• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 추계학술대회 논문집
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• pp.229-230
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• 2012

The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh-Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. The numerical results validate the proposed approach.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1997년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Fall 1997
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• pp.107-114
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• 1997

A dynamic fluid-structure-soil interaction analysis method is developed to investigate the effects of rocking motion on the seismic response of the 3-D flexible rectangular liquid storage tanks founded on the deformable ground. The governing equation of 3-D rectangular tanks subjected to the translational and rocking motions is obtained by Rayleigh-Ritz method. The dynamic stiffness matrix of the rigid surface foundation resting on the surface of a stratum are calculated by hyperelement method. The seismic responses of a 3-D flexible tank model founded on the deformable ground is calculated by combining the governing equation of the structural motion with the dynamic stiffness matrix of the rigid surface foundation.

• Structural Engineering and Mechanics
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• 제12권4호
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• pp.363-376
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• 2001

Sandwich plates are widely used in lightweight design due to their high strength and stiffness to weight ratio. Due to the heterogeneous structure of sandwich plates, they can exhibit local instabilities (wrinkling), which lead to a sudden loss of stiffness in the structure. This paper presents an analytical solution to the wrinkling problem of sandwich plates. The solution is based on the Rayleigh-Ritz method, by assuming an appropriate deformation field. In contrast to the other approaches up to now, this model takes arbitrary and different orthotropic face layers, finite core thickness and orthotropic core material into account. This approach is the first to cover the wrinkling of unsymmetric sandwiches and sandwiches composed of orthotropic FRP face layers, which are most common in advanced lightweight design. Despite the generality of the solution, the computational effort is kept within bounds. The results have been verified using other analytical solutions and unit cell 3D FE calculations.

• Steel and Composite Structures
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• 제34권2호
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• pp.289-297
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• 2020

In the present research post-buckling of a cut out plate reinforced through carbon nanotubes (CNTs) resting on an elastic foundation is studied. Material characteristics of CNTs are hypothesized to be altered within thickness orientation which are calculated according to Mori-Tanaka model. For modeling the system mathematically, first order shear deformation theory (FSDT) is applied and using energy procedure, the governing equations can be derived. With respect to Rayleigh-Ritz procedure as well as Newton-Raphson iterative scheme, the motion equations are solved and therefore, post-buckling behavior of structure will be tracked. Diverse parameters as well as their reactions on post-buckling paths focusing cut out measurement, CNT's volume fraction and agglomeration, dimension of plate and an elastic foundation are investigated. It is revealed that presence of a square cut out can affect negatively post-buckling behavior of structure. Moreover, adding nanocompsits in the matrix leads to enhancement of post-buckling response of system.

• Steel and Composite Structures
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• 제33권2호
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• pp.163-180
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• 2019

A semi analytical method is employed to analyze free vibration characteristics of uniform and stepped functionally graded circular cylindrical shells under complex boundary conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy complex boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behavior of functionally graded circular cylindrical shells were obtained by approach of Rayleigh-Ritz. To confirm the dependability and validity of present approach, numerical verifications and convergence studies are conducted on functionally graded cylindrical shells under various influencing factors such as boundaries, spring parameters et al. The present method apparently has rapid convergence ability and excellent stability, and the results of the paper are closely agreed with those obtained by FEM and published literatures.

• Steel and Composite Structures
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• 제46권2호
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• pp.203-210
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• 2023

In the present research, dynamic deflections of a sandwich beam having functionally graded (FG) porous core have been investigated assuming that the sandwich beam is exposed to a pulse load of blast type. The two layers of sandwich beam have been made of a polymeric matrix reinforced by graphene oxide powder (GOP). The micromechanical formulation of the layers has been done via Halpin-Tsai model. The solution method is chosen to be Ritz method which is an efficient method to solve the system of equations of beams modeled based on a higher-order theory. To derive the time history of sandwich beam under pulse load, Laplace method has been used. The porosity content of the core, the GOP content of the layers, thickness of the layer and also duration of the applied load have great influences of the responses of sandwich beam.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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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.

• Advances in aircraft and spacecraft science
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• 제4권4호
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• pp.449-465
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• 2017

The aim of the present work is to present a computational study of the non-linear aero-elastic behavior of a multi-layered Thermal Protection System (TPS). The severity of atmospheric re-entry conditions is due to the combination of high temperatures, high pressures and high velocities, and thus the aero-elastic behavior of flexible structures can be difficult to assess. In order to validate the specific computational model and the overall strategy for structural and aerodynamics analyses of flexible structures, the simplified TPS sample tested in the 8' High Temperature Tunnel (HTT) at NASA LaRC has been selected as a baseline for the validation of the present work. The von $K{\acute{a}}rm{\acute{a}}n^{\prime}s$ three dimensional large deflection theory for the structure and a hybrid Raleigh-Ritz-Galerkin approach, combined with the first order Piston Theory to describe the aerodynamic flow, have been used to derive the equations of motion. The paper shows that a good description of the physical behavior of the fabric is possible with the proposed approach. The model is further applied to investigate structural and aero-elastic influence of the number of the layers and the stitching pattern.

• Steel and Composite Structures
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• 제49권1호
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• pp.81-89
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• 2023

A simplified calculation method of natural vibration characteristics of high-speed railway multi-span bridge-longitudinal ballastless track system is proposed. The rail, track slab, base slab, main beam, bearing, pier, cap and pile foundation are taken into account, and the multi-span longitudinal ballastless track-beam-bearing-pier-cap-pile foundation integrated model (MBTIM) is established. The energy equation of each component of the MBTIM based on Timoshenko beam theory is constructed. Using the improved Fourier series, and the Rayleigh-Ritz method and Hamilton principle are combined to obtain the extremum of the total energy function. The simplified calculation formula of the natural vibration frequency of the MBTIM under the influence of vertical and longitudinal vibration is derived and verified by numerical methods. The influence law of the natural vibration frequency of the MBTIM is analyzed considering and not considering the participation of each component of the MBTIM, the damage of the track interlayer component and the stiffness change of each layer component. The results show that the error between the calculation results of the formula and the numerical method in this paper is less than 3%, which verifies the correctness of the method in this paper. The high-order frequency of the MBTIM is significantly affected considering the track, bridge pier, pile soil and pile cap, while considering the influence of pile cap on the low-order and high-order frequency of the MBTIM is large. The influence of component damage such as void beneath slab, mortar debonding and fastener failure on each order frequency of the MBTIM is basically the same, and the influence of component damage less than 10m on the first fourteen order frequency of the MBTIM is small. The bending stiffness of track slab and rail has no obvious influence on the natural frequency of the MBTIM, and the bending stiffness of main beam has influence on the natural frequency of the MBTIM. The bending stiffness of pier and base slab only has obvious influence on the high-order frequency of the MBTIM. The natural vibration characteristics of the MBTIM play an important guiding role in the safety analysis of high-speed train running, the damage detection of track-bridge structure and the seismic design of railway bridge.

• 한국소음진동공학회논문집
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• 제14권3호
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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.