Experimental and simulation studies on similitude design method for shock responses of beam-plate coupled structure

The similitude theory helps to understand the physical behaviors of large structures through scaled models. Several papers have studied the similitude of shock issues. However, the dynamic similitude for shock responses of coupled structures is rarely incorporated in open studies. In this paper, scaling laws are derived for the shock responses and spectra of coupled structures. In the presented scaling laws, the geometric distortion and energy loss are considered. The ability of the proposed scaling laws is demonstrated in the simulation and experimental cases. In both cases, the similitude prediction for the prototype's time-domain waveform and spectrum is conducted with the scaled model and scaling laws. The simulation and experimental cases indicate that the predicted shock responses and spectra agree well with those of the prototype, which verifies the proposed scaling laws for predicting shock responses.

Effect of Froude similitude deviation on curved channel simulations: A case study in the Middle Yangtze River

Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-world situations.This study developed several fixed-bed river models with various curvatures to determine the effect of Froude similitude deviation on curved channel modeling.Models were constructed according to the characteristics of the Middle Yangtze River.Differences in longitudinal slope,transverse slope,and main stream line location were measured by varying Froude similitude deviation.The deviations of longitudinal slope and velocity were negligible because friction similitude was accounted for.The transverse slope varied significantly with the Froude similitude deviation,and the main stream line varied with the curvature and Froude similitude deviation.Formulae were derived to estimate the slope deviation.These analyses helped to clarify the feasibility of the method of Froude similitude deviation for curved channels.

Experimental Study on the Ride Comfort of a Crawler Power Chassis Scale Model Based on the Similitude Theory

The ride comfort experimental assessment of crawler off-road vehicle is relatively overlooked, and is expensive and difficult to execute with higher and higher ride comfort performance requirements. To trade off between precise and cost, an experimental method based on the similitude theory is proposed. Under the guidance of the similitude theory, a 1：5 crawler power chassis scale model equipped with a kind of variable stiffness suspension system is used. The power spectrum density（PSD）, the root mean square（RMS） of weighed acceleration, peak factor, average absorbed power（AAP） and vibration dose value（VDV） are selected as ride comfort evaluation indexes, and tests results are transformed via similarity indexes to predict the performance of full-scale power chassis. PSD shows that the low-order natural frequency of the vertical natural frequency（z axis） is 1.1 Hz, and the RMS, AAP and VDV values indicate the ride comfort performance of this kind of power chassis is between the ＂A little uncomfortable＂ and ＂Rather uncomfortable＂. From the results, low-order vertical natural frequency, obtained by PSD, validates that the similarity relationship between two models is satisfied, and 1：5 scale model used in experiment meets the similarity relationship with the full-scale model; consequently, the ride comfort prophase evaluation with the 1：5 scale model is feasible. The attempt of applying the similitude theory to crawler vehicle ride comfort test study decreases the cost and improves the test feasibility with sufficient test precise.

Investigation of acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure

In this paper, the acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure are investigated. The similitude conditions and relations between the similitude model and its prototype were studied in the references. This paper investigates the acoustic scale effects for the similitude model, which are influenced by loss factor, shear and rotatory inertia. At the same time, the boundary effects which are influenced by surface sound reflection are investigated in the experiment of similitude model. The results show that the acoustic scale effects may be controlled with model designing, the boundary effects can be controlled with experimental designing between the similitude model and its prototype.

Compliant Mechanism Synthesis by Using Elastic Similitude

Compliant mechanisms have several advantages, especially smaller number of elements and therefore less movable joints. The flexural members furthermore allow an integration of special functions like balancing or locking. Especially fiber reinforced materials exhibit a wide range of function integration considering their compliance in passive as well active applications. To take advantage of compliant elements in applications a robust synthesis tool is needed. The synthesis based on topology optimization method or the pseudo rigid body approach leads to complex structures. Considering the use of fiber reinforced material a synthesis approach which leads to less complex structures is more suitable. For building up simple structures, with only one cantilever beam as compliant element（B） a graphical approach using the elastic similitude is the most efficient method. A step-by-step synthesis procedure is presented to synthesize compliant mechanisms with rotatory joints（R） and prismatic joints（P） to develop RRB/PRB- and RPB-linkages. Using the elastic similitude to implement these results into a graphical synthesis algorithm is the innovation part of this paper. It can be shown that this approach leads to a comfortable handling of beam elements during the synthesis, where the two free parameters can be directly coupled to scale and fix the orientation of the beam element. This advantage inherently shortens the development process. In giving an example the focus lies of the experimental approach, which also shows that the simple BERNOULLI beam model is valid and so the synthesis by using the elastic similitude. The method is presented and discussed by using an application for a cup holder mechanism made of fiber reinforced material.

Application of Froude dynamic similitude in anaerobic baffled reactors to prediction of hydrodynamic characteristics of a prototype reactorusing a model reactor

An anaerobic baffled reactor is a system developed in recent decades and has been used as part of the treatment of high-strength wastewater. Since the function of this system is based on its hydrodynamic features, hydrodynamics and the regime of the flow through the reactor are crucial. In this study, a prototype reactor with eight chambers, which had a total volume of 48 L, and a model reactor, whose dimensions were half of those of the prototype reactor, were used. The Froude dynamic similitude in these reactors was investigated. The results show that the curve dimensionless variances were 0.089 and 0.096 for the prototype and model reactors, respectively, the short-circuiting indices were 0.483 and 0.489 for the prototype and model reactors, respectively, the effective volume and short-circuiting index measurement errors were both 1%, the hydraulic efficiency error was 2%, and the Peclet and dispersion number errors were both 7%. Most of the compared indices were close to one another in value. Therefore, the model reactor can be used based on the Froude dynamic similitude to determine hydrodynamic charac-teristics of a baffled reactor at a full scale.

Evaluation of the Power Generation Capacity of Hydrokinetic Generator Device Using Computational Analysis and Hydrodynamic Similitude

This paper presents a similitude and computational analysis of the performance of a scaled-down model of a paddle wheel style hydrokinetic generator device used for generating power from the flow of a river. The paddle wheel dimensions used in this work are one-thirtieth scale of the full-size paddle wheel. The reason for simulating the scaled-down model was to prepare for the testing of a scaled-down physical prototype. Computational Fluid Dynamics using ANSYS Fluent 14.0 software was used for the computational analysis. The scaled-down dimensions were used in the simulations to predict the power that can be generated from the scaled size model of the paddle wheel, having carried out similitude analysis between the scaled down size and its full-size. The dimensionless parameters employed in achieving similitude are the Strouhal number, power coefficient, and pressure coefficient. The power estimation of the full-size was predicted from the scaled size of the paddle wheel based on the similitude analysis.

Feature Selection Based on Difference and Similitude in Data Mining

Feature selection is the pretreatment of data mining. Heuristic search algorithms are often used for this subject. Many heuristic search algorithms are based on discernibility matrices, which only consider the difference in information system. Because the similar characteristics are not revealed in discernibility matrix, the result may not be the simplest rules. Although differencesimilitude（DS） methods take both of the difference and the similitude into account, the existing search strategy will cause some important features to be ignored. An improved DS based algorithm is proposed to solve this problem in this paper. An attribute rank function, which considers both of the difference and similitude in feature selection, is defined in the improved algorithm. Experiments show that it is an effective algorithm, especially for large-scale databases. The time complexity of the algorithm is O（｜ C ｜^2｜U ｜^2）.

On similitude law of sub-systems

Based on Buckingham＇s π-Theorem, dimensional analysis has achieved considerable success over the past near-century. Model testing has long been a powerful tool in both scientific studies and engineering applications. However, the prototype objects are becoming more and more complicated nowadays, and many of the prototype systems can contain several sub-systems. The conventional theories on model-prototype similarity and dimensional analysis have only limited application since the π-Theorem itself does not distinguish between the original system and subsystems. This is particularly true in the field of structural dynamics, where the structure is often modeled as a multi-degree-of-freedom system. In this paper, we attempt to show that, if a system can be decoupled into several nontrivial subsystems, then, in each subsystem, the number of π-terms will be reduced and therefore simplify the model testing. On the other hand, if a system cannot be decoupled into subsystems, then using model testing with reduced π-term analysis, both experimentally and theoretically, may introduce severe errors.

Effect of artesian water on the mine floor water inrush and significance of similitude simulation to it

According to the in situ statistics data, indoor rock hydraulic fracturing experiments and numerical simulation results, the role of artesian water quantity was analyzed, emphasis was put on the analysis of the damage mechanics of artesian water to rocks under the floor and the softening, solution and scouring action of artesian water were also researched. At the end of the paper, practical significance of similar material simulation to the influence of artesian water on water inrush under the floor was discussed and hoped to provide references to the artesian water hydraulics simulation experiment devices design and test based on the indoor similar material simulation platform.

ON SIMILITUDE OF CROSS-FLOW FAN IN DYNANIC PERFORMANCE AND NOISE CHARACTER

Thesimilitudeofacross-flowfanisinvestigatedbytestingtwofanswhicharedifferentinsizebutsimilaringeometry.Theresultsshowed:ThereexistsacriticalReynoldsnumberwhosevalueincreas-esasthefansiaegetslarger.AbovethecriticalReynoldsnumber,thesimilitudeistenabletobothaerody-namicandnoisecharacters.Thefansizeandtheclearancebetweentheimpellerandthetonguehaseffectonsimilitudeofthecross-flowfan.Craes-flow,fan,Similitude,Test

Study on Energy Law of Similitude for Laser Propulsion in Repetitively-pulsed Mode

Energy law of similitude for laser propulsion refers to the law that there is an optimum nozzle configuration for the largest value of impulse coupling coefficient at certain incident laser energy. A dimensionless factor combined with incident laser energy, nozzle configuration parameters and working gas parameters is introduced. Energy law of similitude is established by means of theoretical analysis, experimental study and numerical simulation of radiation gas-dynamics. The qualitative results obtained from theoretical analysis are verified by experimental and numerical results. Physical meaning and engineering application of dimensionless factor and energy law of similitude are analyzed. Results indicate that ① impulse coupling coefficient has a maximurn value with dimensionless factor of about 0.4; ② impulse coupling coefficient is independent of incident laser energy when dimensionless factor is constant. Conclusions and recognitions acquired in this article can not only present optimum nozzle configurations for the present laser energy level, but also provide a good guide for the optimum nozzle configuration design once the laser energy is amplified to a high level.

Similitude design for the vibration problems of plates and shells： A review

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achieve- ments of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

Prediction of Large Structure Welding Residual Stress by Similitude Principles

On basis of the similitude principles, the conception of virtual simulative component and the auxiliary value of welding residual stress, which is deduced by the welding conduction theory, the relation of the welding residual stress between the simulative component and the practical component was attained. In order to verify the correctness of the relation, the investigation was done from the view of the welding experiment and the numerical simulation about the simulative component and the practical component. The results show that the distribution of welding residual stress of the simulative component is the same as that of the practical component. The ratio of welding residual stress attained by the experiment or the simulation method between the practical runner and the simulative component was compared with the ratio obtained by the similitude principles. Moreover, the error is less than 10%. This provides a new idea to predict the welding stress distribution of large practical structure by the contractible physical model, which is important for the welding experiment and the numerical simulation.

A modified similitude analysis method for the electro-mechanical performances of a parallel manipulator to solve the control period mismatch problem

Due to the discrete feature and performance limitation of the numerical controller,the control period sometimes cannot meet the constraints of the scaled model in similitude analysis,which brings the control period mismatch problem.The traditional similitude analysis methods are not able to solve this problem since the controller is treated as continuous system in these methods.This paper proposes a modified similitude analysis method to solve the control period mismatch problem,and the electro-mechanical performances of a 2-DOF parallel manipulator is predicted.Based on the model of dynamic and control system,most of the similitude laws are derived by taking the controller as continuous system.Then the transfer function of the controller in discrete form is established,and the similitude law related to control period is derived to figure out the cause of mismatch problem.The modified method,named long period equivalent,is proposed to solve the mismatch problem by using the least square method and superposition principles.Finally,the scaled model of the parallel manipulator is determined based on the modified similitude analysis method.

Balancing method without trial weights for rotor systems based on similitude scale model

A balancing method without trial weights based on the dynamic similitude scale model was proposed as a solution to the balancing problem of a large-scale rotor system. This method could be used to directly obtain the required coefficients for the balancing problem of the prototype system through a similarity model test without a prototype test. Thus, the weight test process of the prototype system was effectively eliminated in the proposed balancing method. First, with the rotor system as the research object, the analytical expression of the influence coefficient was derived on the basis of rotor dynamics theory. Then, through calculation and dimen- sional analysis methods, the similitude relationships of the rotor system and the influence coefficient were deduced on the basis of dynamic similitude theory. The correctness of the proposed similitude relationships was verified through numerical simulation and experiment. The balancing method without trial weights was proposed based on the similitude relationship of the influence coefficient. The effect of the balancing method without trial weights was compared with that of the traditional influence coefficient method through numerical simulation, and the results verified the correctness and effectiveness of the proposed balancing method. The results of this study provide theoretical supplements for the balancing method and the similitude design of the rotor system.

A Similitude Method and the Corresponding Blade Design of a Low-Speed Large-Scale Axial Compressor Rotor

A similitude method to model the tip clearance flow in a high-speed compressor with a low-speed model is presented in this paper.The first step of this method is the derivation of similarity criteria for tip clearance flow,on the basis of an inviscid model of tip clearance flow.The aerodynamic parameters needed for the model design are then obtained from a numerical simulation of the target high-speed compressor rotor.According to the aerodynamic and geometric parameters of the target compressor rotor,a large-scale low-speed rotor blade is designed with an inverse blade design program.In order to validate the similitude method,the features of tip clearance flow in the low-speed model compressor are compared with the ones in the high-speed compressor at both design and small flow rate points.It is found that not only the trajectory of the tip leakage vortex but also the interface between the tip leakage flow and the incoming main flow in the high-speed compressor match well with that of its low speed model.These results validate the effectiveness of the similitude method for the tip clearance flow proposed in this paper.

THE CONSISTENT ANALYSES OF SCALE SIMILITUDE IN RIVER MODEL EXPERIMENT

Law of the propagation of errors caused by the inconsistency of the boundary scale similitude in river model experiment is presented in this paper. The fluctuation of scale transfers along the characteristic line,if the discharge and sediment at entrance and the water level at the tail gate drift. The fluctuation of scale propagates with the derived scale function due to topographic deviation. All errors will accumulate to the final measured data

Analytic computation on the forcible thawing temperature field formed by a single heat transfer pipe with unsteady outer surface temperature

A comprehensive and systematic research on the forcible thawing temperature field formed by a single heat transfer pipe with unsteady outer surface temperature was carried out by analytic computation according to the theory of similitude. The distribution law of thawing temperature field, calculation formulas of thawing radius b, heat flux density q and average thawing temperature T were obtained. It theoretically explains that the main influential factors of thawing radius b, heat flux density q and thawing average temperature T are K,f, Lx and co（l）, but Lc affects little. Finally, based on the forcible thawing project of Hulusu air shaft lining, the field data indicate that the analytical formulas of this article are comparatively accurate.

Shaking Table Test of Pile-Water-Pier Superstructure

The model test of seismic simulation shaking table is an important method to study the seismic design of bridge structure. In order to evaluate the seismic response and dynamic characteristics of pile-water-pier system for developing more reliable design procedures, shaking table model tests of a submerged bridge pier system, including pile groups-cap-pier and inertia mass, were conducted. Since different similitude laws corresponding to different test objectives affected the validity of test results, the similitude law with the aim to consider the effect of hydrodynamic pressure was proposed and confirmed through an actual example. Based on the test results, the effect of water around model on seismic response under seismic excitation input was analyzed and the failure level was judged by observing the variation of basic frequency. The test results indicate that the transfer function of analytical model with water is different from that without water, the natural frequency without water is always higher than that with water, and the first modal shapes are various. It is also concluded that the similitude law is suitable for practical application and the dynamic characteristics and seismic response of the structure system can be changed because of the existence of the surrounding water, which should be paid much attention in the further investigation.