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1.
Dynamic responses of structures due to earthquake excitation are the important problems in engineering, thus, the information concerned is plenty. However, most of the literature is relating to the discrete methods, particularly to the finite element method (FEM), and the one relating to the method combining both the “continuous” and “discrete” models is rare. The objective of this paper is to provide some information in this respect. First, the analytical solution for the natural frequencies and normal mode shapes of a “continuous” tower, without contacting water (or “dry” tower), carrying an eccentric tip mass possessing rotary inertia is determined. Next, the partial differential equation of motion for the forced vibration of the tower, contacting water (or “wet” tower), subjected to support excitation is transformed into a matrix equation by using the last natural frequencies and normal modes shape of the freely vibrating dry tower. Finally, the numerical integration method is used to solve the matrix equation to yield the seismic response of the wet tower. In theory, the mode superposition method is correct only if the total number of modes considered approaches infinity, however, numerical results of this paper reveal that superposition of only the lowest six modes will yield excellent results to be very close to the corresponding ones obtained from the conventional FEM. For this reason, the CPU time required by the presented approach is less than 5% of that required by the conventional FEM. 相似文献
2.
In this paper, a beam without contact with water is called the “dry” beam and the one in contact with water is called the “wet” beam. For a partially (or completely) immersed uniform beam carrying an eccentric tip mass possessing rotary inertia, the conventional analytical (closed-form) solution is achieved by considering the inertial forces and moments of the tip mass and rotary inertia as the boundary conditions at the tip end of the beam. However, it has been found that the approximate solution for the last problem may be achieved by two techniques: Method 1 and Method 2. In Method 1, the basic concept is the same as the conventional analytical method; but in Method 2, the tip end of the beam is considered as a free end, while the inertial forces and moments induced by the tip mass and rotary inertia are considered as the external loads applied at the tip end of the beam. The main differences between the formulation of Method 1 and that of Method 2 are: In Method 1, the “normal” shapes of the “dry” beam are functions of the frequency-dependent boundary conditions but the external loads at the tip end are equal to zero; On the contrary, in Method 2, the “normal” mode shapes of the “dry” beam are determined based on the zero boundary conditions at the tip end of the beam but the external loads at the tip end due to the inertial effects of the tip mass and rotary inertia must be taken into consideration for the free vibration analysis of the “wet” beam. Numerical results reveal that the approximate solution obtained from Method 2 are very close to that from Method 1 if the tip mass moment of inertia is negligible. Besides, the two approximate solutions are also very close to the associated analytical (closed-form) solution or the finite element solution. In general, it is hoped that there exist several methods for tackling the same problem so that one may have more choices to incorporate with the specified cases. It is believed that the two approximate methods presented in this paper will be significant from this point of view. 相似文献
3.
This paper presents a calculation method of derivatives of natural frequencies and mode shapes to parameters affecting vertical hull girder vibration based on design sensitivity analysis. The method premises free vibration analysis of hull girder using the transfer matrix method. Governing sensitivity equation is derived from the direct differentiation of state vector and transfer matrix to design variables. Derivatives of natural frequencies and mode shapes are determined after two trial calculations of the equation. By using the obtained derivatives, the changes of natural frequencies can be rationally and efficiently predicted in case of ship design modification and loading variation. 相似文献
4.
In this paper theoretical models are proposed for computing the natural frequencies and modal shapes of two-dimensional asymmetric and symmetric moonpools in the finite water depth. The boundary value problem is solved by using a domain decomposition approach. On the outer vertical boundary bounded by the beam of the two bodies, linearized velocity potential is assumed to be nil. Eigenvalue problem is formulated by matching the velocity potential and fluid flux on the common boundaries to obtain the natural frequencies and modal shapes of the free surface elevation. In the symmetric moonpool cases, so-called single mode approximations (SMA) have been derived and can be adopted for rapid estimation of the natural frequencies for both piston and sloshing modes. The present results have been extensively compared with the solutions using the two-dimensional infinite water depth model developed by Molin [1], the numerical solutions and experimental data by Faltinsen et al. [2]. It is found that the solutions have been improved from the infinite water depth model. It is demonstrated that the proposed models can well predict the resonance frequencies and modal shapes for the two-dimensional asymmetric and symmetric moonpools. 相似文献
5.
为了分析带支腿浮式结构水下桩腿处于不同的长度时振动固有频率的变化情况,采用有限元方法和三维线性水弹性理论对一理想的带支腿浮式结构进行研究,分工况计算了3种弹性模态的干、湿固有频率。结果表明对于同一阶弹性模态来说,结构主体平台振型是决定水动力系数大小的主要因素,桩腿水下长度是次要因素,而振型又受到桩腿长度的制约;桩腿水下长度的改变对带支腿浮式结构的干模态固有频率以及湿固有频率都有较明显地调制作用。对于干模态固有频率来说,桩腿关于船身越趋于对称分布时结构的共振频率越高;对于湿固有频率来说,水下桩腿长度地增加有迫使共振频率趋向低频方向移动趋势。 相似文献
6.
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. 相似文献
7.
《中国海洋工程》2021,(4)
The flapwise bending vibrational equations of tapered Rayleigh beam are derived based on Hamilton's principle. The corresponding vibrational characteristics of rotating tapered Rayleigh beams are investigated via variational iteration method(VIM). Natural frequencies and corresponding mode shapes are examined under various rotation speed, taper ratio and slenderness ratio focusing on two types of tapered beam. The convergence of VIM is examined as part of the paper. Validation of VIM solution is made by referring to results available in other literature and corresponding results show that VIM is capable of yielding precise results in a very efficient way. 相似文献
8.
Sloshing in a two-dimensional rectangular tank in horizontal motion is analysed based on the velocity potential theory. It is found that even when the first-order excitation is away from all the natural frequencies of the tank, second-order resonance can still occur when the sum-frequency or the difference-frequency is equal to one of the natural frequencies corresponding to the even mode. However, such resonance is not excited when the sum or difference frequency is equal to the natural frequency of an odd mode. 相似文献
9.
Crack detection procedures by different modal parameters are analyzed for identitying a crack and its location and magnitude in a jacket plafform. The first ten natural frequencies and modal shapes of the jacket models are obtained by numerical experiments based on NASTRAN Code. A crack at different locations and of different magnitudes is imposed in the model at the underwater beams. Then, the modal evaluation parameters are calculated numerically, to illustrate the evaluation of modal parameter criteria used in jacket crack detection. The sensitivities of different modal parameters to different cracks are analyzed. A new technique is presented for predicting the approximate location of a breakage in the absence of the data of an intact model. This method can be used to detect a crack in underwater menbers by use of incomplete mode shapes of the top members of the jacket. 相似文献
10.
By means of Lagrange's equation, the “coupled” equations of motion for a horizontal plate carrying a U-type tuned liquid damper (TLD) are derived. The “uncoupled” equations of motion for the liquid (in the TLD) and the structural system are then obtained by decoupling the “coupled” ones. Unlike the existing literature to indirectly determine the natural frequencies of a damped vibrating system by using the resonant method, the “complex” eigenvalues of the coupled damped system are obtained directly from the associated eigenvalue equations. Besides, the pressure intensities in the two air chambers and the sizes of the two vertical tanks together with the horizontal conduit are arbitrary in the formulation of this paper. The influence of some key parameters of the TLD on the dynamic responses of the structural system is studied. 相似文献
11.
Free spanning analysis of offshore pipelines 总被引：1，自引：0，他引：1
H. S. Choi 《Ocean Engineering》2001,28(10)
A rigorous procedure was established on the free span analysis of offshore pipelines. The closed form solutions of the beam–column equation, considering tension and compressive force, were derived for the various possible boundary conditions. The solutions can be used to find the natural frequencies of the free spans using the energy balance concept. The results can be applied to improve the current design codes. The improved procedure will yield more realistic calculations of the allowable free span lengths of offshore pipelines. Some calculations are included to present the sensitivity of the axial forces on the allowable free spanning lengths. 相似文献
12.
Dynamic analysis of tension leg platform for offshore wind turbine support as fluid-structure interaction 总被引：2，自引：1，他引：1
Tension leg platform (TLP) for offshore wind turbine support is a new type structure in wind energy utilization.The strong-interaction method is used in analyzing the coupled model,and the dynamic characteristics of the TLP for offshore wind turbine support are recognized.As shown by the calculated results:for the lower modes,the shapes are water’s vibration,and the vibration of water induces the structure’s swing;the mode shapes of the structure are complex,and can largely change among different members;the mode shapes of the platform are related to the tower’s.The frequencies of the structure do not change much after adjusting the length of the tension cables and the depth of the platform;the TLP has good adaptability for the water depths and the environment loads.The change of the size and parameters of TLP can improve the dynamic characteristics,which can reduce the vibration of the TLP caused by the loads.Through the vibration analysis,the natural vibration frequencies of TLP can be distinguished from the frequencies of condition loads,and thus the resonance vibration can be avoided,therefore the offshore wind turbine can work normally in the complex conditions. 相似文献
13.
A vector hydrophone is composed of two or three spatially collocated but orthogonally oriented velocity hydrophones plus an optional collocated pressure hydrophone. A vector hydrophone may form azimuth-elevation beams that are invariant with respect to the sources' frequencies, bandwidths and radial location (in near field as opposed to the far field). This paper characterizes the spatial matched filter beam patterns (a.k.a. fixed or conventional or maximum signal-to-noise ratio beam patterns) and the minimum variance distortionless response (MVDR) beam patterns associated with a single underwater acoustic vector hydrophone distant from any reflecting boundary. 相似文献
14.
The theoretical model of Molin [6] is extended to the case of rectangular moonpools with one or two recesses, as can be found in some drillships. Obtained natural frequencies and modal shapes of the piston and first sloshing modes are compared with experimental results available in literature, with good agreement. An approximation easy to implement is proposed for the natural frequency of the piston mode. Further illustrative results are presented when some geometrical parameters of the moonpool are being varied. 相似文献
15.
提出利用折射率成阶跃性变化的轴棱锥产生局域空心光束(bottle beam).讨论了折射率沿径向成阶跃式减小或增加两种模型,从几何光学角度分析了它们产生bottle beam的原理,利用衍射积分理论数值模拟两种轴棱锥光传输的光场分布和不同距离处的二维光斑图,研究结果表明折射率沿径向阶跃减小的轴棱锥产生单个bottle beam,而折射率沿径向阶跃增加的轴棱锥产生具有周期再现的bottle beams.bottle beam在原子引导和囚禁、光学俘获及光镊等方面有广泛的应用, 因此本文的研究对bottle 相似文献
16.
研究计入弹性变形铰接塔平台在深水中的非线性动力响应。将铰接塔平台简化为顶部具有集中质量,底部具有扭转线性弹簧约束的均匀弹性梁,考虑波浪对平台的作用,应用莫里森(Morison)公式计算铰接塔平台瞬时位置所受水动力,建立了铰接塔平台横向运动的偏微分方程,采用伽辽金方法计算波浪作用下铰接塔平台非线性动力响应。计算了铰接塔平台的固有频率和模态,得到了铰接塔平台不同频率波浪激励下各阶模态的动力响应。计算结果表明,在波浪激励下系统二阶模态将发生2、34、倍超谐共振运动,并且揭示了弹性铰接塔平台在波浪作用下振动的不对称性。 相似文献
17.
一种推导Timoshenko梁频率方程的新方法 总被引：1，自引：0，他引：1
在Timoshenko梁横向弯曲自由振动方程的基础上,首次推导建立两端受弹性约束梁的频率方程,通过此方程,研究两端受弹性约束梁的性质,并通过简支梁模型,初步估计剪切变形与转动惯量对Timoshenko梁频率的影响,估算Timoshenko梁与Euler梁频率之间的关系,给出估算公式,并用数值算例进行验证,结果表明数值法解Timoshenko频率方程的可靠性. 相似文献
18.
Sidali Denine Sadok Feia Rawaz Dlawar Muhammed Jean Canou Jean-Claude Dupla 《Marine Georesources & Geotechnology》2013,31(5):599-608
AbstractAn experimental study about the effects of initial conditions of soil and geotextile reinforcement on the mechanical behavior of reinforced sand is presented in this paper. A series of direct shear tests are conducted on reconstituted specimens of dry and moist natural sand prepared with different initial water content (w?=?0, 1.5, 3, and 5%) and including the two arrangements of geotextile layers (one and two layers, respectively). Both S41 and PEC55types of non-woven geotextile were used and placed at different heights of the specimens to investigate the effect of geotextile reinforcement on the behavior of sand. Test specimens were prepared at Dr =80% of relative density and were subjected to three different normal stresses of 100, 200, and 300?kPa. The experimental results showed that the deposition mode (wet and dry) and the geotextile reinforcement have significant effects on the behavior of reinforced sand. The increase in shear strength is relatively more significant for specimens prepared with dry deposition mode as compared to those prepared with wet deposition mode and it increases with the number of geotextile layers, this effect becomes less significant for wet specimens. The experimental results also demonstrated that (PEC55) non-woven geotextile shows a better performance than the (S41) of geotextile. These results can be explained by the effective tensile strength property of polyester yarns of the (PEC55) non-woven geotextile that it has led to a significant increase in the shear strength. 相似文献
19.
An object that is partially insonified by a collimated sound beam may have a scattering cross section sometimes much larger than when the object is totally covered by the incident beam. We quantitatively study this partial insonification problem here, under the classical method of physical optics. The importance of this study stems from the fact that partial coverage of the target by the beam is the situation most likely to occur in many cases of practical importance. We consider several basic target shapes partially insonified by finite beams. These shapes include the spherical, the infinite and finite cylinder, the flat plate, and the capped sphere. High-frequency approximations of the resulting integrals, obtained by means of the saddle-point method, show the relative importance of the scattering centers located at the beam's specular reflection points, or at the edges of the spots that the beam shines on the scatterers. The physical-optics method is extended to obtain formulas for the bistatic cross sections of partially insonified objects. The results are numerically evaluated and graphically displayed in many pertinent instances and compared to the predictions of approaches, such as the Fresnel-zones method and the Geometrical Theory of Diffraction (GTD). The predictions of the physical-optics method have all the advantages and deficiencies of this method and, with very minor modifications, hold equally well for the partial illumination of objects by beams of electromagnetic radiation. 相似文献
20.
海洋立管复模态动力特性分析 总被引：1，自引：0，他引：1
考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。 相似文献