The free vibration analysis of submerged cantilever plates

Based on empirical added mass formulation, this work presents a simple procedure to determine the vibration frequencies and mode shapes of submerged cantilever plates. Once the added mass formulation is derived, the procedure can be used to analyze free vibration response easily. An analytical and numerical study is also performed for the vibrations of cantilever plates in air and in water, with these results compared with experimental and numerical data from pertinent literature. Besides, the frequency parameters of the submerged plate for various aspect ratios and thickness ratios are given in design data sheet form and are appropriate for engineering design applications.     

Modelling a spade rudder as a hollow two-way tapered Kirchhoff’s plate : free dry and wet vibration study with numerical verification

A semi-analytical approach to free dry and wet vibration of a trapezoidal, 2-way tapered, pivoted hollow spade rudder is presented. The rudder is modeled as a hollow Kirchhoff’s plate, with a NACA0018 profile chord section. The rudder pivot is modeled as a combination of a translational spring and a rotational spring. The span-wise and chord-wise non-uniform beam vibration is first analyzed by the Rayleigh-Ritz method, to establish the non-uniform beam modeshapes, which act as admissible functions to the Galerkin’s method for plate vibration. Eigenvalue analysis generates the plate natural frequencies and the plate modeshapes. Alternately, uniform beam modeshapes themselves are used as admissible functions into the Galerkin’s method. Frequencies are analyzed for various pivot positions, taper ratios, and NACA sections. For the wet vibration, constant strength source distribution technique is used to generate the added mass of a 2D aerofoil. Also, 3D panel method is used to generate the modal added masses, and hence the wet natural frequencies. The added mass coefficient is generated for various aerofoil fineness ratios, pivot fixities, taper ratios, aspect ratios.     

Draft effect on wave action with a semi-infinite elastic plate

1Introduction Wave action on coastal and offshore structuresis investigated by many researches. In the recent pa-pers we can seen that Li et al. (2006) developed athree-dimesional(3D) numerical model for obliquewave action on vertical walls, Li et al. (20…     

Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications

This investigation arose from the practical necessity of placing a centrifugal pump rigidly attached to a thin, circular cover plate of a water tank in a medium size ocean vessel. Due to lack of space, it was necessary to locate the system off—center of the circular configuration. It was considered necessary to calculate the fundamental frequency of the coupled system.The first part of the present study is concerned with the determination of the fundamental frequency of vibration of a circular plate carrying a concentrated mass at an arbitrary position, using a variational approach.Numerical results are obtained for the stated problem for several combinations of the intervening geometric and mechanical parameters.An experimental investigation is also performed in the case of clamped plates.Based on the results for solid circular plates, the fundamental frequency of annular plates with a free inner edge and a concentrated mass is also obtained.Circular plates are fundamental structural elements in ocean engineering applications: from off-shore platforms to underwater acoustic transducers. In a great variety of circumstances, they must carry operational systems in an eccentric fashion. Since the dynamic performance is always of interest, one must know at least some of the basic dynamic parameters.     

Free vibrations of rectangular plates elastically restrained against rotation with circular or square free openings

The fundamental frequency of vibration of plates elastically restrained against rotation along the edges and with centrally located circular or square holes is determined by means of the optimized Rayleigh's method. Independent solutions are also obtained using the finite element method.A comparison with experimental values is also presented in the case where the plate is rigidly clamped along the four edges.     

Numerical experiments on the Rayleigh-Ritz method when applied to doubly connected plates in the case of free edge holes

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.     

Some additional results on vibrating, simply supported rectangular plates with free, rectangular cut-outs

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…     

Experimental study on loss factor for corrugated plates by bandwidth method

The material loss factor for technically orthotropic plates was measured by half-power bandwidth method. Rectangular and trapezoidal corrugated plates of steel were considered. A simple isotropic steel plate was also considered for comparison of the results. The concept of single degree of freedom system was adopted. The tests were undertaken at very low frequency range (0–100) Hz. The plate models were suspended freely with two wires to minimize or prevent excessive extraneous energy dissipation. Out of plane point force, random in nature was applied to the top middle of the plates and the responses were measured from the middle point of the plates by FFT analyzer using miniature small mass accelerometer as sensor. The aim of these tests is to investigate the effects of bending rigidity and mode orders over material loss factor. The values of estimated modal damping loss factors are compared and tabulated for the plates models considered. Natural frequencies of some of the initial modes of the plates are also presented.It is observed that the higher the value of bending rigidity of the plates, the larger the values of loss factor of it. There was a significant increase in value of loss factor in corrugated plates to that of the isotropic plate.     

Free surface flow impacting on an elastic structure: Experiment versus numerical simulation

The purpose of this study is to investigate the phenomenon of free surface flow impacting on elastic structures, which is a research topic of great interest in ship and ocean engineering. A series of quasi two-dimensional experiments on dam-break with an elastic plate are conducted. The main features of free surface flow impacting on elastic structures including large impacting force, structural vibration, violent free surface flow, are investigated. The coupled FDM–FEM method developed by the authors is applied for numerical simulation of such dam-break problem. Extensive analysis and discussion based on the comparisons between experimental data and numerical results are made and presented in this paper.     

变截面劲性水泥土桩承载特性室内模型试验研究

研究变截面劲性水泥土桩的几何特征对承载特性的影响,结果表明:具有1个扩大盘或2个扩大盘间距较大的变截面桩,盘下部的土体发生压缩和局部剪切破坏现象,上部的土体则发生梨形滑落;盘间距较小时,上下两盘之间的土体与两盘成为一体;变截面桩的桩侧荷载分担值均远大于桩端荷载分担值,盘的数量及间距对桩侧及桩端荷载分担值影响不大;1个盘时,其位置对承载力有一定的影响;2个等间距盘的变截面桩,盘位置越高承载力越高;盘间距对承载力影响不显著;3个盘的承载力大于2个盘的承载力,但结果相差不大;变截面桩的承载力得到显著提高,其承载力不小于与扩大盘直径相等的等截面桩;随着桩顶荷载的增大,盘承担的荷载增加显著,盘以下桩身的轴力因盘承担大部分而骤减,其降低幅度与盘的数量、位置及间距有关.     

Spar平台垂荡板水动力特性强迫振动试验研究

采用强迫振动试验的方法,对Spar平台不同振幅和不同振动频率下的附加质量系数和粘性阻尼系数进行了系统研究。分析研究了实心垂荡板和开孔垂荡板对Spar平台水动力特性的影响,并将Spar平台整体模型的试验结果与圆柱体和单独考虑垂荡板时的试验结果比较,结果表明垂荡板结构能有效提高Spar平台的附加质量系数和粘性阻尼系数,在KC=0.2～1.3时,开孔率为5%的开孔垂荡板Spar平台和实心垂荡板Spar平台相比,粘性阻尼有所提高但是附加质量减小。试验进一步研究了垂荡板间距对Spar平台水动力性能的影响,得到了水动力系数随垂荡板间距的变化情况,研究成果对实际工程中Spar平台的优化设计具有一定的指导意义。     

Analysis of vibrating orthotropic rectangular plates by a modified Rayleigh-Ritz method

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.     

Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method

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.     

Analytic Solution of Interaction Between Surface Waves and Floating Elastic Plates with Elastic End-Restraints

Based on the dynamic theories of water waves and Mindlin plates,the analytic solution of interaction between surface waves and two-dimensional floating elastic plates with edge-restraint is constructed by use of the Wiener-Hopf technique.Firstly,without regard for elastic edge restraint,the wave-induced responses of elastic floating plate analyzed by the present method are in good agreement with the results from literature and experimental results.Therefore,it can be shown that the present method is valid.Secondly,three end-restraint cases(i.e.,the left-end elastic restraints,the both-end elastic restraints,and the right-end elastic restraints)are proposed to reduce the vibration of floating plates,in which the spring is used to connect the sea bottom and the floating plate's left(or right)edge.The relations between the spring stiffness and the parameters of wave-induced responses of floating plates are discussed.Moreover,the effective method to reduce the vibration of floating elastic plates can be obtained through comparison.     

Hydrodynamic Characteristics of Square Heaving Plates with Opening Under Forced Oscillation

The existence of the heaving plates can improve the heaving motion performance of an offshore structure significantly by providing both extra added mass and damping. In the current research, numerical investigation is carried out on the hydrodynamic characteristics of both isolated square heaving plate and double square heaving plates with opening by an immersed boundary-lattice Boltzmann method. The effects on hydrodynamic performance of plates due to Keulegan-Carpenter(KC) number, frequency number, opening ratio, opening distribution and spacing of plates are examined. It is found that the heaving plates with optimized opening ratio can provide additional damping compared with the plates without opening. Better hydrodynamic characteristics of double plates can be obtained with the increase of plate spacing.     

Vibrations of a rectangular orthotropic plate with a free edge: a comparison of analytical and numerical results

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 γ_i. The results are in excellent agreement with those obtained by means of a finite element algorithmic procedure.     

A comparative experimental study on the blast-resistant performances of single and multi-layered thin plates under close-range airblast loading

The performance of multilayered thin steel plates subjected to close-range air blasts has been experimentally studied and compared with that of monolithic plates made of the same material and having equal mass. In present experiments, multilayered plates are in-contact four-layered thin steel plates and two types of deformation/failure modes were observed for them. Comparisons concerning deformation/failure modes, strain distributions and energy absorptions between the multilayered plate and its monolithic counterpart were conducted. It is found that the multilayered plate is much superior to its monolithic counterpart in the ability to deform against blast loading. Furthermore, under intense airblast loading, the multilayered plate can not only absorb much more energy but also effectively reduce the secondary destruction ability of structural fragments in comparison with its monolithic counterpart.     

Free and damped vibrations of an orthotropic rectangular plate with one edge free while the rest are elastically restrained against rotation

This paper is concerned with the vibrations of an orthotropic rectangular plate with one edge free while the rest are elastically restrained against rotation. The plate is assumed to be thin and its vibration amplitudes small. The plate is in contact with an ideal fluid of infinite extent and the plate-fluid interaction is considered to be quasi-coupled. The calculations are carried out by the Ritz method and the fundamental frequencies for the free and damped vibrations of the rectangular plate are presented. The fluid effect upon the fundamental frequency is briefly discussed.     

A Computational Investigation of the Group Effect of Pits on the Ultimate Strength of Steel Plates

In this work, we focus on assessing the group effect of localized corrosion on the ultimate strength of the marine structural plates and study the load-deformation behaviors of plates of various slenderness and uniaxial compression. Meanwhile, we investigate different corroded patterns from a single circular pit to 25 circular pits distributed over the plate and carry out hundreds of nonlinear finite element simulations by combining the number, depth, distribution of pits with imperfections and slenderness of plate. The distribution of multiple pits causes scattering of stress concentration on the plate, then the plastic section of plate changes with wider distribution of damage simultaneously. The ultimate strength arises when un-loading zone comprised of the yielding strips and holes extends across the plate. It can be concluded that the corroded condition defined as group effect of pits manipulates the deformation state and the loading capacity of plate at the ultimate strength mode that coincides with the proportion of effective loading area and section in the process of post-buckling. To validate the effect of pits group, we perform the numerical experiments of the post-buckling of steel plates containing pits in a row with different orientation.     

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).