• Steel and Composite Structures
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• v.20 no.5
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• pp.1023-1042
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• 2016

Based on Hamilton's principle, the flexural vibration differential equations and boundary conditions of the steel-concrete composite beam (SCCB) with comprehensive consideration of the influences of the shear deformation, interface slip and longitudinal inertia of motion were derived. The analytical natural frequencies of flexural vibration were compared with available results previously observed by the experiments, the results calculated by the FE model and the other similar beam theories available in the open literatures. The comparison results showed that, the calculation results of the analytical and Timoshenko models had a good agreement with the results of the experimental test and FE model. Finally, the influences of shear deformation and interface slip on the flexural natural frequencies of the SCCB were discussed. The shear deformation effect increases with the increase of the mode orders of flexural natural vibration, and the flexural natural frequencies of the higher mode orders ignoring the influence of shear deformations effect would be overestimated. The interface slip effect decrease with the increase of the mode orders of flexural natural vibration, and the influence of the interface slip effect on flexural natural frequencies of the low mode orders is significant. The influence of the degree of shear connection on shear deformation effect is insignificant, and the low order modes of flexural natural vibration are mainly composed of the rotational displacement of cross sections.

• Journal of KSNVE
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• v.11 no.2
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• pp.323-328
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• 2001

The paper describes a theoretical study on the flexural vibration of an elastic rectangular plate with periodically nonuniform material properties. The approximate solution of the natural frequency and mode shape has been obtained using the perturbation technique for sinusoidal modulation of the flexural rigidity and mass density. It has been shown that distributed modes exist in the plate which Is a two-dimensional model of the flat panel speaker.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.303-314
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• 2004

An artificial neural network (ANN) application is presented for flexural and axial vibration analysis of elastic beams with various support conditions. The first three natural frequencies of beams are obtained using multi layer neural network based back-propagation error learning algorithm. The natural frequencies of beams are calculated for six different boundary conditions via direct solution of governing differential equations of beams and Rayleigh's approximate method. The training of the network has been made using these data only flexural vibration case. The trained neural network, however, had been tested for cantilever beam (C-F), and both end free (F-F) in case the axial vibration, and clamped-clamped (C-C), and Guided-Pinned (G-P) support condition in case the flexural vibrations which were not included in the training set. The results found by using artificial neural network are sufficiently close to the theoretical results. It has been demonstrated that the artificial neural network approach applied in this study is highly successful for the purposes of free vibration analysis of elastic beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1333-1337
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• 2000

The flexural vibration of laminated composite beams with active and passive constrained-layer damping has been investigated to design structure with maximum possible damping capacity. The equations of motion are derived for flexural vibrations of symmetrical, multi-layer laminated beams. The damping ratio and modal damping of the first bending mode are calculated by means of iterative complex eigensolution method. This paper addresses a design strategy of laminated composite under flexural vibrations with active control.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.737-742
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• 2000

The paper describes a theoretical study on the flexural vibration of an elastic rectangular plate with periodically nonuniform material properties. The approximate solution of the natural frequency and mode shape has been obtained using the perturbation technique for sinusoidal modulation of the flexural rigidity and mass density. It has been shown that distributed modes exist in the plate which is a two-dimensional model of the flat panel speaker.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.3
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• pp.258-263
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• 2011

The direction of the cutting tool plays a critical role in elliptical vibration cutting(EVC) where the cutting tool cuts workpiece in a trochoidal motion. In this study, EVC cutting device was developed using two parallel piezoelectric materials and it was observed that the rotation direction of the tool reverses as the EVC device undergoes resonance at which either flexural(cutting direction) or longitudinal( thrust direction) mode shapes occurs. To analytically explain reversal of the rotation direction, kinematic motion analysis of the tool was modified to incorporate amplification of the vibration amplitude and phase introduced by resonance. It successfully demonstrated, through Matlab simulation, reversal of the rotation direction of the cutting tool as the excitation frequency increases beyond resonance frequencies at which either flexural or longitudinal vibration occurs.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.964-969
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• 2002

The flexural vibration of laminated composite beams with passive constrained layer damping has been investigated to design structure with maximum possible damping capacity. The equations of motion are derived for flexural vibrations of symmetrical, multi-layer laminated beams. The damping ratio and modal damping of the first bending mode are calculated by means of Iterative complex eigensolution method. This paper addresses a design strategy of laminated composite under flexural vibrations.

• Journal of the Korean Wood Science and Technology
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• v.33 no.5 s.133
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• pp.13-20
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• 2005

This paper deals with flexural vibration techniques as a means of predicting bending strength properties for quarter-sawn and flat-sawn planes of red pine containing knots. Dynamic modulus of elasticity $(MOE_d)$ was calculated from resonance frequency obtained from the flexural vibration induced by a magnetic driver in quarter-sawn and flat-sawn planes of red pine containing knots. The dynamic MOE were well correlated to bending strength properties. Their correlation coefficients ranged from 0.866 to 0.800 for the regression between dynamic MOE and static bending MOE or MOR. The difference of the values between quarter-sawn and flat-sawn was very small. These values were higher than correlation between percentage of total knot diameter to total width of red pine specimen $(K_T(%))$ as well as $K_O(%)$ base upon ASTM D 3737 and static bending strength properties (correlation coefficient r = 0.448~0.704), and were similar to those between static bending MOE and bending MOR (r = 0.850). These results indicate that dynamic MOE obtained from resonance frequency induced by flexural vibration of magnetic driver is able to effectively use for predicting of static bending strength of red pine containing knots as well as static MOE.

• Journal of Sensor Science and Technology
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• v.18 no.6
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• pp.461-466
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• 2009

This paper represents a piezoelectric ultrasonic linear actuator with flexural vibration mode. The actuator is composed of two piezo ceramics, the elastic body, and the connecting tip. It is driven by the frictional force between the connecting tip and the linear motion guide. Unimorph actuators have flexural vibration. Its middle point is fixed so that suitable to the flexural vibration of $3/2\lambda$. These vibrations contribute to elliptical motion by mixed mode between longitudinal and transverse mode. It was generated when the ultrasonic electrical signals with 90 degree phase difference are applied to two ceramics. A linear movement can be easily obtained using the elliptical motion. The ATILA, FEM simulator has been used to design actuator and verify the kinetic and dynamic analysis. We used the ceramics of $20\times10\times1$ mm size and confirmed the flexural vibration of the $3/2\lambda$ at the 79 kHz through the scanning of 3D-vibrometer. The maximum velocity of actuator was 221 mm/sec and the thrust force of actuator was 2.7 N in 200Vp-p of additional voltage.