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.     

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.     

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.     

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.     

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.     

Impact of narrow plates on broader liquid bodies

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.     

Effect of Longitudinal Plastic Bending of Pipeline on Buckle Propagation Pressure

A plastic ring-beam model simulating the longitudinal transition zone of submarine pipelines in the buckle propagation is presented. The nonlinear relationships between the buckle propagation pressure and the length of the transition zone and the position parameter of the longitudinal plastic hinge are derived using the energy principle. The related values are obtained by means of solving a set of nonlinear equations. The model conforms better to reality than the ring models for considering the effect of the longitudinal plastic bending of the transition zone. The computations for some stainless steel and aluminium tubes with different geometrical parameters are performed. The results obtained agree better with the experimental results than existing theoretical predictions.     

Numerical experiments on dynamic stiffening of beams and plates

By introducing continuous or discontinuous variations in the thickness of beams, arches and plates, it is possible in many practical situations to raise the value of the fundamental frequency and, at the same time, to lower the weight of the structural element. This is a beneficial situation, especially in those cases where weight reduction and large dynamic stiffness are of interest. The present paper surveys some recent practical accomplishments in this area.The rigorous procedure consists, from a general structural optimization viewpoint, of minimizing an objective function (for instance, total volume) subject to constraints on the geometry and behavior (natural frequencies, buckling loads, etc.). In many instances it is convenient to reverse the problem: one fixes or limits the weight or volume and constructs some quantity which describes the desired behavior of the system e.g. the fundamental frequency.The problems under study in the present paper are considerably more modest in scope, since the procedure is performed by numerical experiments.     

The hydrodynamics of thin floating plates

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.     

Ultimate Bending Capacity of Strain Hardening Steel Pipes

Based on Hencky’s total strain theory of plasticity, ultimate bending capacity of steel pipes can be determined analytically assuming an elastic-linear strain hardening material, the simplified analytical solution is proposed as well. Good agreement is observed when ultimate bending capacities obtained from analytical solutions are compared with experimental results from full-size tests of steel pipes. Parametric study conducted as part of this paper indicates that the strain hardening effect has significant influence on the ultimate bending capacity of steel pipes. It is shown that pipe considering strain hardening yields higher bending capacity than that of pipe assumed as elastic-perfectly plastic material. Thus, the ignorance of strain hardening effect, as commonly assumed in current codes, may underestimate the ultimate bending capacity of steel pipes. The solutions proposed in this paper are applicable in the design of offshore/onshore steel pipes, supports of offshore platforms and other tubular structural steel members.     

受轴向压力开孔板极限强度有限元分析研究

使用有限元方法对不同边界条件下受轴向压力的多种类型开孔板的极限强度进行了研究。考虑到板的极限强度所涉及的非线性问题,运用ABAQUS/Standard弹塑性大挠度分析来求解极限强度。在计算了系列不同开孔位置及开孔大小的板的屈曲强度后,分析了各种边界条件及开孔形式对开孔板的极限强度的影响程度。最后在得到规律的基础上提出了适用于一定边界条件下的经验公式,可以在初步设计中用于估算开孔板的极限强度值。     

三维复杂结构Spar平台垂荡板垂荡水动力性能研究

对三维复杂结构Spar平台垂荡板进行垂荡运动的数值模拟,并对垂荡板附近流场及水动力系数进行对比分析。结果表明:在主板尺寸相同情况下,主板边缘附近较小的角钢结构会对垂荡板流场产生明显影响,并导致水动力性能的较大差距;水动力系数计算结果与流场分析的结论一致。虽然复杂板架结构的三维建模及网格划分难度很大,但是在Spar平台垂荡板工程设计中不能完全采用简化光滑平板代替真实、复杂结构形式的垂荡板进行水动力性能的计算。     

圆形网箱框架用PE管材的弯曲疲劳试验

网箱框架在风、浪、流单一载荷或其复合载荷的作用下,始终处于动态变化中,在这样的工况条件下,很容易发生疲劳破坏。本文通过对网箱框架工况条件的分析,认为网箱框架在沿直径方向的弯曲疲劳为主要因素,且在弯曲过程中周长保持不变。以圆形框架在直径方向产生20%的压缩变形为极端条件,通过几点假设,将工况条件向试验条件进行转化,提出1种圆形网箱框架用PE管材的弯曲疲劳试验方法。采用此方法对3种改性配方的聚乙烯管材样品进行了弯曲疲劳试验。结果表明,经10万次弯曲试验,3种配方的试样表面均无开裂等破坏现象,各配方的最大应力水平分别下降了14.3%,9.4%和16.9%。     

Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports

Vortex induced vibration (VIV) of circular cylinders is widely accepted as depending weakly on Reynolds number (Re) and strongly on reduced velocity, mass ratio, and damping. Experiments are conducted in the regime right before transition from laminar to turbulent flow (high-Reynolds 2×l0⁴?4×l0⁴<Re<3.5×l0⁵?6×l0⁶) in the Low Turbulence Channel at the University of Michigan. Limited experimental data are available in that regime. This research was initiated in 2004 studying high-damping VIV to convert hydrokinetic energy from ocean/river currents to electricity using the VIVACE Converter.The following experimental observations are made: low and high Reynolds VIV significantly differ. The range of synchronization of the upper branch increases with increase in Reynolds number. Amplitude ratio (A/D) increases with Reynolds number within the upper branch. For high-Reynolds, A/D=1.9 is achieved routinely in spite of high damping. The lower branch disappears, overtaken by extended upper branch. High-Reynolds VIV enters into the 2P domain in the Williamson–Roshko (W–R) map beginning with the initial branch. Hysteresis is not observed in these experiments possibly because parameters remain in the 2P-domain. High Reynolds numbers have a stronger influence than mass ratio on A/D. High-damping high-Reynolds VIV amplitudes are double of those predicted by the modified Griffin plot by extrapolation.     

Hydrodynamic shape optimization of thin floating plates

In this work, the problem of optimizing the shape of a thin floating plate (sometimes called a dock) to maximize radiation damping is investigated. The plate is modeled with zero draft and floats on the surface of an irrotational, incompressible ocean of infinite extent. For simplicity, only rigid heave motions are considered. The flow problem is analyzed using the Chen and Mei variational principle wherein the potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion and matched on the hemisphere to an outer field described by distributing sources on the hemisphere. The plate shape is parameterized using a Fourier series which is suitable for use with the variational principle. Gradients of the damping coefficient with respect to the shape parameters are developed by solving an adjoint flow problem whose potential is shown to be a scalar multiple of the original flow potential. Optimal plate shapes are determined using the well-known optimization code NPSOL which makes use of the damping coefficient calculation and gradients.     

加筋板的轴压强度受加筋随机点蚀的影响研究

船舶与海洋结构在服役期间会遭受电化学和微生物侵蚀等多种腐蚀环境影响,加筋板作为此类结构的主要受力构件,其表面易产生不规则形态的点蚀,引起构件的强度退化。利用ANSYS有限元软件构建加筋腹板遭受随机点蚀损伤的加筋板有限元模型,研究带板长宽比、带板长细比、加筋长细比和腐蚀体积损失率对加筋板极限强度的影响。研究结果表明,加筋遭受同等腐蚀体积损失率下,带板长宽比变化对极限强度退化的影响很小,但带板长细比和加筋长细比变化产生的影响明显;带板长细比越大,极限强度退化越严重,而加筋长细比越大,极限强度退化反而越小。针对文中研究的加筋板,当加筋长细比为 0.2时,腐蚀体积率为14%的随机点蚀导致结构极限强度退化程度达到约14.0%。因此,加筋的随机点蚀损伤会显著削弱加筋板结构的极限强度,其影响不可忽略。     

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.     

Effect of under connected plates on the hydrodynamic efficiency of the floating breakwater

In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.     

Tidal asymmetry in suspended sand transport on a macrotidal intermediate beach

Time-series of nearbed horizontal flow velocities and suspended sediment concentrations obtained from a colocated electromagnetic current meter (EMCM) and optical backscatter sensor (OBS), respectively, are used to examine the relative importance of steady and fluctuating components to the total sediment transport over a full tidal cycle on a macrotidal, intermediate beach (Spurn Head, UK). Fluctuating sediment fluxes are decomposed into gravity and infragravity contributions using co-spectral techniques. The relative importance of the oscillatory (gravity and infragravity) and steady (mean) transport components to the total sediment transport is analysed throughout the tidal cycle.

A continuum of 34 discrete suspended sediment-cross-shore velocity co-spectra are computed over a full tidal cycle for the OBS and EMCM measurements 0.10 m above the bed. These net transport spectra vary greatly both with cross-shore location and tidal state. In particular, a marked asymmetry in transport processes is evident between the flood and ebb tides, with high levels of sediment resuspension and transport occurring on the ebbing tide approximately two hours after high water (just seaward of the breakpoint). At this time the dominant transport was directed offshore (co-spectral peak, 0.04 kg/m²/s) at incident wave frequency.

Typical patterns are observed in transport spectra outside the surf zone and within the inner surf zone. Outside the narrow surf zone cross-shore transport spectra show weak offshore transport (co-spectral peak = 0.002 kg/m²/s) associated with bound long waves and stronger onshore transport (co-spectral peak = 0.006 kg/m²/s) at incident wave frequencies. Conversely, co-spectra computed within the inner surf zone show the offshore sediment fluxes (spectral peak = 0.010 kg/m²/s) at infragravity frequencies to be greater in magnitude than the corresponding onshore transport (co-spectral peak = 0.008 kg/m²/s) occurring at incident wave frequencies.     

Hydrodynamic performance of solid and porous heave plates

Heave plates have been widely utilized in floating offshore structures as they can provide additional damping and added mass to improve the hydrodynamic response of the system. This study investigates the hydrodynamic characteristics (added mass and damping) of oscillatory solid or porous disks using model scale experiments. All experiments were conducted via forced oscillation model tests using a planar motion mechanism (PMM). The hydrodynamic coefficients of the solid or porous disk obtained from the force measurements are analysed and presented. The sensitivities of the damping and added mass coefficients to both motion amplitude and the disk porosity are examined.