Forced vibrations of rectangular plates subjected to harmonic loading distributed over a rectangular subdomain

Quite frequently naval and ocean structural designers confront the problem of a plate or slab which supports a motor or engine which excites, dynamically, the structural element. Very often the excitation is treated as a concentrated force but, obviously, it acts over a finite area. The present study deals with the title problem for several combinations of boundary conditions by means of a variational approach and also using the finite element method. Dynamic displacement and bending moment amplitudes are determined.     

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…     

Transverse vibrations of rectangular orthotropic plates with one or two free edges while the remaining are elastically restrained against rotation

A survey of the literature reveals that the title problem has not been previously solved. The fundamentals frequency of transverse vibration of the orthotropic structural element is determined by expanding the displacement amplitude function in terms of simple polynomial coordinate functions which satisfy identically the essential boundary conditions and approximately some of the natural edge requirements.The Ritz method is then used to generate the frequency equations.     

Free vibration of rectangular plates with circular openings

The optimized Rayleigh-Ritz method is applied to generate values of the fundamental frequency coefficient and the one corresponding to the first fully antisymmetric mode for rectangular plates elastically restrained against rotation and with located circular holes. The results of this study are compared with existing data and the agreement is quite good.     

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.     

Analytical and experimental investigation on vibrating rectangular plates with two opposite free edges and internal supports while the remaining are elastically restrained against rotation

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.     

Transverse vibrations of circular annular plates with edges elastically restrained against rotation, used in acoustic underwater transducers

Simply supported or clamped boundary conditions are rather ideal situations difficult to satisfy from a physical viewpoint. This paper considers a more “moderate” restriction: the case of edges elastically restrained against rotation for which no exact solution appears in the open literature. Eigenvalues corresponding to a wide range of the intervening geometric and mechanical parameters are determined. Good agreement is obtained with frequency coefficients determined two decades ago by means of a variational method. Obviously the problem is of basic interest in many ocean engineering applications: from the design of certain underwater acoustic transducers to pump and compressor elements passing through the design of naval vehicles and ocean structures.     

Analysis of vibrating, thin, rectangular plates with point supports by the method of differential quadrature

The title problem is solved by an approach first suggested by Bellman early in the 1970s and which has recently been used in the solution of solid mechanics problems. It is shown that the methodology offers several important advantages from the point of view of naval analysts and designers.     

双浮板液舱晃荡特性的数值研究

基于黏性流理论,采用动网格技术和6自由度模型,以及动量源方法,建立了双浮板液舱晃荡的数值模型。分别采用3种不同空间步长的网格离散计算区域,进行了网格收敛性验证。通过光滑液舱晃荡的模型试验和解析得到的爬高最大值,验证了数值模型的精确性。在载液率为50%,激励幅值为2 mm条件下,对双浮板液舱晃荡进行了数值计算,与光滑液舱相比,双浮板液舱晃荡的最大爬高明显减小。通过一个激励周期内双浮板液舱晃荡的波面显示发现,液舱晃荡模式由光滑液舱的驻波模式变为U管模式,晃荡模式的改变起到了明显地抑制液舱晃荡的效果。     

A unified, polynomial approach for the approximate solution of thermoelastic problems in rectangular plates

The present paper, of a tutorial nature, solves two different thermoelastic problems using a unified approach: (a) thermoelastic stresses and deflections in thin, rectangular plates with edges elastically restrained against rotation when small-deflection theory is used and stress resultants in the middle plane of the plates are neglected; and (b) thermoelastic plane stress situations in rectangular plates with stress-free edges subjected to a two-dimensional temperature distribution.The first problem is attacked using polynomial coordinate functions which identically satisfy the governing boundary conditions, and the Ritz method is used to determine the plate response. When the flexibility coefficients approach zero (clamped edge conditions) the calculated results practically coincide with the exact solution for the test case treated in this paper. On the other hand this degenerate solution turns out to be a very convenient approximation for obtaining a solution to Airy's problem described in the second place and which is also solved in a straightforward manner using a variational approach.     

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.     

Vertical uplift resistance of close-spaced shallow rectangular group anchor plates embedded in sand

Abstract

This study describes an analytical solution for determining the ultimate vertical uplift resistance of a group of two and multiple number of close-spaced shallow rectangular anchor plates embedded horizontally in sand. The analysis was performed by using an upper bound theorem of limit analysis with the employment of the kinematically admissible three-dimensional (3D) rigid wedge collapse mechanisms. Results are obtained in terms of dimensionless uplift factors F_γ and F_q due to the components of soil self-weight and surcharge pressure acting on the ground surface for a wide range of parameters. It was found that the magnitude of uplift factors decreases substantially with a decrease in the clear spacing between the anchors, soil friction angle, and embedment ratio, and an increase in the aspect ratio of anchors. Further, it was noticed that when the clear spacing between the anchors is greater than or equal to the certain critical value, the interaction effect of anchors vanishes and the magnitude of uplift factors associated with a group of anchors becomes equal to that of single isolated anchors. The present solutions are found to compare reasonably well with those theoretical, numerical, and experimental results available in the literature.     

Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory

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.     

Research on the hydrodynamic characteristics of heave plate structure with different form edges of a spar platform

The hydrodynamic characteristics of heave plates with different form edges of Truss Spar Platform are studied in this paper.Numerical simulations are carried out for the plate forced oscillation by the dynamic mesh method and user defined functions of FLUENT.The added mass coefficient and the damping coefficient of heave plate with tapering condition and the chamfer condition are calculated.The results show that,in a certain range,the hydrodynamic performance of heave plate after being tapered is better.     

流速分布及锚链自身刚度对弹性单锚链系统变形和受力的影响

在锚链系统中,锚链本身的刚度和水流对其作用是影响锚链变形和受力的主要因素。应用分段外推的数值方法,分别对不同刚度和同一弹性锚链在均匀流作用以及同一弹性锚链在不同流速分布(流速在水深方向呈抛物线分布、对数分布)的水流作用下的变形和受力进行了分析和计算,得出了锚链自身的不同刚度及不同流速对锚链的变形及受力的影响情况。结果表明,刚度对锚链受力及变形影响明显,不同流速分布对锚链的偏移量几乎无影响,但对锚链的受力影响较大,选取抛物线型流速分布对锚链安全有利。     

On the parametric excitation of vertical elastic slender structures and the effect of damping in marine applications

The dynamic behaviour of vertical slender structures for marine applications under parametric excitation is considered. The governing equations are treated using two different numerical schemes. The effect of parametric excitation is examined in cases where the excitation frequency lies in the vicinity of nonlinear resonances. First, the un-damped case is considered and the features of the dynamic response are properly identified and discussed. For explaining the particulars of the un-damped behaviour, the governing equations are treated analytically by applying the method of normal forms. The effect of damping is examined through comparative numerical computations of the system's behaviour. It is shown that the inclusion of hydrodynamic drag in the describing model eliminates the impacts of internal resonances excited due to the parametrically imposed motions. Finally, the paper demonstrates the significance of the terms that describe the coupling between the longitudinal and transverse vibrations.     

Buckling of circular, solid and annular plates with an intermediate circular support

The title problem is solved in the case where uniform applied loading is present at the plate outer boundary. Two independent solutions are obtained: the optimized Rayleigh–Ritz method and the finite element algorithmic procedure. Good engineering agreement is shown to exist. The proposed analytical procedure is convenient from a designer's viewpoint. Admittedly exact analytical solutions can be found in terms of Bessel functions, the procedure being rather complex from an engineering viewpoint.     

Hydrodynamic coefficients of a two-dimensional,truncated rectangular floating structure in shallow water

The paper seeks to examine hydrodynamic coefficients of a rectangular structure in shallow water and to establish analytical formulae for fast computations. A two-dimensional rectangular profile is considered with the under-bottom clearance assumed to be small compared with structure dimensions and the water depth. Following the method of matched asymptotic expansions, the radiation problem is solved under assumptions of the linear wave theory, by matching two ‘outer’ flows with the ‘inner’ flow near the structure edge. Closed asymptotic formulae are obtained for all hydrodynamic coefficients for heave, sway and roll motions. The zero and infinite frequency values of the added mass are examined and formulae are derived intended for quick engineering estimations. Numerical results compare well with those published in literature, and the approach is shown to be consistent with known fundamental relations in the body–wave interaction theory.     

Transverse vibrations of a rectangular cantilever plate with thickness varying in a discontinuous fashion

A numerical solution is obtained for the title problem by means of the popular finite element method. An experimental investigation of the problem is also presented for plates of square planform. The agreement between theoretical and experimental values is very good in the case of the fundamental frequency, and reasonably good when the second and third normal modes of transverse vibration are considered. It is concluded that beneficial effects are obtained in the sense that one generates a lighter structural element with higher fundamental frequency of transverse vibration. Hence, dynamic stiffening is achieved.