• Title/Summary/Keyword: Rayleigh theory

Search Result 156, Processing Time 0.034 seconds

Evaluation on the Lost Prestressing Force of an External Tendon Using the Combination of FEM and HGA: I. Theory (FEM과 HGA의 조합을 이용한 외부 긴장재의 손실 긴장력 평가: I. 이론)

  • Park, Taehyo;Jang, Hang-Teak;Noh, Myung-Hyun;Park, Kyu-Sik
    • Journal of the Korea institute for structural maintenance and inspection
    • /
    • v.13 no.5 s.57
    • /
    • pp.109-120
    • /
    • 2009
  • This paper introduces a new method to estimate the loss of prestressing force for the externally prestressing tendon. The proposed method that combines of HGA and FEM is able to identify the lost tensile force of a externally prestressed tendon. The identification variables of the proposed method is a exteranlly prestressed tendon of tension, effective nominal diameter, mass per unit length and Rayleigh damping coefficients. First of all, a finite element model system is constructed to consider the effect of damping, and these variables are identified using inverse analysis technique - updating algorithm. Finally, throughout total 3 cases of numerical tests, the numerical propriety of the proposed method is verified. Here, it is seen that the errors in the estimated variables by the proposed method are about 1% except in the case of Rayleigh damping coefficients.

Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT

  • Jamali, M.;Shojaee, T.;Mohammadi, B.;Kolahchi, R.
    • Advances in nano research
    • /
    • v.7 no.6
    • /
    • pp.405-417
    • /
    • 2019
  • This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

Frequency Dependence of High-frequency Bottom Reflection Loss Measurements (고주파 해저면 반사손실의 주파수 종속성 측정)

  • 박순식;윤관섭;최지웅;나정열
    • The Journal of the Acoustical Society of Korea
    • /
    • v.22 no.8
    • /
    • pp.652-659
    • /
    • 2003
  • High-frequency(40∼120 kHz) reflection loss measurements on the water-sandy sediment with a flat interface were conducted in a water tank for various grazing angles. The water tank(5×5×5 m) was filled with a 0.5 m-thick-flat bottom of 0.5ø-mean-grain-size sand. Reflection losses, which were experimentally obtained as a function of grazing angle and frequency, were compared with the forward loss model, APL-UW model (Mourad & Jackson, 1989). For frequencies below 60 kHz, the observed losses well agree with the reflection loss model, however, in cases for frequencies above 70 kHz, the observed losses are greater by 2∼3 dB than the model results. The model calculation, which does not fully account for the vertical scale of roughness due to grain size, produce less bottom losses compared to the observations that correspond to large roughness based on the Rayleigh parameter in the wave scattering theory. In conclusion, for the same grain-size-sediment, as frequencies increase, the grainsize becomes the scale of roughness that could be very large for the frequencies above 70 kHz. Therefore, although the sea bottom was flat, we have to consider the frequency dependence of an effect of roughness within confidential interval of grain size distribution in reflection loss model.

Fluid bounding effect on FG cylindrical shell using Hankel's functions of second kind

  • Khaled Mohamed Khedher;Shahzad Ali Chattah;Mohammad Amien Khadimallah;Ikram Ahmad;Muzamal Hussain;Rana Muhammad Akram Muntazir;Mohamed Abdelaziz Salem;Ghulam Murtaza;Faisal Al-Thobiani;Muhammad Naeem Mohsin;Abeera Talib;Abdelouahed Tounsi
    • Advances in nano research
    • /
    • v.16 no.6
    • /
    • pp.565-577
    • /
    • 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.

Exact Error Rate of Dual-Channel Receiver with Remote Antenna Unit Selection in Multicell Networks

  • Wang, Qing;Liu, Ju;Zheng, Lina;Xiong, Hailiang
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.10 no.8
    • /
    • pp.3585-3601
    • /
    • 2016
  • The error rate performance of circularly distributed antenna system is studied over Nakagami-m fading channels, where a dual-channel receiver is employed for the quadrature phase shift keying signals detection. To mitigate the Co-Channel Interference (CCI) caused by the adjacent cells and to save the transmit power, this work presents remote antenna unit selection transmission based on the best channel quality and the maximized path-loss, respectively. The commonly used Gaussian and Q-function approximation method in which the CCI and the noise are assumed to be Gaussian distributed fails to depict the precise system performance according to the central limit theory. To this end, this work treats the CCI as a random variable with random variance. Since the in-phase and the quadrature components of the CCI are correlated over Nakagami-m fading channels, the dependency between the in-phase and the quadrature components is also considered for the error rate analysis. For the special case of Rayleigh fading in which the dependency between the in-phase and the quadrature components can be ignored, the closed-form error rate expressions are derived. Numerical results validate the accuracy of the theoretical analysis, and a comparison among different transmission schemes is also performed.

Modeling of Low Velocity Impact Damage in Laminated Composites (라미네이트 복합재 판의 저속 충격 손상 모델링)

  • Kong, Chang-Duk;Lee, Joung-Whan;C., Soutis
    • Proceedings of the Korean Society For Composite Materials Conference
    • /
    • 2005.04a
    • /
    • pp.240-244
    • /
    • 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.

  • PDF

An Experimental Study of Silica Particle Growth in a Coflow Diffusion Flame Utilizing Light Scattering and Local Sampling Technique (I) - Effects of Flame Temperature - (광산란과 입자포집을 이용한 동축류 확산화염 내의 실리카 입자의 성장 측정(I) - 화염온도의 영향 -)

  • Cho, Jaegeol;Lee, Jeonghoon;Kim, Hyun Woo;Choi, Mansoo
    • Transactions of the Korean Society of Mechanical Engineers B
    • /
    • v.23 no.9
    • /
    • pp.1139-1150
    • /
    • 1999
  • The evolution of silica aggregate particles in coflow diffusion flames has been studied experimentally using light scattering and thermophoretic sampling techniques. The measurements of scattering cross section from $90^{\circ}$ light scattering have been utilized to calculate the aggregate number density and volume fraction using with combination of measuring the particle size and morphology through the localized sampling and a TEM image analysis. Aggregate or particle number densities and volume fractions were calculated using Rayleigh-Debye-Gans and Mie theory for fractal aggregates and spherical particles, respectively. Of particular interests are the effects of flame temperature on the evolution of silica aggregate particles. As the flow rate of $H_2$ increases, the primary particle diameters of silica aggregates have been first decreased, but, further increase of $H_2$ flow rate causes the diameter of primary particles to increase and for sufficiently larger flow rates, the fractal aggregates finally become spherical particles. The variation of primary particle size along the upward jet centerline and the effect of burner configuration have also been studied.

Effect of Hysteresis on Interface Waves in Contact Surfaces

  • Kim, Noh-Yu;Yang, Seung-Yong
    • Journal of the Korean Society for Nondestructive Testing
    • /
    • v.30 no.6
    • /
    • pp.578-586
    • /
    • 2010
  • This paper describes a theoretical model and acoustic analysis of hysteresis of contacting surfaces subject to compression pressure. Contacting surfaces known to be nonlinear and hysteretic is considered as a simple spring that has a complex stiffness connecting discontinuous displacements between two solid contact boundaries. Mathematical formulation for 1-D interfacial wave propagation between two contacting solids is developed using the complex spring model to derive the dispersion relation between the interface wave speed and the complex interfacial stiffness. Existence of the interface wave propagating along the hysteretic interface is studied in theory and discussed by investigating the solution to the dispersion equation. Unlike the linear interface without hysteresis, there can exist only one distinct mode of interface waves for the hysteretic interface, which is anti-symmetric motion. The anti-symmetric mode of interface wave propagates with the velocity faster than the Rayleigh surface wave but less than the shear wave depending on the interfacial stiffness. If the contacting surfaces are compressed so much that the linear interfacial stiffness is very high, the hysteretic stiffness does not affect the interface wave velocity. However, it has an effect on the speed of interface wave for a loosely contact surfaces with a relatively low linear stiffness. It is also found that the phase velocity of anti-symmetric wave mode converges to the shear wave velocity in despite of the linear stiffness value if the hysteretic stiffness approaches 0.5.

Vibration Analysis of Partially Fluid-filled Continuous Cylindrical Shells with Intermediate Supports (유체가 부분적으로 채워진 내부지지 연속 원통셸의 진동해석)

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

Complex modes in damped sandwich beams using beam and elasticity theories

  • Ahmad, Naveed;Kapania, Rakesh K.
    • Advances in aircraft and spacecraft science
    • /
    • v.2 no.1
    • /
    • pp.57-76
    • /
    • 2015
  • We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.