• Advances in nano research
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• 제12권5호
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 춘계학술대회 논문집
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• pp.578-582
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• 2000

When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with the separation plate, including some experimental works. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics and the dynamic response of a fixed-free beam which has restrained motion at the free end by the separation plates. Results are presented for various magnetic forces and gaps between stops.

• Structural Engineering and Mechanics
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• 제88권5호
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

• Earthquakes and Structures
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• 제25권6호
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• pp.455-467
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• 2023

This study focuses on demonstrating the effectiveness of vibration control of tuned rotary mass damper (TRMD) for reducing the bidirectional and torsional response of the irregular asymmetric structure with voided slabs under earthquake excitations. The TRMD arranged in plane of one-story eccentric structure is proposed as a distributed tuned rotary mass damper (DTRMD) system. Lagrange's equation is used to derive the equations of motion of the controlled system. The optimum position and number of TRMD are numerically investigated under harmonic excitation and the control effects of different distributions are discussed. Furthermore, a shaking table test is conducted under different excitation cases, including free vibration, forced vibration and seismic wave to investigate the absorption performance of the device. The numerical simulations of different distributions of the TRMDs show that the DTRMDs are more effective in reduction of the displacement response of the asymmetric structure under the same mass ratio, even when the degree of eccentricity becomes large. However, with small degree of eccentricity, the unreasonable asymmetrical arrangement may cause the increase of the peak value of the rotational angular displacement. Finally, the experimental investigations exhibit similar results of translational displacement of the structure. It is concluded that the vibration of the irregular asymmetric structure can be controlled more economically and effectively by reducing the mass ratio through reducing the quantity of TRMDs at the high stiffness end.

• 소음진동
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• 제7권2호
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• pp.247-254
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• 1997

In the case of a precision equipment, it requires a vibration free environment to provide its proper function. Especially, lithography and inspection devices, which have sub-nanometer class high accuracy and resolution, have come to necessity for producing more improved giga class semiconductor wafers. This high technology equipments require very strict environmental vibration standard in proportion to the accuracy of the manufacturing, inspecting devices. The vibration criteria are usually obtained either by the real vibration exciting test on the equipment or by the analytical calculation. This paper proposes a new method to solve this problem at a time. The permissible vibration level to a precision equipment can be easily obtained by analyzing a process of Frequency Response Function. This paper also demonstrates its effectiveness by applying the proposed method to finding the vibration criteria of a Computer Hard Disk Driver by Impact Test.

• Structural Engineering and Mechanics
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• 제49권5호
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• pp.537-554
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• 2014

In this paper, free vibration of a sandwich curved beam with a functionally graded (FG) core was investigated. Closed-form formulations of two-dimensional (2D) refined higher order beam theory (RHOBT) without neglecting the amount of z/R was derived and used. The present RHOBT analysis incorporated a trapezoidal shape factor that arose due to the fact that stresses through the beam thickness were integrated over a curved surface. The solutions presented herein were compared with the available numerical and analytical solutions in the related literature and excellent agreement was obtained. Effects of some dimensionless parameters on the structural response were investigated to show their effects on fundamental natural frequency of the curved beam. In all the cases, variations of the material constant number were calculated and presented. Effect of changing ratio of core to beam thickness on the fundamental natural frequency depended on the amount of the material constant number.

• Structural Engineering and Mechanics
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• 제47권3호
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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.

• Smart Structures and Systems
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• 제4권3호
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• pp.279-290
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• 2008

The modeling and parameter estimation of a damped one-degree-of-freedom mass-spring system is examined. This paper presents a method for estimating the system parameters (damping coefficients and natural frequency) from measured free-vibration motion of a system that is modeled to include both subcritical viscous damping and kinetic Coulomb friction. The method applies a commercially available least-squares curve-fitting software function to fit the known solution of the equations of motion to the measured response. The method was tested through numerical simulation, and it was applied to experimental data collected from a laboratory mass-spring apparatus. The mass of this apparatus translates on linear bearings, which are the primary source of light inherent damping. Results indicate that the curve-fitting method is effective and accurate for both perfect and noisy measurements from a lightly damped mass-spring system.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.602-607
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• 2000

Fuel-storage tank is a representative example of liquid-structure interaction systems. In order to prevent the undesired structural failure by a variety of external loads, the reliable analysis of the dynamic response of such structural system is of a great importance. In this paper, we address the analytical study on free vibration of axisymmetric cylindrical fuel-storage tanks together with the parametric investigation of eigen-characteristics with respect to the relative fuel fill-height and the relative tank height. Numerical results illustrating theoretical results are also included.

• Structural Engineering and Mechanics
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• 제33권1호
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• pp.79-93
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• 2009

This paper investigates the possibility of controlling the response of typical portal frame structures to blast loading using a combination of semi-active and passive control devices. A one storey reinforced concrete portal frame is modelled using non-linear finite elements with each column discretised into multiple elements to capture the higher frequency modes of column vibration response that are typical features of blast responses. The model structure is subjected to blast loads of varying duration, magnitude and shape, and the critical aspects of the response are investigated over a range of structural periods in the form of blast load response spectra. It is found that the shape or length of the blast load is not a factor in the response, as long as the period is less than 25% of the fundamental structural period. Thus, blast load response can be expressed strictly as a function of the momentum applied to the structure by a blast load. The optimal device arrangements are found to be those that reduce the first peak of the structural displacement and also reduce the subsequent free vibration of the structure. Semi-active devices that do not increase base shear demands on the foundations in combination with a passive yielding tendon are found to provide the most effective control, particularly if base shear demand is an important consideration, as with older structures. The overall results are summarised as response spectra for eventual potential use within standard structural design paradigms.