Dynamic Deformation Monitoring of Lotsane Bridge Using Global Positioning Systems (GPS) and Linear Variable Differential Transducers (LVDT)

The measurements and analysis of deformation of engineering structures such as dams, bridges and high-rise buildings are important tasks for civil engineers. It is evident that, all civil engineering structures are susceptible for deterioration over a period of time. Bridges in particular, deteriorate due to loading conditions, environmental changes, earth movement, material used during construction, age and corrosion of steel. Continuous monitoring of such structure is the most important aspect as it provides quantitative information, assesses the state of the structure, detects unsafe positions and proposes early safety measures to be taken before it can threaten the safety of vehicles, goods and human life. Despite government’s efforts to construct roads and highways, bridge deformation monitoring has not been given priority in most of African countries and ultimately causes some bridges to collapse unexpectedly. The purpose of this research is to integrate Global Positioning System (GPS) and Linear Variable Differential Transducers (LVDT) to monitor deformation of a bridge. The horizontal positions of reference and monitoring points were determined using Global Positioning System (GPS) while the vertical deflections, accelerations and strain were determined using Linear Variable Differential Transducers (LVDT). The maximum displacements obtained between zero and first epochs in x, y and z components were 0.798 m, at point LT08, 0.865 m at point BR13, and 0.56 m at point LT02 respectively. The maximum deflections for LVDT 1, 2 and 3 are 28.563 mm, 31.883 mm and 40.926 mm respectively. Finally, the correlation coefficient for the observations was 0.679 with standard deviations of 0.0168 and 0.0254 in x and y respectively. Our results identified some slight displacements in horizontal components at the bridge.

A SEMI-ANALYSIS METHOD OF DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS UNDER COMPLICATED BOUNDARY CONDITIONS

Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential equations with variable coefficients. On most occasions and due to the nonuniformity nature, nonlinearity property can cause the equations of the kinds. Using the model, the satisfactory valuable results with only a few units can be obtained.

EXACT ANALYTIC METHOD FG(?) SOLVING VARIABLE COEFFICIENT DIFFERENTIAL EQUATION

Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.

DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

The theoretical analysis of dynamic response on cantilever beam of variable stiffness

The paper presents the theoretical analysis of a variable stiffness beam. The bending stiffness EI varies continuously along the length of the beam. Dynamic equation yields differential equation with variable co- efficients based on the model of the Euler-Bernoulli beam. Then differential equation with variable coefficients becomes that with constant coefficients by variable substitution. At last, the study obtains the solution of dy- namic equation. The cantilever beam is an object for analysis. When the flexural rigidity at free end is a constant and that at clamped end is varied, the dynamic characteristics are analyzed under several cases. The results dem- onstrate that the natural angular frequency reduces as the fiexural rigidity reduces. When the rigidity of clamped end is higher than that of free end, low-level mode contributes the larger displacement response to the total re- sponse. On the contrary, the contribution of low-level mode is lesser than that of hi^h-level mode.

Optimization design and experiment of the variable differential gear train planting mechanism

In order to improve the adaptability of the planting mechanism for different plant spacings,a variable differential gear train planting mechanism based on precise pose and trajectory control was proposed by combining the open chain 2R rod group and the variable differential gear train.According to the pose requirements of receiving seedling point,transporting seedling point and planting point,three precise pose points of constrained planting trajectory were determined.Through the three-position motion generation structural synthesis method,combined with computer-aided optimization design software,a set of mechanism parameters that meet the planting requirements were optimized.Based on the optimized mechanism parameters,by only changing the coordinates of two trajectory shape control points,three planting trajectories with key point position information adapted to 300 mm,400 mm and 500 mm plant spacing were obtained by interpolation,and three pairs of total transmission ratio of three groups of variable differential gear trains were calculated.When distributing the total transmission ratio of the mechanism,the fixed axis gear train and the differential gear train are combined.The fixed axis gear train included a pair of non-circular gear pairs and a pair of positive gear pairs,which were convenient for disassembly and assembly.The former drives the sun gear at variable speed,and the latter drives the planet carrier at uniform speed.Based on this structure,the transmission ratio of the positive gear pair is-1,and the transmission ratio of the differential gear train is 0.5.The sub-transmission ratio of the single-stage non-circular gear pair was calculated and the pitch curves of three pairs of noncircular gears were solved.Three pairs of non-circular gear pairs with different transmission ratios were replaced in turn and three sets of planting mechanisms were modeled in three dimensions.The virtual prototype motion simulation was completed by ADAMS software,and the physical prototype was built for vegetable pot seedling planting test.The theoretical solution was consistent with the attitude and trajectory of the actual test.When the test sample size was 100 plants,the actual average plant spacing was measured to be 303 mm,402 mm,and 503 mm,with errors of 1.3%,1.25%,and 1.88%.The width of the moving hole was 72 mm,70 mm,and 71 mm,and the planting success rate were 94%,96%,and 95%.The test results verified the correctness of the optimization design results of the mechanism,indicating that the variable differential gear train planting mechanism can adapt to a variety of plant spacing and has good planting effect.

Line-element based nonlinear adaptive piecewise compensating correction for LVDT sensors

In order to solve the linear variable differential transformer （LVDT） displacement sensor nonlinearity of overall range and extend its working range, a novel line-element based adaptively seg- menting method for piecewise compensating correction was proposed. According to the mechanical structure of LVDT, the output equation was calculated, and then the theoretic nonlinear source of output was analyzed. By the proposed line-element adaptive segmentation method, the nonlinear output of LVDT was divided into linear and nonlinear regions with a given threshold. Then the com- pensating correction function was designed for nonlinear parts employing polynomial regression tech- nique. The simulation of LVDT validates the feasibility of proposed scheme, and the results of cali- bration and testing experiments fully prove that the proposed method has higher accuracy than the state-of-art correction algorithms.

Experimental Behavior of Recycled Aggregate Concrete Filled Steel Tubular Columns

During the modernization or rehabilitation activity,the demolished structural waste causes large soil pollution and unavailability of natural aggregate is the big concern for the construction industry.Therefore,this manuscript deals with the Composite Steel Circular Column(CSCC)with Recycled Aggregate concrete(RAC)as infill is partly used,with the replacement of 25%and 50%in M30 grade of Concrete.And internal reinforcement steel is fully replaced by rolled steel tubes(circular and square)with varied thickness,ISA-unequal angle.Around 14 specimens are cast and examined under axial load for analysis of the deflection characteristics,the load-bearing capacity along with its buckling behavior.The experimental values are estimated through LVDT(linear variable differential transducer)at 3-phase.The curve of load-deflection is drawn with the load pattern.From the date interpretation,it is found column made of 50%-RAC has more than 25%-RAC.

Fuzzy Modeling, Tracking Control and Synchronization of the Rossler's Chaotic System

In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.

Global Exponential Stability of Variable Delay and Time－varying Measure Differential Systems with Impulse Effect

This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.

On a Linear Partial Differential Equation of the Higher Order in Two Variables with Initial Condition Whose Coefficients are Real-valued Simple Step Functions

By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.

System integration for on-machine measurement using a capacitive LVDT-Iike contact sensor

In this study, an air-bearing capacitive linear variable differential transformer （LVDT）-like contact sensor with a rounded diamond tip was mounted to a desktop machine tool to construct an on-machine （OM） measuring system. The measuring system was capable of decoding the digital signals of linear encoders mounted on the machine tool and acquiring the analog signal of the contact sensor. To verify the measuring system, experimental examinations were performed on an oxygen-free copper （OFC） convex aspheric mold with a diameter of 5 mm and a curve height of 0.46 mm. The acquired signals were processed by the implemented Gaussian regression filter （GRF）, removing the tilt of measured profile, and compensating for the radius of probe tip. The profile obtained was compared to that measured using a commercially available device, and a maximum deviation of 14.6μm was found for the rough cutting. The compensation cutting was then performed according to the form error of OM measurement. As a result, the PV form error compared with the designed profile was reduced from 19.2μm over a measured diameter of 4 mm to 9.7 μm over a measured diameter of 3.1 mm, or a percentage improvement of 35.4% in form accuracy. Through the examination for aspheric machining, the effectiveness of the implemented OM measuring system was demonstrated, and the technical details of system implementation were presented. Further improvement was suggested to reduce the diameter of probe tip and measuring force.