• Structural Engineering and Mechanics
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• 제21권3호
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• pp.351-367
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• 2005

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

• Journal of Ginseng Research
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• 제16권2호
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• pp.129-137
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• 1992

This study was carried out to investigate the localization of lipids and lipase activity with lipid staining and cytochemical technique in endosperm cells of Panax ginseng C.A. Meyer seed. In endosperm cells of indehiscent seed, protein bodies facing the umbiliform layer are different in electron density during the various degraded processes. Gradually, protein matrix near the cell wall was lysed and electron lucent inclusions appeared on umbiliform layer. The protein body with high electron density and the spherosome with low electron density were observed in endosperm cells. As a result of lipid staining, electron density of spherosome is more intense than those of the protein matrix within the protein body in endosperm cells of indehiscent seed. Free spherical spherosomes within the umbiliform layer have a high electron density. The spherical spherosomes were more electron densed and were uniform in comparison with the cytoplasmic proteinaceous granules in endosperm cells of seed with red seed coat. The major component of spherosome was determined to be lipid. Lipase activity occurs in the spherosome and near the endosperm cell wall facing the umbiliform layer. Cytochemical reaction products of lipase were observed in the spherosome membrane and in the inner regions of spherosome. After protein bodies were digested, lipase activities were observed in free spherosomes and near the cell wall of endosperm cells. Umbiliform layer composing of fibrillized wall and digested materials of the endosperm cell showed a little lipase reaction products.

• Journal of Advanced Marine Engineering and Technology
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• 제7권1호
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• pp.49-63
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• 1983

Coupled transverse shaft vibrations have become the target of great concern in high powered ships such as container ships. Due to increasing ship's dimensions and high propulsive power, resonance frequencies of the propeller shaft system tend to decrease and can appear in some cases within the operating speed range of engine. In this connection, the coupled free transverse vibrations of shaft system in two planes are theoretically investigated. This shaft system carries a number of discs and is flexibly supported by a number of bearing stiffness are considered for the calculation. Transfer matrix method is applied to calculate the shaft responses in both planes. A digital computer program is developed to calculate the shaft responses of the coupled transverse vibrations in two planes. An experimental model shaft system is made. It is composed of a disc, shafts, ball bearings thrust bearings and flexible bearing supports. The shaft system is excited by an electrical magnet, and shaft vibration responses in two planes are measured with the strain gage system. From these measurements, the natural frequencies of the shaft system in both planes are found out. The developed program is also used to calculate the shaft vibration responses of experimental model shaft system. From the results of these calculations, the natural frequencies of shaft system in two planes are derived. Theoretical predictions of model shaft natural frequencies show good agreements with its esperimental measurements.

• Steel and Composite Structures
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• 제45권3호
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• pp.331-348
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• 2022

The main goal of this article is to develop the finite element formulation based on the nonlocal strain gradient and the refined higher-order deformation theory employing a new function f(z) to investigate the static bending and free vibration of functionally graded porous (FGP) nanobeams. The proposed model considers the simultaneous effects of two parameters: nonlocal and strain gradient coefficients. The nanobeam is made by FGP material that exists in un-even and logarithmic-uneven distribution. The governing equation of the nanobeam is established based on Hamilton's principle. The authors use a 2-node beam element, each node with 8 degrees of freedom (DOFs) approximated by the C¹ and C² continuous Hermit functions to obtain the elemental stiffness matrix and mass matrix. The accuracy of the proposed model is tested by comparison with the results of reputable published works. From here, the influences of the parameters: nonlocal elasticity, strain gradient, porosity, and boundary conditions are studied.

• Advances in nano research
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• 제16권1호
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• pp.11-26
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• 2024

In this study, free vibration analysis of FG porous spherical cap reinforced by graphene platelets resting on Winkler-type elastic foundation has been surveyed for the first time. Three different types of porosity patterns are considered for the spherical cap whose two types of porosity patterns in the metal matrix are symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in the metal matrix. Tsai-Halpin and extended rule of the mixture are used to determine the Young modulus and mass density of the shell, respectively. Employing 3D FEM elasticity in conjunction with Hamilton's Principle, the governing motion equations of the structure are obtained and solved. The impact of various parameters including porosity coefficient, various porosity distributions in conjunction with different GPL patterns, the weight fraction of graphene Nano fillers, polar angles and stiffness coefficient of elastic foundation on natural frequencies of FG porous spherical cap reinforced by GPLs have been reported for the first time.

• 대한조선학회논문집
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• 제42권4호
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• pp.396-401
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• 2005

In this study, the assumed mode method using characteristic polynomials of Timoshenko beam is applied to the free vibration analysis for the stiffened plate of ship tank side in contact with water. The hydro-elastic effect of the fluid-structure interaction is considered by fluid velocity potential, derived from boundary conditions for fluid and structure, and utilized in the calculation of added mass matrix using assumed modes. To verify the validity and effectiveness of the presented method, free vibration analysis for the stiffened plates in contact with finite and infinite fluids have been carried out and its results were compared with those obtained by a general purpose FEA software.

• Journal of Plant Biology
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• 제36권4호
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• pp.313-319
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• 1993

Photoproduction of hydrogen by free and polyvinylalcohol (PVA)-immobilized spinach chloroplasts was investigated. Immobilization of chloroplast with PVA increased the functional stability of the chloroplast during storage. PVA-immobilized chloroplasts preserved photosynthetic electron transport activity much better than free chloroplasts. The hydrogen production of free chloroplast decreased to 17% of initial activity after storage of six days. The hydrogen production of the PVA-immobilized chloroplast, however, showed 44% of initial activity after storage of 15 days. The maximal rate of hydrogen production was accomplished at 2$^{\circ}C$ under the light intensity above 116 $\mu$E.m-2.s-1. The amount of hydrogen produced was proportional to the chlorophyll concentration. The hydrogen production was inhibited by DCMU treatment, indicating hydrogen production is dependent on photosynthetic electron transport. These results suggest that PVA is a good candidate for the immobilization matrix of chloroplasts for the photoproduction of hydrogen.

• 전기학회논문지
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• 제58권7호
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• pp.1411-1417
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• 2009

In this paper, we consider the design of $H_{\infty}$ control of linear discrete-time systems having no mathematical model. The basic approach is to use Q-learning which is a reinforcement learning method based on actor-critic structure. The model-free control design is to use not the mathematical model of the system but the informations on states and inputs. As a result, the derived iterative algorithm is expressed as linear matrix inequalities(LMI) of measured data from system states and inputs. It is shown that, for a sufficiently rich enough disturbance, this algorithm converges to the standard $H_{\infty}$ control solution obtained using the exact system model. A simple numerical example is given to show the usefulness of our result on practical application.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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• pp.353-358
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• 1998

In general, we have used the finite element method(FEM) to find natural frequencies of plates. In this method, however, it is necessary to use a large amount of computer memory and computation time because the FEM requires many degrees of freedom for finding natural frequencies of plates correctly. Therefore it was very difficult to analyze the free vibration of plates correctly on personal computer. For overcoming this disadvantage of the FEM, the authors have developed the finite element-transfer stiffness coefficient method(FE-TSCM) which is based on the concept of modeling techniques in the FEM and the transfer of the stiffness coefficient in the transfer stiffness coefficient method. In this paper, we formulate free vibration analysis algorithm of rectangular plates using the FE-TSCM. Some numerical examples of rectangular plates are proposed, and their results and computation times obtained by the FE-TSCM are compared with those by the FEM and the finite element-transfer matrix method in order to demonstrate the accuracy and efficiency of the FE-TSCM.

• 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.