• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.4
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• pp.118-123
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• 1997

The study suggests a method to analyze the vibration of the multi-stepped beam having the different circular cross-sections. The rotatory inertia, the shear deformation and the torque applied at both ends of the beam are considered in the governing equation. The complex displacement and the variable separation are introduced to derive the solution of the equation of each uniform beam element having constant cross-section. Then boundary conditions are applied to solve the total system. This method uses the mathematically exact solutions unlike numerical method such as the finite element method in solving the problem having the simultaneous differential equations of Timoshenko beam theory. the natural frequencies and the corresponding mode shapes are precise, especially the mode shapes are continuous.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.1
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• pp.63-69
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• 2006

New design equations for calculating the lateral-torsional buckling moment resistances of singly stepped I-section beams subjected to general loading on the top flange are suggested based on the investigations of elastic finite-element analyses. The new equations presented in this study are compared with current moment gradient modifiers presented by other researchers and specifications. The study considered almost loading cases on buildings and bridges. The proposed equations should be easily used to calculate the lateral-torsional buckling moment resistance of stepped I-beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.200-205
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• 1998

Although discretization methods such as the transfer matrix method (TMM) and the finite element method (FEM) have played an important role in the design or analysis of rotor-bearing systems, continuous system modeling and analysis are often desirable especially for sensitivity analysis or design. The present paper proposes a comprehensive modeling procedure to obtain exact solution of general rotor-bearing systems. The proposed method considers a Timoshenko beam model and makes use of complex coordinate in the formulation. The proposed method provides exact eigensolutions and frequency response functions (FRFS) of general multi-stepped rotor-bearing systems. The first numerical example compares the proposed method with FEM. The numerical study proves that the proposed method is very efficient and useful for the analysis of rotor-bearing systems.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.8
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• pp.583-591
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• 2014

The mathematical modeling on the free vibration and stability of a multi-stepped shaft of turbo compressor is performed in this study. The multi-stepped shaft is modeled as a non-uniform Timoshenko beam supported by anisotropic bearings. It is assumed that the shaft is spinning with constant speed about its longitudinal axis and subjected to a conservative axial force induced by front and rear impellers attached to the shaft. The structural model incorporates non-classical features such as transverse shear and rotary inertia. A structural coupling between vertical and lateral motions is induced by Coriolis acceleration terms. The governing equations are derived via Hamilton's variational principle and the equations are transformed to the standard form of an eigenvalue problem. The implications of combined gyroscopic effect, conservative axial force, bearing stiffness and damping are revealed and a number of pertinent conclusions are outlined. In this study analytical results are compared with those from ANSYS finite element analysis and experimental modal testing.

• Ocean Systems Engineering
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• v.13 no.2
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• pp.195-224
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• 2023

This paper proposes a method for the acoustic imaging wherein the traditional requirement of the relative movement between the transmitter and target is overcome. This is facilitated through the beamforming acoustic array in the transmitter, in which the target is illuminated by the array at various azimuth and elevation angles without the physical movement of the acoustic array. The concept of beam steering of the acoustic array facilitates the formation of the beam at desired angular positions of azimuth and elevation angles. This paper substantiates that the combination of illumination of the target from different azimuth and elevation angles with respect to the transmitter (through the beam steering of beam forming acoustic array) and the beam steering at multiple frequencies (through SF) results in enhanced reconstruction of images of the target in the underwater scenario. This paper also demonstrates the possibility of reconstruction of the image of a target in underwater without invoking the traditional algorithms of Digital Image Processing (DIP). This paper comprehensively and succinctly presents all the empirical formulae required for modelling the acoustic medium and the target to facilitate the reader with a comprehensive summary document incorporating the various parameters of multi-disciplinary nature.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.701-717
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• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2812-2818
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• 1996

A cantilever beam with a mass and a spring at the end can be use to model a miniature flexible arm. It is necessary to know the natural frequencies and mode shapes to discuss its free vibration, especially when modal analysis is employed. A beam is clamped-free. In this paper we look at the lateral vibration of beams that have step changes in the properties of their cross sections. The frequency equation is derived by Bernoulli-Euler formulation and is sloved by the separation of variable. The parameters of the beam, 'mass and spring stiffness' are defined as nondimensionalized parameters for wide application of the results. According to the change of eigenvalues and mode shape are presented for this beam. The results presented are the eigenvalues and the natural frequencies for the first three modes of vibration. Results show that the parameters have a significant effect on the natural frequency.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1320-1332
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• 1996

In the present study, we consider modified 5-node equivalent solid element which has smallest degree of freedom among 2-dimensional solid elements accounting bending deformation as well as extensional and shear deformations, We shall investigate static and dynamic characteristics of this element, which is very effective in thin beam, thick beam, large displacement problems, beam of variable thickness, and asymmetrically stepped beam, etc., as well as relatively simple problems of beam. The degree of freedom of this element is 10, which is smaller than 18 of 9-node element, 16 of 8-node elemtns, 12 of modified 6-node element and Q6 element. Therefore, this element is expected to broaden the effective range of application of the solid elements in the bending problems further.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.9
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• pp.947-956
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• 2008

In this paper, miniaturized conically stepped COBRA is proposed. In order to prevent electrical breakdown, COBRA, which consists of hem and lens, has to get bigger if it is designed with conventional method. Because of the phase error increase, shortening the length of the antenna without changing the aperture size leads to the reduction of the antenna gain. To avoid this, the phase error at the aperture is compensated by transforming the COBRA lens into conically stepped form. The simulations result shows that the proposed antenna has higher gain than the conventional COBRA in spite of the size reduction from 1,300 mm to 600 mm. The fabricated and measured COBRA has the gain of 26.2 dBi.

• Smart Structures and Systems
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• v.26 no.6
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• pp.681-692
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• 2020

Conventional Piezoelectric Energy Harvesters (CPEH) have been extensively studied for maximizing their electrical output through material selection, geometric and structural optimization, and adoption of efficient interface circuits. In this paper, the performance of Stepped Piezoelectric Energy Harvester (SPEH) under harmonic base excitation is studied analytically, numerically and experimentally. The motivation is to compare the energy harvesting performance of CPEH and SPEHs with the same characteristics (resonant frequency). The results of this study challenge the notion of achieving higher voltage and power output through incorporation of geometric discontinuities such as step sections in the harvester beams. A CPEH consists of substrate material with a patch of piezoelectric material bonded over it and a tip mass at the free end to tune the resonant frequency. A SPEH is designed by introducing a step section near the root of substrate beam to induce higher dynamic strain for maximizing the electrical output. The incorporation of step section reduces the stiffness and consequently, a lower tip mass is used with SPEH to match the resonant frequency to that of CPEH. Moreover, the electromechanical coupling coefficient, forcing function and damping are significantly influenced because of the inclusion of step section, which consequently affects harvester's output. Three different configurations of SPEHs characterized by the same resonant frequency as that of CPEH are designed and analyzed using linear electromechanical model and their performances are compared. The variation of strain on the harvester beams is obtained using finite element analysis. The prototypes of CPEH and SPEHs are fabricated and experimentally tested. It is shown that the power output from SPEHs is lower than the CPEH. When the prototypes with resonant frequencies in the range of 56-56.5 Hz are tested at 1 m/s2, three SPEHs generate power output of 482 μW, 424 μW and 228 μW when compared with 674 μW from CPEH. It is concluded that the advantage of increasing dynamic strain using step section is negated by increase in damping and decrease in forcing function. However, SPEHs show slightly better performance in terms of specific power and thus making them suitable for practical scenarios where the ratio of power to system mass is critical.