• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.946-949
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• 2007

This paper discusses the lateral vibration of a beam with boundary condition of one end fixed and the other end free. The uniform beam has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function or mathematical solution could not exist. Even if the solution of Bessel's function exists, as Bessel function is a series function, we must get the solution by numerical method. Author had proposed the solution of the matrix method by Ritz's method and a new mode shape function, and had earned the good results for a wedge beam. Hereby a vibration analysis for the tapered beam with circle cross section was executed, and so good results were showed.

• Advances in nano research
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• v.13 no.1
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• pp.63-75
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• 2022

The nonlinear dynamic behavior of a nonuniform small-scale nonlocal beam is investigated in this work. The nanobeam is theoretically modeled using the nonlocal Eringen theory, as well as a few of Von-nonlinear Kármán's theories and the classical beam theory. The Hamilton principle extracts partial differential equations (PDE) of an axially functionally graded (AFG) nano-scale beam consisting of SUS304 and Si₃N₄ throughout its length, and an elastic Winkler-Pasternak substrate supports the tapered AFG nanobeam. The beam thickness is a function of beam length, and it constantly varies throughout the length of the beam. The numerical solution strategy employs an iteration methodology connected with the generalized differential quadratic method (GDQM) to calculate the nonlinear outcomes. The nonlinear numerical results are presented in detail to examine the impact of various parameters such as nonlinear amplitude, nonlocal parameter, the component of the elastic foundation, rate of cross-section change, and volume fraction parameter on the linear and nonlinear free vibration characteristics of AFG nanobeam.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.11
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• pp.18-26
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• 1999

Recently, various simplified simulation techniques such as firite-difference beam propagation method and non-orthogonal coupled-mode theory have proposed to analyze the optical characteristics of tapered directional couplers supported by the coupling of two propagating modes. Although these approaches are often in sufficiently accurate, they do not provide the detailed solutions encountered in the analysis of tapered guiding structures. For this purpose, we introduce and utilize a newly developed modal transmission-line theory to analyze rigorously power transfer of the directional coupler. The numerical result reveals that the propagation constants of even and odd modes converge to a single value as increasing the spacer thickness between two symmetric tapered guides. Furthermore, 97% of the power incident into a guiding channel is transmitted to the other channel at the tapered angle ${\theta}=0.1^{\circ}$, and the efficiency of power transfer decreases dramatically as increasing the angle.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.5
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• pp.1023-1031
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• 1994

The closed forms of consistent mass matrix with rotational inertia matrix are developed for free vibration analysis in space sutructures containing linearly tapered members with cross section of thin-walled I-sections. The exact displacement functions are used for formulating mass matrices. The very small slopes of the tapered member are used in usual practice, such that the series expansion forms of these are also developed to avoid numerical failure in vibration analysis. Significant improvements of accuracy and efficiency of free vibation analysis are achieved by using the mass matrices developed in this study. Frequencies of free vibation of tapered members are compared with solutions based upon stepped representation of beam element in the ANSYS. The mass matrices presented in this study can be used for the free vibration analysis of tapered and prismatic members.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.87-95
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• 2000

The two eigenvalues (elastic critical load and natural frequency of lateral vibration) of sinusoidally tapered bats with simply supported ends were determined by the finite element method. For the convenience of structural engineers who are engaged in the structural design or vibration analysis of tapered beam-columns, eigenvalue coefficients were expressed by simple algebraic equations. The validity of each algebraic equation was confirmed by the value of unity for each correlation coefficient. The influence of axial thrust on the lateral vibration frequency was also investigated. For this purpose, the axial thrust was increased successively and the corresponding frequency was calculated. The approximate linear relationship between the axial thrust and the square of the frequency was confirmed lot each of the tapered members.

• Journal of the Korea Convergence Society
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• v.9 no.12
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• pp.175-180
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• 2018

In this study, CFRP was manufactured with the laminate angle of $45^{\circ}$. The specimen of TDCB bonded with the adhesive for structure was designed by CATIA and the analysis was progressed by using the finite element analysis program of ANSYS. This study model was designed on the basis of British industry and ISO standard and the configuration factor(m) was established with variable according to the angle of model configuration. As the study result of this paper, the maximum deformations at the specimens with the tapered angles of $4^{\circ}$ and $8^{\circ}$ become most as 12.628 mm and least as 12.352mm respectively. Also, the maximum equivalent stresses at the specimens with the tapered angles of $6^{\circ}$ and $8^{\circ}$ become most as 9210.3 MPa and least as 4800.5 MPa respectively. The damage data of TDCB structure with the laminate angle which was manufactured with CFRP could be secured through this study result. As the damage data of TDCB structure bonded with CFRP obtained on the basis of this study result are utilized, the esthetic sense can be shown by being grafted onto the machine or structure at real life.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.12
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• pp.822-829
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• 2015

A transfer matrix method has been developed to determine the more accurate natural frequencies for the bending vibration of Bernoulli-Euler beam with linearly reduced width and a concentrated tip mass. The proposed method can be computed an infinite number of the natural frequencies using a single element. Using the differential equation, shear force, and bending moment in which can be deduced by the diverse variational principles, a transfer matrix is formulated. The roots of the differential equation are computed by the Frobenius method. The effect of the concentrated mass for the natural frequencies of width-tapered beams is examined through a parametric study, and to show the accuracy of the proposed method, the computed results compared with those obtained from commercial finite element analysis program(ANSYS).

• Steel and Composite Structures
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• v.11 no.6
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• pp.435-454
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• 2011

Bonding composite materials to structural members for strengthening purpose has received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs. In this paper, a numerical solution using finite - difference method is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends with different thinning profiles. These latter, can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

• Journal of electromagnetic engineering and science
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• v.10 no.1
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• pp.18-24
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• 2010

A Ka-band microstrip array antenna for wide-range detection of moving targets is analyzed through a photonicassisted reactive-near-field characterization technique. The antenna array employs a 3-dB-tapered feed network to suppress the sidelobe level while retaining a wide azimuth beamwidth for a wide detection range. The relative nearelectric field patterns of the array and its 3-dB-tapered feed lines have been measured using an electro-optic fieldmapping technique for minimally invasive millimeter-wave sensing. A number of typical limitations on the technique, involving bandwidth, low signal-modulation depth, and high laser-induced noise in high-frequency applications, have been overcome by suppressing the carrier portion of the optical interrogation beam.

• Journal of Korean Society of Steel Construction
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• v.17 no.6 s.79
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• pp.699-705
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• 2005

This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.