• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.240-244
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• 2005

In this study a simple model is developed that predicts impact damage in a composite laminate using an analytical model. The model uses a non-linear approximation method (Rayleigh-Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point impact load at its centre. It is assumed that the deformation due to a static transverse load is similar to that occurred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with FEM predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture mechanics model developed by the second investigator and co-workers to calculate the compression after impact strength of such laminates. This approach could save significant running time when compared to FEM solutions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.3
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• pp.244-252
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• 2004

The theoretical method is developed to investigate the vibration characteristics for the partially fluid-filled continuous cylindrical shells with the intermediate supports. The intermediate supports are simulated by two types of artificial springs : the translational spring for the translation for each direction and the rotational spring for a rotation. The springs are continuously distributed along the circumferential direction. By allowing the spring stiffness to become very high compared to the stiffness of the structure, the rigid intermediate supports are approximated. In the theoretical procedure, the Love's thin shell theory is adopted to formulate the theoretical model. The frequency equation of the continuous cylindrical shell is derived by the Rayleigh-Ritz approach based on the energy method. Comparison and convergence studies are carried out to verify and establish the appropriate number of series term and the artificial spring stiffness to produce results with an acceptable order of accuracy. The effect of intermediate supports, their positions and fluid level on the natural frequencies and mode shapes are studied.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Steel and Composite Structures
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• v.35 no.3
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• pp.405-413
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• 2020

Current study on the buckling analysis of steel plate in composite structures normally focuses on applying finite element method to derive the buckling stress. However, it is time consuming, computationally complicated and tedious for general use in design by civil engineers. Therefore, in this study an analytical study is conducted to predict the buckling behavior of steel plates in composite structures. Hand calculation method was proposed based on energy principle. Novel buckling shapes with biquadratic functions along both loaded and unloaded direction were proposed to satisfy the boundary condition. Explicit solutions for predicting the critical local buckling stress of steel plate is obtained based on the Rayleigh-Ritz approach. The obtained results are compared with both experimental and numerical data. Good agreement has been achieved. Furthermore, the influences of key factors such as aspect ratio, width to thickness ratio, and elastic restraint stiffness on the local buckling performance are comprehensively discussed.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.5
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• pp.793-800
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• 2006

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.401-411
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• 2005

The influence of cracks on the elastic deflection and ultimate bearing capacity of eccentric thin-walled columns with both ends pinned was studied in this paper. First, a method was developed and applied to determine the elastic deflection of the eccentric thin-walled columns containing some model-I cracks. A trigonometric series solution of the elastic deflection equation was obtained by the Rayleigh-Ritz energy method. Compared with the solution presented in Okamura (1981), this solution meets the needs of compatibility of deformation and is useful for thin-walled columns. Second, a two-criteria approach to determine the stability factor ${\varphi}$ has been suggested and its analytical formula has been derived. Finally, as an example, box columns with a center through-wall crack were analyzed and calculated. The effects of cracks on both the maximum deflection and the stability coefficient ${\varphi}$ for various crack lengths or eccentricities were illustrated and discussed. The analytical and numerical results of tests on the columns show that the deflection increment caused by the cracks increases with increased crack length or eccentricity, and the critical transition crack length from yielding failure to fracture failure ${\xi}_c$ is found to decrease with an increase of the slenderness ratio or eccentricity.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1A
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• pp.125-133
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• 2008

According to longer and longer span, dynamic instability of stay cable should be prevented. Dynamic instability occurs mainly symmetric 1st mode and antisymmetric 1st mode in stay cable. Especially symmetric 1st mode has a lot of influence on sag. Therefore fundamental frequency of stay cable is different from that of taut sting. Irvine, Triantafyllou, Ahn etc. analyzed dynamic behavior of taut cable with sag through analytical technical and their researches give important results for large bounds of Irvine parameter. But each research shows mutually different values out of characteristic (cross-over or mode-coupled) point and each solution of frequency equations of all researchers can be very difficultly found because of their very high non-linearity. Presented study focuses on fundamental frequency of stay cable. Generalized mechanical energy with symmetric 1st mode vibration shape satisfied boundary conditions is evolved by Rayleigh-Ritz method. It is possible to give linear analytic solution within characteristic point. Error by this approach shows only below 3% at characteristic point against existing researches. And taut cable don't exceed characteristic point. I.e. high accuracy, easy solving techniques, and a little bit limitations. Therefore presented study can be announced that it is good study ergonomically.

• Advances in nano research
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• v.16 no.6
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• pp.565-577
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• 2024

Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. 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. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.3
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• pp.116-125
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• 1995

In ship and of offshore structures, there exist many local panels of various shapes having many kinds of attachments reducible to damped spring-mass systems. For the vibration analysis of panels, analytical methods such as Rayleight-Ritz method or the assumed mode method can be efficiently applied. There have been many studies on the vibration analysis of rectangular panels using the analytical methods but relatively few for arbitrary shape panels. An efficient formulation based on the assumed mode method is presented for the vibration analysis of an arbitrary quadrangular plate having concentrated masses, supporting springs such as pillars and spring-mass systems. In the formulation, the natural coordinate system is used for the efficient treatment of an arbitrary quadrangular shape. Through some numerical calculations, accuracy and efficiency of the presented method are shown.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.565-573
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• 2007

This paper is concerned with the dynamic modeling, active vibration controller design and experiments for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Rayleigh-Ritz method based on Donnel-Mushtari shell theory. The actuator and sensors for the MFC actuator equations were derived based on pin-force model. The equations of motion were then reduced to modal equations of motion by considering the modes of interest. The sensor equations were also converted to a reduced form. An aluminum shell was fabricated to demonstrate the effectiveness of modeling and control techniques. The boundary conditions at both ends of the shell were assumed to be shear diaphragm. Theoretical natural frequencies were calculated and compared to experimental result. It was observed that the theoretical result is in good agreement with experimental result for the first two modes. The multi-input and multi-output positive position feedback controller, which can cope with first two modes, was then designed based on the blockinverse theory and implemented using DSP. It was found from experiment that vibrations can be successfully suppressed.