• Steel and Composite Structures
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• v.28 no.2
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• pp.149-165
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• 2018

Using the modified couple stress theory and Euler-Bernoulli beam theory, this paper studies nonlinear vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation. Using the Hamilton's principle, the set of the governing equations are derived and solved numerically using differential quadrature method (DQM), Newark beta method and arc-length technique for all kind of the boundary conditions. First convergence and accuracy of the presented solution are demonstrated and then effects of radius of gyration, Poisson's ratio, small scale parameters, temperature changes and coefficients of the foundation on the linear and nonlinear natural frequencies and dynamic response of the microbeam are investigated.

• Smart Structures and Systems
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• v.25 no.6
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• pp.669-678
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• 2020

This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.5
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• pp.90-95
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• 2010

The dynamic instability and natural frequency of elastically restrained pipe conveying fluid with the attached mass are investigated in this paper. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using extended Hamilton's Principle. The influence of attached mass and its position on the dynamic instability of a elastically restrained pipe system is presented. Also, the critical flow velocity for the flutter and divergence due to the variation in the position and stiffness of supported spring is studied. Finally, the critical flow velocities and stability maps of the pipe conveying fluid with the attached mass are obtained by changing the parameters.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Journal of electromagnetic engineering and science
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• v.8 no.1
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• pp.6-11
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• 2008

Advances in low power design open the possibility to harvest energy from the environment to power electronic circuits. Electrical energy can be harvested from piezoelectric transducer. Piezoelectric materials can be used as mechanisms to transfer mechanical energy usually vibrating system into electrical energy that can be stored and used to power other devices. Micro- to milli-watts power can be generated from vibrating system. We developed definitive and analytical models to predict the power generated from a cantilever beam attached with piezoelectric transducer. Analytical models are pin-force method, enhanced pin-force method and Euler-Bernoulli method. Harmonic oscillations and random noise will be the two different forcing functions used to drive each system. It has been selected the best model for generating electric power based upon the analytical results obtained.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.6_spc
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• pp.721-728
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• 2016

The combined rotational and translational dynamic vibration absorbers (DVA) with no dampers for the beam vibration control can effectively isolate the vibration within the external excitation force region. This paper investigates the damping efficacy for the combined rotational and translational dynamic vibration absorbers to impose some robustness to the DVA system for the excitation force frequency variation. The beam is assumed to be subjected to a concentrated harmonic excitation force. The solution to the problem is found based on Galerkin method.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.5
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• pp.114-121
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• 2004

Recently, the finite element absolute nodal coordinate formulation (ANCF) was developed for the large deformation analysis of flexible bodies in multi-body dynamics. This formulation is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. In this paper, a computation method of dynamic stress in flexible multi-body dynamics using absolute nodal coordinate formulation is proposed. Numerical examples, based on an Euler-Bernoulli beam theory, are shown to verify the efficiency of the proposed method. This method can be applied for predicting the fatigue life of a mechanical system. Moreover, this study demonstrates that structural and multi-body dynamic models can be unified in one numerical system.

• Journal of the Korean Society for Precision Engineering
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• v.3 no.2
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• pp.28-38
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• 1986

An analytical and experimental investigation is made to the dynamic responese of a cantilever with a tip mass that models some of the basic phenomena involved in the response of a flexible manipulator with a tip mass on its free end under the given rotating motion. The system equation is derived from the Hamilton's principle on the basis of the Euler-Bernoulli hypothesis and an approximate solution is obtained from model analysis using Galerkin's method for the vibation response of the system subjected to a sudden stop after an impulsive rotation. Experiment was performed to verify the validity of the theoretical analysis. Results are given for the vibration amplitude of the free end with respect to tip mass ratio, non-dimensionalized rotating velocity, rotating angle and non- dimensionalized hub length. The rotating condition to minimize the vibration amplitude of the free end can be determined for the given basic paramenters.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.5
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• pp.121-131
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• 2008

In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid with an attached mass is investigated. Also, the effect of attached masses on the dynamic stability of a simply supported pipe conveying fluid is presented for the different positions and depth of the crack. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by the energy expressions using extended Hamilton's principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of a fracture and to be always opened during the vibrations. Finally, the critical flow velocities and stability maps of the pipe conveying fluid are obtained by changing the attached masses and crack severity. As attached masses are increased, the region of re-stabilization of the system is decreased but the region of divergence is increased.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.419-426
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• 2004

In this paper, studied about the effect of open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass, the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. Therefore, the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow is increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The position of the crack is located in the middle point of the pipe, the mid-span deflection of simply supported pipe presents maximum deflection.