• Advances in nano research
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• v.10 no.2
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• pp.165-174
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• 2021

This paper based on Sanders theory aims to investigate the vibration of SWCNTs considering the clamped-simply supported, clamped-free, clamped-clamped and simply supported-simply supported end conditions. After developing the governing equation of the objective system, the Rayleigh-Ritz technique is implemented for the purpose of obtaining the frequency equation in the eigen form. In addition, the applicability of this model for the analysis of vibration of CNTs is examined with the effect of length and ratio of height-to-radius. A detailed description of different types of SWCNTs with different indices is provided in the theoretical methodology. The effect of extended length is stimulated with increasing the radii and the model is effective because it also predicts the effect of thickness on vibration of SWCNTs. For different boundary conditions, the present results are verified with earlier literature.

• Geomechanics and Engineering
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• v.35 no.5
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• pp.465-473
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• 2023

The higher order shear deformable model and an exact analytical method is used for analytical bending analysis of a cylindrical shell subjected to mechanical loads, in this work. The shell is modelled using sinusoidal bivariate shear strain theory, and the static governing equations are derived using changes in virtual work. The eigenvalue-eigenvector method is used to exactly solve the governing equations for a constrained cylindrical shell The proposed kinematic relation decomposes the radial displacement into bending, shearing and stretching functions. The main advantage of the method presented in this work is the study of the effect of clamping constraints on the local stresses at the ends. Stress, strain, and deformation analysis of shells through thickness and length.

• The Journal of the Acoustical Society of Korea
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• v.37 no.6
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• pp.422-427
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• 2018

The purpose of this study is to investigate the effect of acoustic radiation force on the standing wave acoustic levitation phenomenon, which is the levitation of small objects near the pressure node of the standing wave, using the Bernoulli principle. The source and scheme of the acoustic radiation force, which is the cause of the levitation, are conceptually explained through comparison with the graph of the acoustic radiation force versus the distance from the transducer. A series of experiments supporting this explanation was performed with a BLT(Bolt-clamped Langevin Type) ultrasonic transducer to confirm that the objects are floating near the pressure nodes and that it satisfies the condition for the standing wave formation when the object is levitating. Furthermore, the vertical alignment of floating objects, which is a characteristic of standing wave acoustic levitation phenomenon, could be explained.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.399-406
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• 2006

The natural frequencies of Al square plates with a brass inclusion were analyzed by the rule of mixtures. The rule of mixtures is the method to derive natural frequency mutiplying effective inplane wane speed and nondimensional frequency parameters. Numerical models were Al square plates with an inclusion with cantilever type, 2 clamped edge-2 free edge type, 3 clamped edge-1 free edge type and fully clamped edge type. In cantilever type plates, 2 clamped edge-2 free edge type plates and 3 clamped edge-1 free edge plates with an inclusion, good agreement within 10% obtained from rule of mixtures' results and numerical analysis results within inclusion area ratio 1/9. It was found that the natural frequencies of the cantilever type, 2 clamped edge-2 free edge type and 3 clamped edge-1 free edge type plates with an inclusion decrease as the size of inclusion increases when inclusion is located center of plates. And when the density of inclusion is less than the plates, natural frequency of plates with an inclusion increases as the size of inclusion increases.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2010.10a
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• pp.101-109
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• 2010

This paper reports active control of clamped beams using acceleration feedback controllers (AF). The equations of motion of clamped beam under force and moment pairs were derived and the equations of AF controllers were formulated. The effect of the parameters - gain and damping ratio - of the AF controllers on the open loop transfer function was investigated mainly in terms of the system stability. Increasing the gain of the AF controller tuned at a mode, the magnitude of the open loop transfer function is increased at all frequencies. The increase of the damping ratio of the AF controller leads to decrease the magnitude of the open loop transfer function and modifies its phase characteristics to be more stable. Three AF controllers connected in parallel were then proposed. Each AF controller is tuned at the $2^{nd}$, $3^{rd}$ and $4^{th}$ modes, respectively. Their parameters were determined to remain the system to be stable based on the results of the parametric study. A significant reduction in vibration at the 3 modes can be obtained.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.202-213
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• 1999

Effects of the rotary inertia of concentrated masses on the natural vibrations of fluid conveying pipes have been studied by theoretical modeling and computer simulation. For analysis, two boundary conditions for pipe ends, simply supported and clamped-clamped, are assumed and Galerkin's method is used for transformation of the governing equation to the eigenvalues problem and the natural frequencies and mode shapes for the system have been calculated by using the newly developed computer code. Moreover, the critical velocities related to a system instability have been investigated. The main conclusions for the present study are (1) Rotary inertia gives much change on the higher natural frequencies and mode shapes and its effect is visible when it has small value, (2) The number and location of nodes can be changed by rotary inertia, (3) By introducing rotary inertia, the second natural frequency approaches to the first as the location of the concentrated mass approaches to the midspan of the pipe, and (4) The critical fluid velocities to initiate the system unstable are unchanged by introduction of rotary inertia and the first three velocities are $\pi$, 2$\pi$, and 3$\pi$ for the simply supported pipe and 2$\pi$, 8.99, and 12.57 for the clamped-clamped pipe.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.6
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• pp.122-129
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• 2000

The purpose of this study is to investigate both the fundamental and some higher natural frequencies and mode shapes of compressive members resting on the linear elastic foundation. The model of compressive member is based on the classical Bernoulli-Euler beam theory. The differential equation governing free vibrations of such members subjected to an axial load is derived and solved numerically for calculating the natural frequencies and mode shapes. The Improved Euler method is used to integrate the differential equation and the Determinant Search method combined with the Regula-Falsi method to determine the natural frequencies, respectively. In numerical examples, the hinged-hinged, hinged-clamped, clamped-hinged and clamped-clamped end constraints are considered. The convergence analysis is conducted for determining the available step size in the Improved Euler method. The validation of theories developed herein is also conducted by comparing the numerical results between this study and SAP 90. The non-dimensional frequency parameters are presented as the non-dimensional system parameters: section ratio, modulus parameter and load parameter. Also typical mode shapes are presented.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.9-20
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• 1999

An accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and free edge conditions. The prime focus here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners having obtuse angles of the rhombic plates. Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough obtuse angle of 165$^{\circ}$, so that a significant influence of clamped-free corner stress singularities may be understood.

• ETRI Journal
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• v.31 no.4
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• pp.478-480
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• 2009

The design of a CMOS clamped-clamped beam resonator along with a full custom integrated differential amplifier, monolithically fabricated with a commercial 0.35 ${\mu}m$ CMOS technology, is presented. The implemented amplifier, which minimizes the negative effect of the parasitic capacitance, enhances the electrical MEMS characterization, obtaining a $48{\times}10^8$ resonant frequency-quality factor product ($Q{\times}f_{res}$) in air conditions, which is quite competitive in comparison with existing CMOS-MEMS resonators.

• Smart Structures and Systems
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• v.19 no.3
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• pp.243-257
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• 2017

In this paper, free vibration of functionally graded (FG) size-dependent nanobeams is studied within the framework of nonlocal Timoshenko beam model. It is assumed that material properties of the FG nanobeam, vary continuously through the thickness according to a power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The non-classical governing differential equations of motion are derived through Hamilton's principle and they are solved utilizing both Navier-based analytical method and an efficient and semi-analytical technique called differential transformation method (DTM). Various types of boundary conditions such as simply-supported, clamped-clamped, clamped-simply and clamped-free are assumed for edge supports. The good agreement between the presented DTM and analytical results of this article and those available in the literature validated the presented approach. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The obtained results show the significance of the material graduation, nonlocal effect, slenderness ratio and boundary conditions on the vibration characteristics of FG nanobeams.