• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1115-1119
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• 2005

The paper proposes the elastic modulus evaluation technique of a cantilever beam by vibration analysis based on time-average electronic speckle pattern interferometry (TA-ESPI) with non-contact and nondestructive and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of thin film are Nano indentation test, Bulge test and Micro-tensile test and so on. They each have strength and weakness in the preparation of test specimen and the analysis of experimental result. ESPI has been developed as a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at a resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI is a clue to find the resonance frequency at each vibration mode shape. And the elastic modules of test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique is able to give the elastic modulus of materials through the simple processing of preparation and analysis.

• Structural Engineering and Mechanics
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• v.51 no.1
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• pp.89-110
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• 2014

In this study, two beam-column elements based on the Elasto-Fiber element theory for reinforced concrete (RC) element have been developed and compared with each other. The first element is based on Elasto Fiber Approach (EFA) was initially developed for steel structures and this theory was applied for RC element in there and the second element is called as Fiber & Bernoulli-Euler element approach (FBEA). In this element, Cubic Hermitian polynomials are used for obtaining stiffness matrix. The beams or columns element in both approaches are divided into a sub-element called the segment for obtaining element stiffness matrix. The internal freedoms of this segment are dynamically condensed to the external freedoms at the ends of the element by using a dynamic substructure technique. Thus, nonlinear dynamic analysis of high RC building can be obtained within short times. In addition to, external loads of the segment are assumed to be distributed along to element. Therefore, damages can be taken account of along to element and redistributions of the loading for solutions. Bossak-${\alpha}$ integration with predicted-corrected method is used for the nonlinear seismic analysis of RC frames. For numerical application, seismic damage analyses for a 4-story frame and an 8-story RC frame with soft-story are obtained to comparisons of RC element according to both approaches. Damages evaluation and propagation in the frame elements are studied and response quantities from obtained both approaches are investigated in the detail.

• Coupled systems mechanics
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• v.3 no.3
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• pp.247-265
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• 2014

This article discusses the dynamic response of Bernoulli-Euler straight beam with angular elastic supports subjected to moving load with variable velocity. A new engineering approach for determination of the dynamic effect from the moving load on the stressed and strained state of the beam has been developed. A dynamic coefficient, a ratio of the dynamic to the static deflection of the beam, has been defined on the base of an infinite geometrical absolutely summable series. Generalization of the R. Willis' equation has been carried out: generalized boundary conditions have been introduced; the generalized elastic curve's equation on the base of infinite trigonometric series method has been obtained; the forces of inertia from normal and Coriolis accelerations and reduced beam mass have been taken into account. The influence of the boundary conditions and kinematic characteristics of the moving load on the dynamic coefficient has been investigated. As a result, the dynamic stressed and strained state has been obtained as a multiplication of the static one with the dynamic coefficient. The developed approach has been compared with a finite element one for a concrete engineering case and thus its authenticity has been proved.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.528-532
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• 2013

In this study, an analytical model of micro-beam structure including thermoelastic damping with irregularly distributed masses is investigated. The significance of thermoelastic damping for micro-scale mechanical resonators is evaluated to design -with high quality factor(Q-factor). The beam model of this work is based on Euler-Bernoulli beam theory. In order to determine the natural frequency of the model, energy method is applied. Also, the thermoelatic damping effects are considered by using heat conduction equations, and the Q-factor can be determined. To derive the equation of motion, non-dimensionalization is employed for systematic analysis. Results of the model are verified, and present mode shapes and Q-factors for the micro-beam with thermoelastic damping including random point masses.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1105-1126
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• 2015

Many vibrating mechanical systems from the real life are modeled as combined dynamical systems consisting of beams to which spring-mass secondary systems are attached. In most of the publications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) published recently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-span helical spring-mass systems were determined via the solution of the established eigenvalue problem, where the springs were modeled as axially vibrating rods. In the present article, the authors used the assumed modes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrived at a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper is simply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quite different way, namely, by using the so-called "characteristic force" method. Further, parametric investigations are carried out for two representative types of supporting conditions of the bending beam.

• Computational Structural Engineering
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• v.10 no.4
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• pp.177-184
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• 1997

In this paper, numerical methods are developed for solving the elastica of simple beams with variable-arc-length subjected to a point loading. The beam model is based on Bernoulli-Euler beam theory. The Runge-Kutta and Regula-Falsi methods, respectively, are used to solve the governing differential equations and to compute the beam's rotation at the left end of the beams. Extensive numerical results of the elastica responses, including deflected shapes, rotations of cross-section and bending moments, are presented in non-dimensional forms. The possible maximum values of the end rotation, deflection and bending moment are determined by analyzing the numerical data obtained in this study.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.10a
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• pp.914-917
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• 2005

The paper proposes a new sonic resonance test for a dynamic elastic constant measurement which is based on time-average electronic speckle pattern interferometry(TA-ESPI)and Euler-Bernoulli equation. Previous measurement technique of dynamic elastic constant has the limitation of application for thin film or polymer material because contact to specimen affects the result. TA-ESPI has been developed as a non-contact optical measurement technique which can visualize resonance vibration mode shapes with whole-field. The maximum vibration amplitude at each vibration mode shape is a clue to find the resonance frequencies. The dynamic elastic constant of test material can be easily estimated from Euler-Bernoulli equation using the measured resonance frequencies. The TA-ESPI dynamic elastic constant measurement technique is able to give high accurate elastic modulus of materials through a simple experiment and analysis.

• Smart Structures and Systems
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• v.7 no.5
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• pp.417-432
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• 2011

The present paper is devoted to vibration canceling and shape control of piezoelastic slender beams. Taking into account the presence of electric networks, an extended electromechanically coupled Bernoulli-Euler beam theory for passive piezoelectric composite structures is shortly introduced in the first part of our contribution. The second part of the paper deals with the concept of passive shape control of beams using shaped piezoelectric layers and tuned inductive networks. It is shown that an impedance matching and a shaping condition must be fulfilled in order to perfectly cancel vibrations due to an arbitrary harmonic load for a specific frequency. As a main result of the present paper, the correctness of the theory of passive shape control is demonstrated for a harmonically excited piezoelelastic cantilever by a finite element calculation based on one-dimensional Bernoulli-Euler beam elements, as well as by the commercial finite element code of ANSYS using three-dimensional solid elements. Finally, an outlook for the practical importance of the passive shape control concept is given: It is shown that harmonic vibrations of a beam with properly shaped layers according to the presented passive shape control theory, which are attached to an resistor-inductive circuit (RL-circuit), can be significantly reduced over a large frequency range compared to a beam with uniformly distributed piezoelectric layers.