco-elastic helical spring-mass, considering the mass of the helical spring. After obtaining the "exact" characteristic equation of the combined system, by making use of a boundary value problem formulation, the characteristic equation is established via a transfer matrix method, as well. Further, the characteristic equation of a reduced system is obtained as a special case. Then, the characteristic equations are numerically solved for various combinations of the physical parameters. Further, comparison of the results with the massless spring case and the case in which the spring mass is partially considered, reveals the fact that neglecting or considering the mass of the spring partially can cause considerable errors for some combinations of the physical parameters of the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.706-711
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• 2000

This paper deals with the free vibrations of horizontally curved beams on an elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, the differential equations governing free vibrations of noncircular curved beams resting on Pasternak-type foundations are derived and solved numerically. The lowest three natural frequencies for parabolic curved beams with hinged-hinged and clamped-clamped end restraints are calculated. Numerical results are presented to show the effects on the natural frequencies of the non-dimensional system parameters: the horizontal rise to span length ratio, the Winkler foundation parameter, the shear foundation parameter, and the width ratio of contact area between the beam and foundation.

• Ocean Systems Engineering
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• v.6 no.4
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• pp.325-344
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• 2016

Using 3D computational fluid dynamics techniques in recent years have shed significant light on the Vortex Induced Vibrations (VIV) encountered by deep-water marine risers. The fatigue damage accumulated due to these vibrations has posed a great concern to the offshore industry. This paper aims to present an algorithm to predict the crossflow and inline fatigue damage for very long (L/D > $10^3$) marine risers using a Finite-Analytical Navier-Stokes (FANS) technique coupled with a tensioned beam motion solver and rainflow counting fatigue module. Large Eddy Simulation (LES) method has been used to simulate the turbulence in the flow. An overset grid system is employed to mesh the riser geometry and the wake field around the riser. Risers from NDP (2003) and Miami (2006) experiments are used for simulation with uniform, linearly sheared and non-uniform (non-linearly sheared) current profiles. The simulation results including inline and crossflow motion, modal decomposition, spectral densities and fatigue damage rate are compared to the experimental data and useful conclusions are drawn.

• Steel and Composite Structures
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• v.33 no.4
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• pp.473-487
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• 2019

A shear-deformable finite element model (FEM) with five nodes and thirteen degrees of freedom (DOFs) for free vibrations of laminated composite beams with arbitrary lay-up is presented. This model can be capable of considering the elastic couplings among the extensional, bending and torsional deformations, and the Poisson's effect. Lagrange's principle is employed in derivation of the equations of motion, and thus the element matrices are obtained. Comparisons of the present element's results with those in experiment, available literature and the 3D finite element analysis software (ANSYS(R)) are made to show its accuracy. Some further results are given as referencing for the future studies in vibrations of laminated composite beamst.

• Steel and Composite Structures
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• v.38 no.3
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• pp.281-291
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• 2021

An equivalent single-layer theory (EST) is put forward for analyzing free vibrations of steel-concrete composite beams (SCCB) based on a higher-order beam theory. In the EST, the effect of partial interaction between sub-beams and the transverse shear deformation are taken into account. After using the interlaminar shear force continuity condition and the shear stress free conditions at the top and bottom surface, the displacement function of the EST does not contain the first derivatives of transverse displacement. Therefore, the C0 interpolation functions are just demanded during its finite element implementation. Finally, the EST is validated by comparing the results of two simply-supported steel-concrete composite beams which are tested in laboratory and calculated by ANSYS software. Then, the influencing factors for free vibrations of SCCB are analyzed, such as, different boundary conditions, depth to span ratio, high-order shear terms, and interfacial shear connector stiffness.

• Journal of Mechanical Science and Technology
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• v.20 no.4
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• pp.467-472
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• 2006

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Pasternak foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.797-807
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• 2019

In this study, an exact transfer matrix expression for a twisted uniform beam considering the effect of shear deformation and rotary inertia is developed. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. The results obtained from this method are independent for a number of subdivided elements, and this method can determine the required number of exact solutions for the free vibration characteristics of a twisted uniform Timoshenko beam using a single element. In addition, it can be used as a useful numerical method for the computation of high-order natural frequencies. To validate the accuracy of the proposed method, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of shear deformation and rotary inertia for a twisted beam.

• Steel and Composite Structures
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• v.1 no.2
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• pp.213-230
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• 2001

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the nonprismatic properties of a 'cracked' steel-concrete beam. This beam model is extended to a sub-frame in which the restraining effects from the adjoining members are considered. Parametric studies are performed on several sub-frame models and the results are used to show that it is possible to correlate the amount of moment redistribution of semi-continuous beam within the sub-frame using an equivalent stiffness of the connection. Deflection equations are derived for semi-continuous composite beams subjected to various loading and parametric studies on beam vibrations are conducted. The proposed method may be applied using a simple computer or spreadsheet program.