• Smart Structures and Systems
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• v.30 no.2
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• pp.135-143
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• 2022

The object of this paper is to investigate the free vibration behavior under the effect of carbon nanotube distribution in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) by using higher-order shear deformation theories. In this work, we present a novel distribution method for carbon nanotubes in the polymer matrix by using a new exponential power law distribution of carbon nanotube volume fraction. It is assumed that the SWCNTs are aligned along the beam axial direction and the distribution of the SWCNTs may vary through the thickness of the beam with different patterns of reinforcement. The rule of mixtures is used in order to obtain material properties of the CNTRC beams. Hamilton's principle is used in deriving the equations of motion. The validity of the free Vibration results is examined by comparing them with those of the known data in the literature. The results that obtained indicate that the carbon nanotube volume fraction distribution play a very important role on the free vibrations characteristics of the CNTRC beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.388-395
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• 2000

Axial fans are widely used in heavy machines due to their ability to produce high flow rate for cooling of engines. At the same time, the noise generated by these fans causes one of the most serious problems. This work is concerned with the low noise technique of discrete frequency noise. The prediction model, which allowed the calculation of acoustic pressure at the blade passing frequency and it's harmonics, has been developed by Farrasat. This theory is founded upon the acoustic radiation of unsteady forces acting on blade. To calculate the unsteady resultant force over the fan blade. Time-Marching Free-Wake Method are used. The ideas of low noise technique are obtained from Blade-Momentum Methods. In this paper, the discussion is confined to the performance and discrete noise of axial fan in heavy equipments.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.415-425
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• 2011

In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, $N_r$. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case.

• Structural Engineering and Mechanics
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• v.47 no.3
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• pp.345-359
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• 2013

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.

• Journal of KSNVE
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• v.8 no.5
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• pp.936-948
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• 1998

A theoretical formulation for the analysis of free vibration of a cylindrical shell with a circular plate attached at an arbitrary axial position of the shell under various kinds of boundary conditions was derived and programed to get the numerical results for natural frequencies and mode shapes of the combined system. The boundary conditions of the shell to be considered here are clamped-free, clamped-simply supported, both ends clamped and both ends simply supported. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. The results showed good agreement with those of ANSYS in frequencies and mode shapes. The program will contribute to the design optimization of a shell/plate combined system through the analysis of natural frequencies and mode shapes for the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.846-851
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• 2003

The differential equations governing free, in-plane vibrations of non-circular arches with non-uniform cross-section, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies. The lowest four natural frequencies are calculated for the prime parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. Three general taper types for rectangular section are considered. A wide range of arch rise to span length ratios, slenderness ratios, and section ratios are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.

• Steel and Composite Structures
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• v.33 no.3
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.695-700
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• 2000

The dynamic stability of spinning beam with free boundary conditions for both edges subjected to a tip follower force $P_0+P_1cos{\Omega}t$ is analyzed. It is studied that the beam has a concentrated mass. and then the effects of the axial locations of the mass are studied. The beam is modelled with the Timoshenko type shear deformations. The Hamilton's principle is used to derive the equations of motion, and the critical spinning speed of a beam subjected to a follower force with various non-dimensional parameters is investigated. The finite elements are used with $C^0$ continuity to analyze the spinning beam model, and the method of multiple scales is tried to investigate the dynamic instability regions. The governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The result shows that the concentrated mass increases the dynamic stability of the spinning free-free beam subjected to a thrust.

• Advances in nano research
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• v.6 no.4
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• pp.323-337
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• 2018

The nonlinear free vibration of a nanorod subjected to finite strain is investigated. The governing equation of motion in material configuration in terms of displacement is determined. By means of Galerkin method, the Fourier series solutions satisfying some typical boundary conditions are determined. The amplitude-frequency relationship and interaction between the modes are studied. The effects of nonlocal elasticity are shown for different length of nanotubes and nonlocal parameter. The results show that nonlocal effects lead to additional internal modal interaction for nanorod vibrations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.11
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• pp.852-859
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• 2003

In order to meet the growing demands for higher storage density as well as lower noise level, the spindles in hard disk drives are to be supported by hydrodynamic bearings in place of conventional ball-type ones. However, the existing models are inappropriate to apply to accurate prediction of vibration characteristics because the HDD spindle tends to take quite a complex shape to secure its performance and cost-effectiveness. In this context, this paper treats analysis of free and forced vibrations of such-designed HDD spindles based on more sophisticated models and validations via experiments. Remarkably, to this end all the components in the system are modeled as elastic adopting the finite element method.