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1.
Transverse vibrations of a rectangular orthotropic plate with a free edge while the others are supported according to four different combinations of boundary conditions are considered in the present paper. The presence of a concentrated mass is also taken into account. In view of the difficulty of satisfying exactly the natural boundary conditions at the free edge, the fundamental frequency of vibration is determined by means of the optimized Rayleigh-Ritz method and a pseudo-Fourier expansion which contains, in its argument, the optimization parameters γi. The results are in excellent agreement with those obtained by means of a finite element algorithmic procedure. 相似文献
2.
Diana V. Bambill Raúl E. Rossi Verónica Jederlinic Carlos A. Rossit 《Ocean Engineering》1997,24(1):45-49
Transverse vibrations of a rectangular plate with three edges elastically restrained against rotation while the fourth is free are studied using (a) an analytical approach based on the optimized Rayleigh-Ritz method and (b) the finite element method. The study was motivated by the necessity of finding out how the lower frequencies of vibration were affected by introducing a step discontinuity in the plate thickness. This variation in the plate thickness was practiced in order to obtain a reduction in the total plate weight. 相似文献
3.
This paper deals with the determination of an approximate fundamental frequency equation for a rectangular plate with two edges (y = 0, b) elastically restrained against rotation while the edges x=0, a are free but internal supports parallel to the free edges are present in the structural system. The algorithmic procedure can be easily implemented on a micro computer or even a hand, programmable calculator.Good engineering agreement with experimental results is shown to exist in the case of a plate with edges y=0,b rigidly clamped. 相似文献
4.
Numerical experiments are performed on the determination of the fundamental frequency of transverse vibration of simply supported rectangular plates having rectangular holes with free edges. This constitutes a rather common technological situation since holes are present in plates or slabs due to operational conditions, namely passage of conduits or ducts, electric conductors, etc., Satisfying exactly the governing natural boundary conditions at the hole edges is practically an impossible task. This study reviews numerical experiments where the displacement function is expanded into a double Fourier series which constitutes the exact solution when the plate is simply connected. Satisfactory convergence is achieved when the plate is doubly connected. 相似文献
5.
Sh. Hosseini Hashemi Mahmoud Karimi H. Rokni Damavandi Taher 《Ocean Engineering》2010,37(2-3):174-185
In this study Free vibration analysis of vertical rectangular Mindlin plates resting on Pasternak elastic foundation and fully or partially in contact with fluid on their one side is investigated for different combinations of boundary conditions. The plate is assumed to be one of vertical rectangular walls of a container in contact with fluid. In order to analyze the interaction of the Mindlin plate with the elastic foundation and fluid system, three displacement components of the plate are expressed in the Ritz method by adopting a set of static Timoshenko beam functions satisfying geometric boundary conditions in a Cartesian co-ordinate system. The method of separation of variables and the method of Fourier series expansion is used to model fluid and to obtain the exact expression of the motion of fluid in the form of integral equations. The fluid domain is finite in depth and width but infinite in the length direction. To demonstrate the accuracy of the present solution, convergence study is first carried out and then a few comparison studies are carried out with the available data in the literature. Finally, natural frequencies of rectangular plates are presented in tabular and graphical forms for different fluid levels, foundation parameters, aspect ratios, thickness to width ratios and boundary conditions. 相似文献
6.
This paper is concerned with the vibrations of a thin plate resting on a fluid-layer subjected to a moving point force. The frequency is assumed to be low and the fluid is deep. Both the fluid and the point force are always in contact with the plate. Hankel Transform and complex integration techniques are used to calculate the lateral displacements withrespect to a moving coordinate system and a coordinate transformation is used to achieve the results with respect to a fixed point. Numerical results are discussed with respect to the velocity of the moving force, its direction of movement and the fluid depth. 相似文献
7.
Wang Gang Li Zhen Chen Tieyun Ph. D. Marine Design Research Institute of China Shanghai Engineer Marine Design Research Institute of China Shanghai Professor Dept. of Naval Architecture Ocean Engineering Shanghai Jiao Tong University Shanghai 《中国海洋工程》1998,(1)
This paper concerns the dynamic plastic response of a circular plate resting on fluid subjectedto a uniformly distributed rectangular load pulse with finite deformation.It is assumed that the fluid isincompressible and inviscous,and the plate is made of rigid-plastic material and simply supported along itsedge.By using the method of the Hankel integral transformation,the nonuniform fluid resistance is de-rived as the plate and the fluid is coupled.Finally,an analytic solution for a circular plate under a mediumload is obtained according to the equations of motion of the plate with finite deformation. 相似文献
8.
The decomposition of a monochromatic wave over a submerged plate is investigated experimentally in a wave flume. Bound and free higher harmonic modes propagating upstream and downstream the structure are discriminated by means of moving resistive probes. The first-order analysis shows a resonant behaviour linked to the ratio of the plate's width and the fundamental mode wavelength over the plate. The second-order analysis shows an energy transfer from the fundamental mode towards free harmonics propagating downstream the structure. This transfer is linked to the ratio of the width of the plate and the bound harmonic wavelength over the plate. We also performed experiments with a submerged step to compare the efficiency of both structures. The submerged plate is shown to be a more efficient breakwater than the step, at the first as well as the second-order. 相似文献
9.
A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies. 相似文献
10.
The present study deals with numerical experiments performed using the doublesine Fourier expansion and the Ritz method to determine natural frequencies of vibration of simply supported rectangular plates with free rectangular holes parallel to the plate sides.The problem is of basic structural interest in naval and ocean engineering systems since holes are frequently practiced in plate-type structural elements to allow for the passage of ducts, elevators, etc… 相似文献
11.
This paper studies the moonpool resonance of two heaving rectangular bodies in a two-layer fluid. A mathematical model is proposed based on an eigenfunction matching approach. The motion of the two-dimensional bodies is assumed to be vertical and harmonic. Heave added mass and damping coefficients are computed to examine the hydrodynamic behavior of the twin bodies. The free surface and internal wave elevations are obtained near the resonant frequencies. The presented results and analyses reveal that there exist both Helmholtz and higher-order resonances in the two-layer fluid system, which is similar to the single-layer fluid case. It is also found that the resonances are closely associated with the free surface elevation inside moonpool gap, not the wave elevation at the interfacial surface. In addition, parametric studies have been performed to identify the dependencies of hydrodynamic behavior on geometry and density stratification. 相似文献
12.
A free vibration analysis of laminated composite plates carrying a distributed patch mass is analyzed and presented in this paper. The Hamilton's Principle, using third-order shear deformation theory, is applied to simply supported rectangular plates. The displacement of the plate is postulated by a double Fourier series. The effects of size and location of the distributed patch mass on the response of the plate are also presented. A thorough comparison with well known published results is presented for the case of free vibration of unloaded plates and good agreement is observed. 相似文献
13.
The radiation and diffraction problems are considered in the frequency domain for a thin elastic plate of rectangular planform floating in an irrotational, incompressible ocean of infinite depth. The inner potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion which suits the geometry and zero-draft nature of the plate. Problems associated with distributing sources in the free surface are avoided. The Chen and Mei variational principle is used to weakly match this inner solution and its normal derivative to an outer field described by distributing sources on the exterior of the hemisphere. The validity of the procedure is first illustrated by considering a heaving circular disk. Numerous hydrodynamic coefficients are presented as benchmark data for floating flexible structures. The transient motion of the plate is simulated using rational approximations (in the frequency domain) to the radiation impedance and diffraction mapping which are implemented as ODE's in the time domain. 相似文献
14.
The fundamental frequency of a rectangular isotropic plate having a linear thickness variation is computed using the method of eigensensitivity analysis. The approach incorporates eigen derivatives to evaluate a Maclaurin series representation of the desired eigenvalue, here the fundamental frequency. Comparison with published results, for various taper ratios, aspect ratios, and support conditions, demonstrates the accuracy and utility of the expression and methodology. 相似文献
15.
Sirilath J. DeSilva Ronald B. Guenther Robert T. Hudspeth 《Applied Ocean Research》1996,18(6):293-302
Oscillatory, two dimensional free-surface, irrotational flows of an incompressible fluid are treated numerically. Rather than basing the treatment on perturbation expansions, the unknown fluid domain bounded by a free surface is mapped onto a rectangular domain. This has the effect of exchanging a boundary value problem for a linear, constant coefficient Laplace equation having nonlinear boundary conditions into a nonlinear elliptic equation specified on the known rectangular domain. In the known transformed domain, compatibility conditions at the corners are derived, the boundary value problem is solved and the results are transformed back to the original domain. 相似文献
16.
Analytical leading-order solutions are given for liquid bodies that hit a rigid plate in impulsive incompressible impact. The liquid bodies are broader than the impacting plate which causes a mixed boundary condition. The initial velocity field, the corresponding pressure impulse field, and the associated virtual masses are calculated. The following liquid body geometries are studied: 2D rectangles hit symmetrically by the plate, including a case with impermeable sidewalls, asymmetric hit of a 2D rectangle, and symmetric hit of a 3D rectangular box, and of a circular cylinder. A plausible estimate for liquid impact is that a marine structure can never be struck by a greater force impulse than the momentum of incoming liquid perpendicular to its own cross section. By comparing the virtual mass with the total projected fluid mass above the plate for the different liquid body geometries, it is found that the estimate holds for all the computed cases. 相似文献
17.
A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results. 相似文献
18.
Bang-Fuh Chen 《Ocean Engineering》1999,26(1):47
A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed. 相似文献
19.
1 .IntroductionRecentlygreatinteresthasbeenshowninthedevelopmentofverylargefloatingstructuressuchasMegaFloatofJapan (Isobe ,1 999)andMOBofUSA (Remmers ,1 999) .Owingtotheirextremelargesizeandgreatflexibility ,thecouplingbetweenthestructuraldeformationandfluidmotionissignifi cant.Thisisatypicalproblemofhydroelasticity .Efficientandaccurateestimationofthehydroelasticresponseofverylargefloatingstructuresinwavesisveryimportantfordesign .Manymethodshavebeenproposedinliteratureforthepredictiono… 相似文献
20.
The title problem is solved in the case where the plate is clamped along two adjacent edges while the remaining are free. A mass is rigidly attached to the plate. The value of the fundamental frequency coefficient is conveniently minimized by means of Schmidt's approach. The methodology presented herewith can be extended without formal difficulties to other vibrating systems, e.g. the case of motors and engines elastically mounted on structural elements. 相似文献