• Journal of Mechanical Science and Technology
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• v.17 no.8
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• pp.1156-1163
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• 2003

The pseudospectral method is applied to the analysis of in-plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of rectangular and circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions and the results are compared with those by transfer matrix method. The present method gives good accuracy with only a limited number of collocation points.

• Journal of KSNVE
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• v.4 no.4
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• pp.451-457
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• 1994

A numerical method is presented to obtain natural frequencies and mode shapes of uniform elastic beams with static deflections due to dead loads. The differential equation governing the free vibration of beam taken into account the static deflection due to deal loads is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged end constraints are applied in the numerical examples. As the numerical results, the lowest three nondimensional frequency parameters are reported as functions of nondimensional system parameters; the load parameters, and the slenderness rations. And some typical mode shapes of free vibrations are also presented in figures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.1
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• pp.66-73
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• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.223-233
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• 2012

This paper deals with free vibrations of the tapered Timoshenko beam with constant volume, in which both the rotatory inertia and shear deformation are included. The cross section of the tapered beam is chosen as the regular polygon cross section whose depth is varied with the parabolic function. The ordinary differential equations governing free vibrations of such beam are derived based on the Timoshenko beam theory by decomposing the displacements. Governing equations are solved for determining the natural frequencies corresponding with their mode shapes. In the numerical examples, three end constraints of the hinged-hinged, hinged-clamped and clamped-clamped ends are considered. The effects of various beam parameters on natural frequencies are extensively discussed. The mode shapes of both the deflections and stress resultants are presented, in which the composing rates due to bending rotation and shear deformation are determined.

• Advances in concrete construction
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• v.9 no.6
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• pp.557-568
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• 2020

In this study, the impact of ring supports around the shell circumferential has been examined for their various positions along the shell axial length using Rayleigh-Ritz formulation. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the ring supports is investigated at various positions. These variations have been plotted against the locations of ring supports for three values of length-to-diameter ratios. Effect of ring supports with middle layer thickness is presented using the Rayleigh-Ritz procedure with three different conditions. The influence of the positions of ring supports for clamped-clamped is more visible than simply supported and clamped-free end conditions. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. The Lagrangian functional is created by adding the energy expressions for the shell and rings. The axial modal deformations are approximated by making use of the beam functions. The comparisons of frequencies have been made for efficiency and robustness for the present numerical procedure. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported frequency curves are higher than that of clamped-simply curves. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• 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.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.12
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• pp.1190-1199
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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 2nd, 3rd and 4th 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.

• Journal of KSNVE
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• v.9 no.5
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• pp.1012-1018
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• 1999

This paper deals with the coupled flexural-torsional vibrations of Timoshenko beams with monosymmetric cross-section. The governing differtial equations for free vibration of such beams are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for three specific examples of beams with free-free, clamped-free, hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effect of warping stiffess on the natural frequencies and mode shapes is discussed and it is concluded that substantial error can be incurred if the effect is ignored.