THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD

The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.

Numerical verification of geometry control method of the construction for super-span cable-stayed bridge

Taking Sutong Bridge as the object investigated, the correctness of the geometry control method is verified by numerical simulation analysis. Taking the impact of geometric nonlinearity into account, the impacts of structural geo- metric profile induced by temporary loads and temperature field during the construction procedure are investigated. The simulation results indicate that only the stage state of the structure during construction is affected. Satisfied outcome of construction control can be achieved based on ~eometrv control method.

Modeling and Analysis of Vibration Characteristics of Rectangular Plate with Circular Through Hole Under Complex Boundary Conditions

This paper presents a method to study the free vibration of a plate with circular holes.The circular hole is regarded as a virtual small plate in which the mass density and Young's modulus are zero.Therefore,the free vibration problem of the circular hole plate can be transformed into the free vibration problem of the equivalent rectangular plate with non-uniform thickness.The model is derived from the spectral geometry method(SGM),and the displacement of the plate with circular holes is expanded by the modified Fourier series.Virtual springs are added to the boundary of the plate to simulate the boundary conditions of simply supported and fixed supports.The accuracy of this method is verified by comparison with the finite element calculation results.The relationship between modal numerical solutions of plates with circular holes and boundary conditions and geometry of the plate is studied.

Travel time and alternative configurations analysis for automated storage/retrieval systems based on geometrical method

In order to evaluate the efficiency of the automated storage/retrieval system(AS/RS)accurately,and compare different layouts of the AS/RS using mean travel time,under randomized storage conditions,an exact,geometry-based analytical model is presented.The model can be used to compute the expected single-command and dual-command travel time for a storage/retrieval(S/R)machine which can travel simultaneously horizontally and vertically as it moves along a storage aisle.The rack may be either square in time or non square in time.Additionally,the alternative layouts of the AS/RS and travel-time models are examined.Comparing with setting the I/O point at the left-lower corner of the rack,setting the I/O point at any point at the vertical edge can help enhance the efficiency of the AS/RS.

Gravity changes and surface deformations due to faults with different geometry

Based on the formulae of the gravity changes and surface deformations raised by the dislocation of a point source,the gravity changes and deformations caused by the dislocations of fault with arbitrary geometry are computed by using numerical method. The results show that both of the dislocation and the geometry of the fault plane are the basic elements that determine the gravity and deformation effects. Gravity changes, vertical deformations and apparent vertical deformations induced by the dislocation are alike in their characteristic patterns. The similarities and differences of these patterns provide us a probability in acquiring the gravity and deformation anomalies due to faulting from the observed data. Thus the geometric and kinematic features of the earthquake-generating faults can be appropriately distinguished and evaluated.

On simulation of precise orbit determination of HY-2 with centimeter precision based on satellite-borne GPS technique

The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so that the observations are not openly released. In order to study the precise orbit determination precision and procedure for HY-2 based on the satellite- borne GPS technique, the satellite-borne GPS data are simulated in this paper. The HY-2 satellite-borne GPS antenna can receive at least seven GPS satellites each epoch, which can validate the GPS receiver and antenna design. What＇s more, the precise orbit determination processing flow is given and precise orbit determination experiments are conducted using the HY-2-borne GPS data with both the reduced-dynamic method and the kinematic geometry method. With the 1 and 3 mm phase data random errors, the radial orbit determination precision can achieve the centimeter level using these two methods and the kinematic orbit accuracy is slightly lower than that of the reduced-dynamic orbit. The earth gravity field model is an important factor which seriously affects the precise orbit determination of altimeter satellites. The reduced-dynamic orbit determination experiments are made with different earth gravity field models, such as EIGEN2, EGM96, TEG4, and GEMT3. Using a large number of high precision satellite-bome GPS data, the HY-2 precise orbit determination can reach the centimeter level with commonly used earth gravity field models up to above 50 degrees and orders.

Configuration Optimization of Two-Rail Sliders on Dynamic Characteristic

An optimal design methodology for the configuration of two rail slider was proposed to get better dynamic performance. The taper length, taper height and the rail width of the reading/writing head are considered as design variables. The complex geometry method is utilized as the search scheme in the optimization process. Optimization results show that the new slider has better dynamic characteristics and is more stable than the original designed slider. The optimization process also demonstrates that the optimum model and optimum method is effective.

Analytic solution for Reissner plate bending based on new symplectic approach

This paper presents the analytic solution for Reissner plate bending derived by the symplectic geometry approach.Firstly,the basic equations for Reissner plate are transferred into Hamilton canonical equations.And then the whole state variables are separated.Finally,the solution is obtained according to the method of eigenfunction expansion in the symplectic geometry.Only the basic elasticity equations of Reissner plate are used in the present study and the pre-selection of the deformation function is abandoned,which is requisite in classical solution methods.Therefore,the utilized approach is completely reasonable and theoretical.To verify the accuracy and validity of the formulations derived,the numerical results are presented to compare with those available in the open literatures.

Distributed Capacitance of Coaxial Line With Perturbed Walls

Perturbation method of boundary geometry(PMOBG) used in Lapiacian problems is dealt with and the three--term perturbation expression of distributed capacitance of a coaxial line with perturbed walls is obtained. As an example,four-order expression of distributed capacitance of a elliptic coaxial line with small eccentricity is given.

NEW SCALAR-TYPE EQUILIBRIUM EQUATIONS OF THE GENERAL SPACE FORCE SYSTEM

Using the principle of analytical geometry, several properties of the space straight lille are proved. Based on these properties, the equilibrium of general space force system is considered and its four new scalar-type equilibrium equations are derived which are equivalent to the vector-type necessary and sufficient conditions far equilibrium.

A new method of broadband constant beamwidth beamforming for arbitrary geometry arrays

A new method of broadband constant beamwidth beamforming for arbitrary ge- ometry arrays is proposed. In this method, the response vector of an arbitrary geometry array is expanded into the form of sum of an infinite series, whose core function is the first kind Bessel function. The high terms of this series are truncated so that the array response vec- tors at different frequencies can be transformed to a reference frequency and then the constant beamwidth beamforming vectors are ready to obtain. With these beamforming vectors, beams at different frequencies are same as the reference beam. A reference beam optimizing method based on adaptive processing is also proposed to optimize the reference beam of arbitrary ge- ometry arrays. Computer simulation for a uniform circular array verified the effectiveness of the new method proposed.

Groove modeling and digital simulation for intersecting structures of circular tubes based on coplanarity of vectors

In order to establish the groove model for intersecting structures of circular tubes,mathematical model of the intersecting line is established by the method of analytic geometry,and parametric equations are thus determined.The dihedral angle,groove angle and actual cutting angle for any position of the intersecting line are derived as well.In order to identify groove vectors for two pipes,a new analytical method,i.e.coplanarity of vectors,is further proposed to complete the groove model.The established model is virtually verified by programming and simulation calculation in the MATLAB environment.The results show that groove vectors of intersecting structures simulated by MATLAB are consistent with the theoretical groove model,indicating that the theoretical groove model established in this paper is accurate,and further proves that the proposed coplanarity of vectors for solving groove vectors is correct and feasible.Finally,a graphical user interface(GUI)is developed by MATLAB software to independently realize functions such as model drawing,variable calculation and data output.The research outcome provides a theoretical foundation for the actual welding of circular intersecting structures,and lays an essential basis for weld bead layout and path planning.

Automated pavement horizontal curve measurement methods based on inertial measurement unit and 3D profiling data

Pavement horizontal curve is designed to serve as a transition between straight segments, and its presence may cause a series of driving-related safety issues to motorists and drivers. As is recognized that traditional methods for curve geometry investigation are time consuming, labor intensive, and inaccurate, this study attempts to develop a method that can automatically conduct horizontal curve identification and measurement at network level. The digital highway data vehicle （DHDV） was utilized for data collection, in which three Euler angles, driving speed, and acceleration of survey vehicle were measured with an inertial measurement unit （IMU）. The 3D profiling data used for cross slope calibration was obtained with PaveVision3D Ultra technology at 1 mm resolution. In this study, the curve identification was based on the variation of heading angle, and the curve radius was calculated with ki- nematic method, geometry method, and lateral acceleration method. In order to verify the accuracy of the three methods, the analysis of variance （ANOVA） test was applied by using the control variable of curve radius measured by field test. Based on the measured curve radius, a curve safety analysis model was used to predict the crash rates and safe driving speeds at horizontal curves. Finally, a case study on 4.35 km road segment demonstrated that the proposed method could efficiently conduct network level analysis.

Decay Rates of the Hyperbolic Equation in an Exterior Domain with Half-Linear and Nonlinear Boundary Dissipations

This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.

On Boundary Stability of Wave Equations with Variable Coefficients

In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemmannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua are generalized to the variable coefficient case by some computational techniques in Riemmannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalitities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.