• Structural Engineering and Mechanics
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• v.10 no.5
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• pp.427-440
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• 2000

The formulas for the perturbation analysis with modes of close eigenvalues are derived in this paper. Emphasis is made on the consistency of the straightforward perturbation process, given the complete terms of perturbations in the zeroth-order, which is a form of Rayleigh quotient, and in the higher-orders. By dividing the perturbation of eigenvector into two parts, the first-order perturbation with respect to the modes of close eigenvalues is moved into the zeroth-order perturbation. The normality condition is employed to compute the higher-order perturbations of eigenvector. The algorithm can be condensed to a single mode with a distinct eigenvalue, and this can accelerate the convergence of the perturbation analysis. The example confirms that the perturbation approximation obtained from the suggested procedure is in a good accuracy on the eigenvalues, eigenvectors, and normality.

• Journal of KSNVE
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• v.9 no.2
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• pp.340-347
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• 1999

The acoustic performance of reactive type single expansion chamber can be calculated theoretically by plane wave theory. But higher order model should be considered to widen the frequency range. Mode matching method has been developed to consider higher order modes, but very complicated algebra should be used. Munjal suggested a numerical collocation method, which can overcome the shortcomings of mode matching method, using the compatibility conditions for acoustic pressure and particle velocity at the junctions of area discontinuities. But the restriction of Munjal's method is that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In this paper, the new method was suggested to overcome the shortcomings of Munjal's method. The predictions by this method was also compared with those by the finite element method and Munjal's method in order to demonstrate the accuracy of the modified method presented here.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.6
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• pp.731-739
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• 2012

Transverse electric modes in parallel plate waveguide of which cut-off frequency is much lower than that of $TE_1$ and $TM_1$ mode generally known as the lowest higher order mode are investigated. Electric and magnetic field components of the modes are evaluated with the assumption that boundaries at both sides are perfect magnetic conductor. The existence of these modes are verified by simulation and experimental measurement of parallel plate waveguide cavity. Changed characteristics from the fact that the boundaries are imperfect are studied.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.8
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• pp.1621-1628
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• 2003

Packaging structures to block the propagation of higher­order modes in the shielded microstrip lines are designed. Packaging for microwave circuits is necessary, basically, to isolate and protect circuits from outside environments both physically and electrically. The drawback of packaging is the possibility of higher­order mode propagation, similar to waveguide modes, as the operating frequency increases. One of Possible choices for the higher­order mode suppression is to insert diaphragms to the housing structure. The shielding effects of diaphragms are analyzed using an FEM code. Several parameters such as dispersion, mode conversion, and higher­order mode transmission and reflection are analyzed. The effect of higher­order mode suppression is eminent as the depth or width of a diaphragm is increased in the air region of the microstrip line. It is shown that inductive diaphragm structure can lower ${S_21}$ for the second­order mode incidence by 30㏈, comparing with the conventional capacitive diaphragm structure. Packaging structure analyzed in this paper can be applied usefully to the design of the microwave system in a package such as transmit/receive modules.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.423-435
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• 2022

In this article, we present torsion-bending analysis of a composite FGM beam with an open section, according to the advanced and refined theory of 1D / 3D beams based on the 3D Saint-Venant's solution and taking into account the edge effects. The (initially one-dimensional) model contains a set of three-dimensional (3D) displacement modes of the cross section, reflecting its 3D mechanical behaviour. The modes are taken into account depending on the mechanical characteristics and the geometrical form of the cross-section of the composite FGM beam. The model considered is implemented on the CSB (Cross-Section and Beam Analysis) software package. It is based on the RBT/SV theory (Refined Beam Theory on Saint-Venant principle) of FGM beams. The mechanical and physical characteristics of the FGM beam continuously vary, depending on a power-law distribution, across the thickness of the beam. We compare the numerical results obtained by the three-beam theories, namely: The Classical Beam Theory of Saint-Venant (Classical Beam Theory CBT), the theory of refined beams (Refined Beam Theory RBT), and the theory of refined beams, using the higher (high) modes of distortion of the cross-section (Refined Beam Theory using distorted modes RBTd). The results obtained confirm a clear difference between those obtained by the three models at the level of the supports. Further from the support, the results of RBT and RBTd are of the same order, whereas those of CBT remains far from those of higher-order theories. The 3D stresses, strains and displacements, obtained by the present study, reflect the 3D behaviour of FGM beams well, despite the initially 1D nature of the problem. A validation example also shows a very good agreement of the proposed models with other models (classical or higher-order beam theory) and Carrera Unified Formulation 1D-beam model with Lagrange Expansion functions (CUF-LE).

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• Journal of the Optical Society of Korea
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• v.18 no.6
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• pp.650-656
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• 2014

We propose a novel active fiber design for selectively generating cylindrical vector beams (CVBs) or cylindrical vector modes (CVMs) which can be applied to conventional fiber lasers. A fiber is designed to have a ring-shaped core refractive index profile which can lead to the best overlap between the active dopant distribution profile and the lowest-order CVM (LCVM) field profile. Therefore, the overlap factor (OVF) of the LCVM becomes even higher than that of the fundamental mode. We emphasize that this condition cannot be satisfied by a conventional step-index core fiber (SICF) but by the ring-doped core fiber (RDCF). Because the lasing threshold is inversely proportional to the OVF, the LCVM can predominantly be stimulated even without going through special procedures to impose extra loss mechanisms to the fundamental mode. We numerically verify that the OVF of the LCVM with the doped ions can significantly exceed that of the fundamental mode if the proposed fiber design is applied. In addition, an RDCF of the proposed fiber design can also operate in a regime containing no higher-order modes besides the LCVM, so that it can selectively and efficiently generate the LCVM without being disrupted by the parasitic lasing of the higher-order modes. We highlight that an optimized RDCF can lead to a >30 % higher OVF ratio than a SICF having the same doped area. The proposed model is expected to be useful for enhancing the efficiency of generating CVBs in an all-fiber format.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.4
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• pp.372-376
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• 2012

The most common type of the piezoelectric energy harvester is the cantilevered beam since it is attached to the host structure and tuned to the frequency of the base excitation easily. However, the excessive strain at the fixed end of cantilevered beam causes some problems such as fatigue and durability. The use of higher vibration modes of the cantilevered beam may reduce the concentration of the strain at the fixed end since the strains of higher modes are distributed along the span. The results show that the use of high vibration mode is not efficient for power generation, but it reduces the excessive strain lever at typical region to prevent the failure by fatigue.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.3
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• pp.580-594
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• 2015

Liquid sloshing in two-dimensional (2-D) and three-dimensional (3-D) rectangular tanks is simulated by using a level set method based on the finite volume method. In order to examine the effect of natural frequency modes on liquid sloshing, we considered a wide range of frequency ratios ($0.5{\leq}fr{\leq}3.2$). The frequency ratio is defined by the ratio of the excitation frequency to the natural frequency of the fluid, and covers natural frequency modes from 1 to 5. When fr = 1, which corresponds to the first mode of the natural frequency, strong liquid sloshing reveals roof impact, and significant forces are generated by the liquid in the tank. The liquid flows are mainly unidirectional. Thus, the strong bulk motion of the fluid contributes to a higher elevation of the free surface. However, at fr = 2, the sloshing is considerably suppressed, resulting in a calm wave with relatively lower elevation of the free surface, since the waves undergo destructive interference. At fr = 2, the lower peak of the free surface elevation occurs. At higher modes of $fr_3$, $fr_4$, and $fr_5$, the free surface reveals irregular deformation with nonlinear waves in every case. However, the deformation of the free surface becomes weaker at higher natural frequency modes. Finally, 3-D simulations confirm our 2-D results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.229-236
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection. which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the buckling problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The accuracy of the present element is demonstrated in the prediction of buckling loads and buckling modes of shells with multiple delaminations. The present shell element should serve as a powerful tool in the prediction of buckling loads and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.