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1.
Abstract Finite amplitude convection in spherical shells with spherically symmetric gravity and heat source distribution is considered. The nonlinear problem of three-dimensional convection in shells with stress-free and isothermal boundaries is solved by expanding the dependent variables in terms of powers of the amplitude of convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. The shell is assumed to be thick and only shells for which the ratio ζ of outer radius to inner radius is 2 or 3 are considered. Three cases, two of which lead to a self adjoint problem, are treated in this paper. The stable solutions are found to be l=2 modes for ζ=3 where l is the degree of the spherical harmonics and an l=3 non-axisymmetric mode which exhibits the symmetry of a tetrahedron for ζ=2. These stable solutions transport the maximum amount of heat. The Prandtl number dependence of the heat transport is computed for the various solutions analyzed in the paper. 相似文献
2.
It is shown that the method recommended by the Nuclear Regulatory Commission to be used to combine spectral response in the case of closely spaced modes is unnecessarily conservative for certain systems. Closely spaced modes arise in structures from symmetry and where there is a light appendage with a frequency close to one of the natural frequencies of the structure. In the former case, the closely spaced modes do not involve significant interaction between components of the system and the Nuclear Regulatory Commission Guide is reasonable. The latter case, that is when there are closely spaced modes where interaction of components occurs as in the examples of light appendages and torsionally unbalanced buildings, must be treated by consideration of the interacting components. The approach proposed here is that the modes that are not closely spaced be treated by modal analysis and the closely spaced modes, in the case of two closely spaced modes, be treated as a coupled two-degree-of-freedom system. If this is done, the beat phenomenon, the most important characteristic of the interaction, is evident, as is the associated result that the peak response of the coupled system is developed much later than the peak responses obtained in the individual modes. It is shown that the square root of the sum of the squares procedure underestimates, as expected, the response for undamped and very lightly damped systems, but for damped systems the square root of the sum of the squares method can be extremely conservative. It follows that the other methods specified by the Nuclear Regulatory Commission for closely spaced modes must be even more conservative. 相似文献
3.
A Galerkin Finite Element formulation for the dynamic stability analysis of liquid-filled shells is given in this paper. The coupling among the axial and circumferential modes is investigated. The dynamic stability characteristics of two liquid-filled storage tanks subjected to vertical, horizontal and rocking seismic excitations are presented. It is shown that a tall tank tends to buckle at distinct frequencies; and for cos θ-type ground excitation, cos 2θ, cos 3θ and cos 4θ are the dominant modes of failure. On the other hand, in a broad tank, buckling regions overlap each other. In particular, for cos θ-type ground excitation, the dominant buckling modes are cos 6θ to cos 9θ, and also cos 12θ to cos 14θ. 相似文献
4.
Hilbert-Huang变换在密频结构阻尼识别中的应用 总被引：14，自引：3，他引：14
Hilbert—Huang变换是一种新的数据处理方法，由经验模分解(Empirical Mode Decomposition)技术及Hilbert变换两部分组成。本文研究此方法对于密频结构阻尼识别的应用。首先对于两自由度系统模型，说明该方法用于阻尼识别的步骤。进而研究存在频率密集现象的高层建筑的阻尼识别问题。上述结果与理论值及由半功率带宽法的识别值进行了比较，对比显示Hilbert．Huang方法较传统方法具有良好的识别密频结构阻尼的性能，适用于大型结构的系统识别。 相似文献
5.
Abstract The linear problem of the onset of convection in rotating spherical shells is analysed numerically in dependence on the Prandtl number. The radius ratio η=r i/r o of the inner and outer radii is generally assumed to be 0.4. But other values of η are also considered. The goal of the analysis has been the clarification of the transition between modes drifting in the retrograde azimuthal direction in the low Taylor number regime and modes traveling in the prograde direction at high Taylor numbers. It is shown that for a given value m of the azimuthal wavenumber a single mode describes the onset of convection of fluids of moderate or high Prandtl number. At low Prandtl numbers, however, three different modes for a given m may describe the onset of convection in dependence on the Taylor number. The characteristic properties of the modes are described and the singularities leading to the separation with decreasing Prandtl number are elucidated. Related results for the problem of finite amplitude convection are also reported. 相似文献
6.
Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
7.
We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the “separable” class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity crit, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation is inversely proportional to the angular velocity of rotation ; the product being proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that at 1 AU only a minority do. We discuss data on two magnetic clouds where we interpret the presence in each of vortical plasma motion about the symmetry axis as a sign of rotation. Our estimates for the angular velocities suggest that the parameters of the two magnetic clouds are below critical values. The two clouds differ in many respects (such as age, bulk flow speed, size, handedness of the magnetic field, etc.), and we find that their rotational parameters reflect some of these differences, particularly the difference in age. In both clouds, a rough estimate of the radial electric field in the rigidly rotating core, calculated in a non-rotating frame, yields values of the order mV m−1. 相似文献
8.
This paper investigates the seismic response of tall cantilever wall buildings subjected to pulse type ground motion, with special focus on the relation between the characteristics of ground motion and the higher‐modes of response. Buildings 10, 20, and 40 stories high were designed such that inelastic deformation was concentrated at a single flexural plastic hinge at their base. Using nonlinear response history analysis, the buildings were subjected to near‐fault seismic ground motions and simple closed‐form pulses, which represented distinct pulses within the ground motions. Euler–Bernoulli beam models with lumped mass and lumped plasticity were used to model the buildings. The response of the buildings to the closed‐form pulses fairly matched that of the near‐fault records. Subsequently, a parametric study was conducted for the buildings subjected to three types of closed‐form pulses with a broad range of periods and amplitudes. The results of the parametric study demonstrate the importance of the ratio of the fundamental period of the structure to the period of the pulse to the excitation of higher modes. The study shows that if the modal response spectrum analysis approach is used — considering the first four modes with a uniform yield reduction factor for all modes, and with the square root of sum of squares modal combination rule — it significantly underestimates bending moment and shear force responses. A response spectrum analysis method that uses different yield reduction factors for the first and the higher modes is presented. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
9.
Harn C. Chen 《地震工程与结构动力学》1993,22(1):63-74
An efficient numerical algorithm is developed to solve the quadratic eigenvalue problems arising in the dynamic analysis of damped structural systems. The algorithm can even be applied to structural systems with non-symmetric matrices. The algorithm is based on the use of Arnoldi's method to generate a Krylov subspace of trial vectors, which is then used to reduce a large eigenvalue problem to a much smaller one. The reduced eigenvalue problem is solved and the solutions are used to construct approximate solutions to the original large system. In the process, the algorithm takes full advantage of the sparseness and symmetry of the system matrices and requires no complex arithmetic, therefore, making it very economical for use in solving large problems. The numerical results from test examples are presented to demonstrate that a large fraction of the approximate solutions calculated are very accurate, indicating that the algorithm is highly effective for extracting a number of vibration modes for a large dynamic system, whether it is lightly or heavily damped. 相似文献
10.
The peak dynamic responses of two mathematical models of a fifteen-storey steel moment resisting frame building subjected to three earthquake excitations are computed by the response spectrum and time history methods. The models examined are: a ‘regular’ building in which the centres of stiffness and mass are coincident resulting in uncoupled modes with well-separated periods in each component direction of response; and an ‘irregular’ building with the mass offset from the stiffness centre of the building causing coupled modes with the translational modes having closely spaced periods. Four response spectrum modal combination rules are discussed and are used to predict the peak responses: (1) the square root of the sum of the squares (SRSS) method; (2) the double sum combination (DSC) method; (3) the complete quadratic combination (CQC) method; and (4) the absolute sum (ABS) method. The response spectrum results are compared to the corresponding peak time history values to evaluate the accuracy of the different combination rules. The DSC and the CQC methods provide good peak response estimates for both the regular and irregular building models. The SRSS method provides good peak response estimates for the regular building, but yields significant errors in the irregular building response estimates. The poor accuracy in the irregular building results is attributable to the effects of coupled modes with closely spaced periods. It is concluded that the DSC and CQC methods produce response estimates of equivalent accuracy. Both methods are recommended for general use. In addition to the DSC and CQC rules, the SRSS method is recommended for systems where coupled modes with closely spaced periods do not dominate the response. 相似文献
11.
Olivia Salmerón-García Jorge Zavala-Hidalgo Adriana Mateos-Jasso Rosario Romero-Centeno 《Ocean Dynamics》2011,61(4):439-448
Regions in the Gulf of Mexico are determined based on the statistical behavior of the long-term monthly means of chlorophyll-a concentration from SeaWiFS satellite estimations. An analysis based on the four largest modes of an empirical orthogonal
decomposition, which account for 84.9% of the variance, results in nine spatial patterns with different statistical behavior
representing 14 connected regions. The time evolution (or principal component) of the first two modes resemble the annual
cycle, but each one with a different phase; the third mode represents a semiannual period and the fourth mode shows three
maxima and minima. A map of the resulting regions is obtained and the oceanographic processes taking place in each region
are discussed. The largest region covers most of the deep Gulf and the continental slope. Other regions in the deep Gulf are
located southeast of the Mississippi River mouth and off-shelf of southern Texas and Tabasco, all associated with seasonal
offshore cross-shelf transports. The shelves are associated with specific regions, but in wide shelves the inner and outer
continental platforms are separated. Among the causes that determine different regions are topographic characteristics and
the seasonal variability of physical processes, mainly entrainment caused by heat and momentum fluxes, upwelling, river plumes,
and cross-shelf transports associated with the convergence of the along-coast currents. 相似文献
12.
Traffic and wind excitation has been used to obtain the dynamic characteristics of the first Bosporus (Bogazici) Suspension Bridge. Structural symmetry and the absence of suspended side-spans allowed attention to be focused on the main span and the Asian tower. For the main span, 18 vertical and 20 lateral modes were obtained, including torsional modes. For the tower, 12 longitudinal and 12 lateral modes were identified. All these models lie in the range 0–1-1 Hz. A detailed comparison is given between these modes and corresponding calculated modes, obtained by use of a three-dimensional finite element model which includes a geometric stiffness matrix. Of particular interest is the validity of the theoretical model used for the box-deck, because of its subsequent use in response studies of asynchronous seismic excitation. Comparison with a more limited study made in 1973 shows that the bridge continues to behave as it was designed to behave, particularly with regard to the deck-tower interface. From natural frequency measurements of two hangers, the load which they carry was assessed. 相似文献
13.
Summary The solution of the internal and external Dirichlet problem is given without assuming rotational symmetry for a body, limited by two intersecting spherical surfaces. The problem is treated in a toroidal system of co-ordinates, using the generalized Mehler integral transform. The results are compared with the solution, presented by Lebedev [1] for the case of rotational symmetry. 相似文献
14.
A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam. 相似文献
15.
本文以两种绝缘内核的发电机为基准,设置内核电导率与外核相同,选择了以固定速度超速旋转和在外核驱动下发生旋转的两种内核旋转模式,比较分析不同模型间的能量差异、磁场强度、磁雷诺数、磁极翻转频率和四个类地发电机参数.结果表明:对于弱偶极子发电机模型,有限导电内核的引入会对其偶极子强度的相对变化量造成较大影响,最高达103.00%;由外核驱动旋转的有限导电内核模型对于本文其他目标研究量所带来的影响比较小,均小于5%;而固定旋转速度的有限导电内核的模型对磁极翻转频率、赤道对称性和纬向性均存在较明显影响,最大变化量达124.62%.综合本文所选用的发电机模型的特征和数值分析结果,可以发现虽然由外核驱动旋转的有限导电内核模型其转速不可控且存在较大波动,但各物理量变化量与实际内核与外核的能量比更为接近,因此可以推断其驱动机制较自驱动模式更为合理可靠. 相似文献
16.
为了探究土层场地放大作用的机制,利用金银岛岩土台阵在四次地震中记录的26组弱震动的三分量加速度时程,采用考虑上行波场与下行波场相消干涉作用的传统谱比法,研究了土层场地的放大作用随深度的变化规律.结果表明：（1）地震波从基岩传播到土层中时,土层的多个振型被激励,放大作用随深度的变化是按照不同振型的特征而有规律地变化.自下而上直至地表,一阶振型的场地放大作用是逐渐增大的;二阶振型的场地放大作用经历了逐渐减小和逐渐增大两个过程;三阶振型的场地放大作用经历了逐渐增大、逐渐减小和逐渐增大三个过程;四阶振型的场地放大作用经历了逐渐减小、逐渐增大、逐渐减小和逐渐增大四个过程;更高阶振型的场地放大作用可以据此类推.（2）四次地震中同一振型的NS和EW两个水平分量的自振频率相差很小;二阶到六阶5个振型与一阶振型的自振频率之比小于相应的理论模型之比.（3）四次地震中均存在一些高阶振型的放大系数大于其一阶振型相应分量的放大系数的现象.目前的场地反应分析中,往往将最大放大系数对应的频率作为场地的卓越频率,这么做的结果,很有可能将不同振型的自振频率作为场地的卓越频率,导致同一地震中不同水平分量的卓越频率相差较大,或者在不同地震中同一水平分量的卓越频率差别较大,难以描述场地的固有特性;而按照不同振型分析场地放大作用的特征,可以从本质上揭示场地的固有特性. 相似文献
17.
Yanadet Sripanich Sergey Fomel Junzhe Sun Jiubing Cheng 《Geophysical Prospecting》2017,65(5):1231-1245
The goal of wave‐mode separation and wave‐vector decomposition is to separate a full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse‐time migration to handle each wave mode independently. Several of the previously proposed methods to accomplish this task require the knowledge of the polarisation vectors of all three wave modes in a given anisotropic medium. We propose a wave‐vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low‐rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low‐symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase‐velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artefacts caused by the local discontinuity of polarisation vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal–noise orthogonalisation. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media. 相似文献
18.
S. M. Molodenskii M. S. Molodenskii M. S. Molodenskaya 《Izvestiya Physics of the Solid Earth》2014,50(5):611-621
In the first part of the paper, we obtained the refined estimates for the periods and Q-factors of the fundamental modes and overtones of spherical and toroidal oscillations with periods longer than 3 min from the data on the free oscillations of the Earth, which were excited by the earthquakes with magnitude 9 that occurred in Sumatra, Japan, and the Sea of Okhotsk. In (Molodenskii et al., 2013), we analyzed the limits of the admissible density distributions in the mantle and liquid core of the Earth, using the data on the amplitudes and phases of the forced nutations, as well as the periods and attenuation factors of the fundamental modes of the free spheroidal and toroidal oscillations of the Earth. These studies were conducted with the fixed values of the total mass and total moment of inertia of the Earth and the fixed distributions of the body seismic waves in the mantle and in the core. The solution was obtained by orthogonalizing the kernels of the integral equations that link the residuals of the observed frequencies and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, with the sought densities and Q-factors of the mantle and liquid core. Below, we present the solution of the same problem with allowance for the results obtained in the first part of this paper, namely, the new data on the periods and attenuation factors of the fundamental modes of free oscillations of the Earth and on the periods of the first four overtones of the free spheroidal and toroidal oscillations. Despite the involvement of the new data on the overtones, which have not been considered in our calculations, the weighted root mean square deviations of the theoretical predictions from the observed periods and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, have significantly decreased. This is due to (1) the noticeable reduction of the real errors in estimating the parameters of the free oscillations described in the first part of the paper and (2) the inclusion of the quantities determining the depth- and frequency dependences of the Q-factor in the mantle in the set of the independently varied parameters. 相似文献
19.
The available procedure for earthquake analysis of axisymmetric intake-outlet towers is extended to towers of arbitrary geometry, but with two axes of plan symmetry, and to include the effects of tower-foundation-soil interaction. The total system is represented as four substructures: tower, surrounding water, contained water and the foundation supported on flexible soil. The substructure representation of the system permits use of the most effective idealization for each substructure. An example earthquake response analysis is presented to demonstrate the results obtained from the analysis procedure. Computation times for several cases are included to demonstrate the efficiency of the analysis procedure. 相似文献
20.
A computationally efficient boundary integral equation technique to calculate the dynamic response of a group of rigid surface foundations bonded to a layered viscoelastic half-space and subjected to external forces and seismic waves is presented. The technique relies on an iterative scheme which minimizes in-core memory requirements and takes advantage of any geometrical symmetry of the foundations. Extensive results for the case of two rigid square foundations placed at different separations and bonded to a viscoelastic half-space are presented. It was found that the choice of discretization of the foundations has a marked effect on the calculated impedance functions for extremely small separations. Illustrative results for a case of several closely-spaced foundations bonded to a layered half-space are also presented. 相似文献