Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

Equivalent bending stiffness of simply supported preflex beam bridge with variable cross-section

In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.

Earth＇s Temporal Principal Moments of Inertia and Variable Rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.

A Measuring Method on Moment of Inertia of Large-scale Ammunition

A compound pendulum based measurement method is put forward and the relevant equipment is designed. By using the variation of angle with the time acquired by an angular displacement sensor, the moment of inertia is obtained through the numerical solution of certain equations, which are deduced from the phase-plane analysis of compound pendulum. The influences of both friction and air resistance on the compound pendulum are already taken into consideration without estimating and measuring the resistances in advance. With this method, the to-be-measured object can be positioned and fixed easily and safely. Numerical simulations show a favorable precision of this method.

Uncertainty analysis of ship model vertical center of gravity and transverse moment of inertia test

The usability of test results of ship model vertical center of gravity and transverse moment of inertia is generally depends on its uncertainty. Referring to the guidelines for uncertainty analysis in examination of liquid dynamic recommended by International Towing Tank Conference （ ITTC）, the results were analyzed, bias limits and precision limits were calculated and total uncertainty was estimated. The total uncertainty of six tests on ship model vertical center of gravity is is 0. 16% of the mean value, and the total uncertainty of six tests on ship model transverse moment of inertia is 5.66% of the mean value. The test results show that the total uncertainty of both the multiple tests and the single test is from the precision limits of ship model vertical center of gravity and transverse moment of inertia tests. Thus, the improved measurement system stability can enormously decrease the total uncertainty of multiple tests and the single test.

THE CALCULATION METHOD OF FLYWHEEL MOMENT OFINERTIA OF CRANE MECHANISM

The origin and substance of the tlywheel moment calculation method of inertia mo ment of crane mechanism are set forth comprehensively and systematically in this paper, that is, the nucleus or the focus ofmoment of inertia calculation is the problem of calculating convertible tlywheelmoment. It is much better for the calculation of flywheel moment of loading move mass of lifting, traveling and rotating mechanism using the low of conservation of energy, the theorem of kinetic energyfor that of radius - changing mechanism, and the law of conservation of energy for that of all parts of gearing mechanism.

Coupling Analysis of Moment of Inertia & Dynamic on Optoelectronic Tracking Turntable

With photoelectric tracking system as the research object,based on the theorem of moment of momentum and Euler dynamic equation,Nonlinear biaxial coupling dynamic model of tracking turntable is established.Effects of moment of inertia coupling,speed coupling and the dynamic coupling between tracking turntable shafts were studied,the analytical relation between them was given in theory.Verify the change trend of theoretical model.And it provides the theory reference and model base,for the future design of the high precision tracking controller And control parameter selection and optimization.In the end,specific measures are made for structure optimization.

Measurement of Moment of Inertia Based on Hilbert Transform

A measurement model based on torsion pendulum was established,in which nonlinear damping and nonlinear restoring force were considered.The calculation method of the moment of inertia was based on Hilbert transform.The motion of torsion pendulum showed the time-frequency characteristics due to the nonlinear factors,which were validated by the experimental data.The analytical signal was formed by Hilbert transform of the angular displacement signal of the test object.The moment of inertia can be computed by the instantaneous undamped natural frequency with Hilbert transform.Prior to the implementation of Hilbert transform,the empirical mode decomposition was used to filter the experimental signal.The moment of inertia of the test object was measured by the torsion pendulum system.The experimental results show that the relative measurement error of the moment of inertia was within 0.7%,which indicated the validity of the measurement method.

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Moments of Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments ofinertia of deformed actinide nuclei is investigated using the particle-number conserving (PNC)method for treating the cranked shell model with monopole and quadrupole pairing interactions. PNCcalculations show that the large odd-even difference in moments of inertia mainly comes from theinterference contributions j(μv) from particles in high j intruder orbitals μ and v quite near theFermi surface, which have no counterpart in the BCS formalism. The effective monopole andquadrupole pairing interaction strengths are determined to fit the experimental odd-even differencesin binding energies and bandhead moments of inertia. The experimental results for the variation ofmoments of inertia with rotational frequency ω are reproduced well by the PNC calculation. Thenearly identical experimental moments of inertia between ~(236)U(gsb) and ~(238)U(gsb) at lowfrequencies hω ≤ 0.20 MeV are also reproduced quite well.

Torque Free Axi-Symmetric Gyros with Changing Moments of Inertia

The properties and characteristics of torque free gyros with rotational symmetry and changing moments of inertia are the subject of the subsequent discussion. It shall be understood that the symmetry can be expressed by the notation (A=B) which does not presuppose geometric symmetry, where A and B are the principle moments of inertia about x and y axes respectively. We study the case of a torque free gyro upon which no external torque is acting. The equations of motion are derived when the origin of the xyz-coordinate system coincides with the gyro’s mass center c. This study is useful for the satellites, which have rotational symmetry and changed inertia moments, the antennas and the solar power collector systems.

Spin Cut-off Parameter of Nuclear Level Density and Effective Moment of Inertia

The spin cut-off parameter of the nuclear level density and effective moment of inertia for a large number of nuclei have been determined from analysis of the experimental data on S-wave neutron resonances and spins of lowlying levels. Contrary to claims made before, it is shown the spin cut-off parameter differs considerably from their corresponding rigid body values, and the energy dependence of the effective moment of inertia confirms the interacting fermion model prediction.

Quadrupole Pairing Correlations and Moments of Inertia of Superdeformed Nuclei

The Harmonic OseiUator Quadruple Pairing Cranking Hartree-Fock-Bogoliubov（HFB）theoreti-cal model is established and applied to the superdeforrned（SD）rotational states.The reduction and col-lapse of the pairing fields,including Y20,Y21 and Y22 fields at superdeformation and high spins,are stud-ied.It is found that the correct rotational frequency ω-dependence of the pairing fields is crucial for thetheory to reproduce the rising behavior of dynamic moment of inertia J（2） observed in the A=190 region,and the Y21 pairing contributes significantly to reducing the rising rate of J（2） and thus may strongly influ-enee the collective properties of SD nuclei.The calculated J（2） of 192H8 is in good agreement with the ex-perimental data up to （?）ω=0.32 MeV.

Role on Moment of Inertia and Vortex Dynamics for a Thin Rotating Plate

In this study, we focused on the lift generation with a thin rotating plate. The objective of this study is to understand the appropriate shape and the role of vortex for rotating thin plate. We determined the shape of the plate through free-flight tests of paper strips and investigated the aerodynamic characteristics of the rotating plate with the selected shape. The rectangular plate with an aspect ratio 7 was relevant from moment of inertia and bending stress. An endplate on a wing tip increased the stability on the lateral vortex structure behind the rotating plate. Velocity field measurement by Particle Image Velocimetry (PIV) showed that the lift force was generated twice in a rotating cycle.

Torsional inertia moment of beam element with complex section analysis based on FEM

Currently, for the analysis of complex bridge based on beam element, the calculation of cross-section torsional inertia moment is still an unresolved technical problem. Most current calculation of section torsional inertia moment is an approximate analytic method for two-dimensional cross-section, which is not fully consistent with the actual situation, and do not consider the effects of diaphragm in bridge. In order to analyze accurately cable-stayed bridge, suspension bridge and other complex bridge structures based on beam element, the calculation method of section torsional inertia moment based on finite element method (FEM) is invented in this paper. Firstly, setting up local cantilever fine model with solid element or shell element and applying torsion on the end of cantilever. Secondly, calculating the torsion angle of cantilever by FEM method and then the torsional moment through equivalent beam method. Finally, the examples of the section torsional moment calculation of concrete model with solid element with diaphragm and steel girder box model with shell element with diaphragm are used to verify the calculation method, which is applied to the suspension bridge design and construction control special software SBNA developed by Research Institute of Highway Ministry of Transport. Taizhou Bridge under construction is one of the examples.

The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth

As an indication of the Earth＇s mass distribution, the principal moments of inertia （PMOI, i.e., A, B, C） of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth＇s interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184~, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 x 10-5 MR2, and the global dynamical flattening （H） is calculated to be 3.29587 ~ 10-3, which is 0.67% different from the latest observation derived value Hobs（3.273795 × 10 ^-3） （Petit and Luzum, 2010）, and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a gener- alized theory of the hydrostatic equilibrium figure of the Earth.

Calculating Methods of Inertia Moment of TurboGenerator Rotor Using Load Rejection Test

Calculated results of inertia moment of turbo-generator rotor can be quite different by methods used in load rejection tests. In view of fluctuation features of rotor speed rise curve during load rejection tests, the measurement principle of rotor inertia moment was expounded. Based on the measured data in load rejection tests for an imported type of domestic 300-MW generating unit, the rotor speed rise curve was fitted with three kinds of functions to get initial runup rate, but the obtained results differed a lot from each other. According to analysis on the mechanism of rotor speed rise, m=2 consecutive points averaging or FFT (Fast Fourier Transform) smoothing technology was introduced to process test data, and then the initial runup rate was determined by the method of linear fitting of rotor speed in the range of governing valve closing time. Although the obtained curves had a fluctuating shape, the results of rotor inertia moment for 50% and 100% load rejection tests were of good consistency.

The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Motions in Complex Plane

In this paper, the Steiner area formula and the polar moments of inertia were expressed during one-parameter closed planar motions in complex plane. The Steiner points or Steiner normal concepts were described according to whe-ther rotation number was different from zero or equal to zero. The moving pole point was given with its components and its relation to the Steiner point or Steiner normal which was specified. The Steiner formula and the polar moments of inertia were expressed for the inverse motion. The fixed pole point was calculated for the inverse motion. The sagittal motion of a tele-scopic crane was considered as an example. This motion was described by a double hinge consisting of the fixed control panel of the telescopic crane and its moving arm. The results obtained in the first section of this study were applied to this motion.

基于火箭简化模型的多状态模型修正研究

火箭发射过程中燃料的不断减少导致火箭结构不断变化,结构的固有频率和模态振型也会随之变化。针对有限元模型的不准确性,以截面惯性矩为修正参数,不同状态下数值仿真结果与试验测试结果的误差最小为目标函数,建立多状态模型修正的优化模型。通过灵敏度分析和一阶泰勒展开对目标函数进行显式化处理,并利用序列线性规划求解得到设计变量的最优解。同时对于多状态结构,以多截面简支梁模型为例,利用锤击法对简支梁进行试验,设计磁吸重物方案模拟多状态模型,以单截面简支梁试验的前4阶频率为目标函数建立优化模型,经过修正将多截面简支梁模型修正为单截面简支梁模型,并且符合截面惯性矩与面积的比例,验证了多状态模型修正方法的准确性。

考虑结合面影响的弯矩载荷下法兰螺栓载荷计算方法

针对法兰结构的结合面和螺栓共同承受外部弯矩载荷,基于梁的纯弯理论,依据梁的弯曲平面假设及单向受力假设,提出一种基于法兰整体惯性矩的螺栓载荷分析方法。该方法通过计算法兰结构在弯矩载荷下法兰结合面、螺栓的整体惯性矩,再根据弯矩载荷计算最大螺栓载荷。该方法根据法兰结合面尺寸、螺栓分布计算螺栓载荷,不受法兰结构形式的影响。采用该方法、有限元法、中心回转计算法、偏心回转计算法对典型法兰结构在弯矩载荷下的螺栓受力进行分析,该方法与有限元分析方法计算结果一致,相对于其他方法具有更高的精度。将该方法、中心回转计算法、偏心回转计算法应用于带有翼板的法兰结构,该方法得到的螺栓载荷相对较小。