• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.1
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• pp.66-73
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• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Journal of the Optical Society of Korea
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• v.13 no.2
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• pp.234-239
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• 2009

This paper presents a theoretical and experimental investigation of the transmission and sensing characteristics of the biconically tapered cladded multimode fibers. The beam propagation method was used to examine the transmission characteristics with various structural parameters. The results show that the transmission of the biconically tapered cladded multimode fibers is sensitive to the mode of the input optical beam and the refractive index of the external medium. A refractive index sensor for the external medium was proposed based on the theoretical analysis, and its feasibility was demonstrated experimentally.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.864-869
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and point masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest four natural frequencies are calculated over a range of non-dimensional system parameters.

• Korean Journal of Materials Research
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• v.34 no.3
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• pp.125-137
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• 2024

Composite laminates are used in a wide range of applications including defense, automotive, aviation and aerospace, marine, wind energy, and recreational sporting goods. These composite beams still exhibit problems such as buckling, local deformations, and interlaminar delamination. To overcome these drawbacks, a novel viscoelastic autoclave bonding with tapered epoxy reinforcement polyurethane films is proposed. In existing laminates, compression face wrinkling and interlaminar delamination is caused in the sandwich beam. The unique viscoelastic autoclave spunbond interlayer bonding is designed to prevent face wrinkling and absorb and distribute stresses induced by external loads, thereby eliminating interlaminar delamination in the sandwich beam. Also, the existing special reinforcement causes stress concentrations, and the core is not effectively connected, which directly affects the stiffness of the beam. To address this, a novel tapered epoxy polyurethane reinforcement adhesive film is proposed, whose reinforcement thickness gradually tapers as it enters the core material. This minimizes stress concentrations at the interface, preventing excessive adhesive squeeze-out during the bonding process, and improves the stiffness of the beam. Results indicate the proposed model avoids the formation of micro cracks, interlaminar delamination, buckling, and local deformations, and effectively improves the stiffness of the beam.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3127-3135
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• 1994

An approach to the simultaneous optimal design of structure and control system for large free-free flexible beam is presented. The flexible beam is modeled by the finite element method. And the reduced model of small degree of freedom is constructed by use of modal analysis. The tapered beam is considered so that the number of design variables is not dependent on the increasing number of finite elements. The width of several points of tapered beam and control gain are taken as design variables. The shape of beam and control gain are optimized simultaneously for the minimum weight of total structure including control system subject to the constraints of the magnitude of displacement of beam. It is shown that the simultaneous optimal design of structure and control systems is indeed useful.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.129-138
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• 2012

This paper deals with geometrical non-linear analyses of the tapered variable-arc-length beam, subjected to the combined load with an end moment and a point load. The beam is supported by a hinged end and a frictionless sliding support so that the axial length of the deformed beam can be increased by its load. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. These differential equations are numerically solved by the iteration technique for obtaining the elastica of the deformed beam. For validating theories developed herein, laboratory scaled experiments are conducted.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.269-281
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• 1997

The overall buckling mode in a composite steel-concrete beam over an internal support is necessarily lateral-distortional, in which the bottom compressive range displaces laterally and twists, since the top flange is restrained by the nearly rigid concrete slab. An efficient finite element method is used to study elastic lateral-distortional buckling in composite beams whose steel portion is tapered. The simplified model for a continuous beam that is presented herein is a fixed ended cantilever whose steel portion is tapered, and is subjected to moment gradient. This is intended to give an insight into distortion in a continuous beam that occurs in the negative bending region, and the differences between the cantilever representation and the continuous beam are highlighted. An eigenproblem is established, and the buckling modes and loads are determined in the elastic range of structural response. It is found from the finite element study that the buckling moment may be enhanced significantly by using a vertical stiffener in the region where the lateral movement of the bottom range is greatest. This enhancement is quantified in the paper.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.1
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• pp.13-22
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• 2013

This paper deals with a novel method for numerical analyses of the tapered geometrical non-linear beam with three unknown parameters, subjected a floating point load. The beams with hinged-movable end constraint are chosen as the objective beam. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The first order simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. A novel numerical method for solving these equations is developed by using the iteration technique. The processes of the solution method are extensively discussed through a typical numerical example. For validating theories developed herein, laboratory scaled experiments are conducted.

• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.479-489
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• 2000

Based on the stiffness equation of the tapered beam element involving the effects of axial force and shear deformation, numerical investigations are carried out on elastic instability for web-linearly tapered columns with I-section of steel portal frames. Effects of shear deformation on the effective length of the tapered columns with I-section are studied. An efficient approach for determining the effective length of the tapered portal frame columns considering effects of shear deformation is proposed.