Bilinear Characteristics Research Articles

Time-Optimal Motions of a Mechanical System with Viscous Friction

Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin’s Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.

Experimental and modeling study of shear strength of unsaturated fine-grained soils with bi-modal water-retention characteristics

The mechanical behavior and strength characteristics of unsaturated fine-grained soils with dual-porosity are of crucial importance in geotechnical designs. Nanyang fine-grained soils have been selected as typical dual-porosity structure soils to perform experimental tests under a wide range of suction and different initial densities while studying its stress-strain-strength properties constitute the main scope of this study. Axial translation and vapor equilibrium techniques are jointly employed to apply a wide suction range. Our data suggest that soil behavior transits from strain-hardening with shear-induced contraction to strain-softening with shear-induced dilation as suction and density increase. By exploiting a bi-modal soil–water retention curve (SWRC) explicitly separating capillarity and adsorption mechanisms, the shear strength is allowed to be analyzed in the capillary suction stress-shear stress space. The strength envelop exhibits bi-linear characteristics. Building upon these findings, we propose a bi-linear shear strength criterion specifically for dual-porosity fine-grained soils. We utilize the obtained test data to evaluate existing strength criteria based on effective stress and dual stress variables that consider the bi-modal SWRC characteristics. The comparison indicates that the proposed bi-linear shear strength criterion can more reasonably represent the variation of shear strength under a wide range of suction for unsaturated dual-porosity fine-grained soils.

Optimization of suspension of rail vehicles with coil springs using marine predators algorithm

The topic of this paper is the usage of the algorithm of marine predator (MPA) in the optimization of the suspension of rail vehicles with coil springs. The aim is to reduce the mass of set of coil springs as the main parts of rail vehicles suspension. The optimized set of coil springs must satisfy the appropriate conditions related to the suspension characteristics, with the aim of achieving the required operation quality and running security of the observed rail vehicle. Starting from the bi-linear characteristic of rail vehicles suspension and the analytical description of its parameters, an optimization problem is formulated. It is composed of six optimization parameters, an objective function and 16 constraints (eight for each coil spring in the set). The developed approach is applied in two specific examples of suspension optimization of four-axled freight wagons, the first with axle load of 200 kN and the second with axle load of 225 kN. The optimization problem is resolved using MPA. The acquired results showed that the given optimization approach with MPA provide a significant mass decrease compared to conventional design method of rail vehicles suspension with coil springs. The mass decrease of one set of coil springs in both examples is about 15.5%. Given that each considered four-axled freight wagon has 16 sets of coil springs, the decrease of the total coil springs mass per wagon in both examples is more than 60 kg. Since certified rail vehicles are commonly produced in large series, the proposed approach can be very significant for increasing profitability in the rail vehicles industry.

Performance of clutched inerter damper for base-isolated structures under near-fault motions

The performance of the supplemental clutched inerter damper (CID) for the base-isolated multi-story structures subjected to near-fault earthquakes is investigated. The isolation system is considered as lead-rubber bearings with bi-linear characteristics and viscous damping. The resisting force of the CID is proportional to the relative acceleration between two terminals under the attached condition and zero when detached. The governing equations of motion of base-isolated structure and the CID are derived and solved using numerical techniques under seven near-fault ground motions data. The variation of peak bearing displacement, top floor absolute acceleration, total base shear, and the CID force is plotted against the inertance mass ratio of the CID. The above peak responses were also analyzed for different values of damping, period of isolation, yield strength of LRB, and superstructure stories. Application of the CID is observed to effectively facilitate the reduction in bearing displacement while the combined effect of isolation and the CID prevents the top floor acceleration to shoot up. The optimum value of inertance mass ratio is also determined by minimizing the total base shear which is the measure of equivalent lateral force on the structure. The optimum inertance lies in the range of 35%–45% of the total mass of the isolated building under near-fault motions. In addition, the performance of the CID base-isolated structure subjected to cycloidal pulses is also investigated. It is observed that the CID is quite effective in controlling the displacement of the isolation system under cycloidal pulses.

Статистическая оптимизация показателей региональной экономики в неоднородной изменчивой среде

The authors modelled the development of a regional socio-economic situation using static optimization of an unknown function that describes the relationship between the economic parameters of a territorial system. They applied the Bayesian approach to formalize relations, identify optimization parameters, classify the situation of geographically homogeneous economic systems, and describe the transformation of socio-economic regimes. By using variables and coefficients as bilinear characteristics, they reflected the unity of internal and external system properties, as well as the joint effect of geographical and historical economic factors and conditions. The analysis of regional economic indices revealed the empirical dependence of domestic investment on industry and agriculture in the Russian regions in 2000–2016. The results show some patterns of investment and production processes in the Irkutsk region economy in the pre-crisis, crisis, and post-crisis periods. For industrial production, the changes in the investment environment corresponded to 2000–2006, 2006–2008, and 2008–2016. Agricultural production demonstrated no such relationship. Therefore, the geo-economic conditions change the environmental indicators of the regional system that affects the optimal investment solutions made by economic activity subjects.

Room temperature and humidity decoupling control of common variable air volume air-conditioning system based on bilinear characteristics

Variable air volume (VAV) air-conditioning (AC) systems are widely employed to achieve a comfortable room thermal and humid environment depending on its better regulation performance and energy efficiency. In the single coil VAV AC system, conventional proportional-integral (PI) control algorithm is usually adopted to track the set-points of the room temperature and humidity by regulating the supply air flow rate and the chilled water flow rate, respectively. However, the control performance is usually not good due to the high coupling of the heat and mass transfer in the air-handling unit (AHU). A model-based control method is developed to realize the decoupling control of the room temperature and humidity according to the bilinear characteristics of the temperature and humidity variation. In this control method, a bilinear room temperature controller is used to track the room temperature set-point based on the real-time cooling load, while a room humidity controller is used to track the room humidity set-point depending on the real-time humidity load. The control performance was validated in a simulated VAV AC system. The test results show that comparing with the conventional PI control, the room temperature and humidity are controlled much more robustly and accurately by using the proposed model-based control method.

Numerical study of the interaction between a moving oscillator and an infinite beam on elastic foundation with bilinear characteristic

This paper presents an analysis of the low frequency vibrations exerted by a simple oscillator travelling along an infinite and uniform beam laid on an elastic foundation having bilinear characteristic. In the railway domain, such a problem is interested because it allows highlighting the influence of the nonlinear track modulus on the interaction between the vehicle and the track. The track model is reduced to an equivalent Euler-Bernoulli beam corresponding to the rail and the inertia of the sleepers, on a bilinear Winkler foundation for the ballast. The vehicle model is a loaded two-degree oscillator representing the wheel, suspension, suspended mass of the carbody corresponding to the wheel (1/4 carbody). The vehicle/track interaction is analysed considering two items: equivalent track modulus and track with bilinear characteristic.

Static mechanical response of sandwich panels with bilinear core

A new theoretical model based on the extended high order sandwich panel theory is established to predict the mechanical response of sandwich panels under static loads with the bilinear constitutive stress–strain relation in the core. The constitutive relations of normal stresses related to the longitudinal and vertical normal strains in the bilinear isotropic hardening core are first formulated. The influence of the in-plane rigidity on the elastoplastic response of sandwich structures is analyzed. An in-plane loaded sandwich structure with the bilinear core is first studied based on extended high order sandwich panel theory, and the effect of the bilinear ratio on the mechanical response is evaluated. The governing equations are derived from the principle of minimum potential energy, and a Ritz-based half-analytical method is applied to get the solutions. The plastic response is acquired by an iterative procedure along with the convergence criteria. The results reveal that the local effect can be captured when the axial rigidity of the core is considered. The bilinear characteristic of the core decreases the maximum normal stress with an increase of the average value. The equivalent plastic region extends with the increase of the bilinear ratio when the sandwich structure is loaded in plane. By comparison with open literatures and finite element results, the present theoretical model is proved to be effective and efficient.

Microstructure and Mechanical Properties of Ultrasonic Spot Welded Mg/Al Alloy Dissimilar Joints

Lightweight structural applications of magnesium and aluminum alloys inevitably necessitate welding and joining, especially dissimilar welding between these alloys. The objective of this study was to examine the feasibility of joining ZEK100 Mg alloy to Al6022 alloy via ultrasonic spot welding, focusing on effects of welding energy. An interface diffusion layer consisting of α-Mg and Al12Mg17 eutectic structure was observed to form, with its thickness increased from ~0.5 µm to ~30 µm with increasing welding energy from 500 J to 2000 J. The tensile lap shear peak load or strength and critical stress intensity of the welded joints first increased and then decreased with increasing welding energy, with their peak values achieved at 750 J. Fatigue life of the joints made at 750 J and 2000 J was equivalent at the lower cyclic loading levels, while it was longer for the joints made at 750 J at the higher cyclic loading levels. Fatigue fracture mode changed from interfacial failure to mainly transverse-through-thickness crack growth with decreasing cyclic loading level, which corresponded well to the bi-linear characteristic of S-N curves. Crack initiation basically occurred at the weld nugget border and at the interface between the two sheets, which can be understood via a theoretical stress analysis.

Dynamics of a beam on elastic foundation - impact of the bilinear characteristic of the foundation upon the propagation of the bending wave

Rail is an important source of noise in the railway traffic and its acoustic power is depending on the rate of decay of vibration. The main characteristic of the track in terms of the vertical elasticity is the so-called track modulus which results from the load-rail deflection curve. In general, this curve is nonlinear and it can be approximated using piecewise linear function with bilinear characteristic. In this paper, the response of a beam on elastic foundation with bilinear characteristic due to constant and harmonic loads is investigated, pointing out the impact of the foundation characteristic on the rail response and the propagation of the bending waves along the track.

Multivariate curve resolution alternating least square (MCR-ALS) analysis on total synchronous fluorescence spectroscopy (TSFS) data sets: Comparing certain ways of arranging TSFS-based three-way array

Total synchronous fluorescence spectroscopy (TSFS)-based three-way array sample×excitation wavelength×Δλ has inherently complex data structure. Multivariate curve resolution alternating least square (MCR-ALS) analysis is a soft mathematical modelling technique that can be used to retrieve pure spectral and contribution profile of the fluorophores of a multifluorophoric mixture provided it is applied to bilinear data sets. In the present work, possibilities of generating bilinear two-way arrays by (i) unfolding and (ii) augmenting the TSFS-based three-way array were studied. Bilinear characteristics of the obtained two-way arrays were tested by subjecting them to MCR-ALS analysis. It was found that lack of analytical–mathematical relationship between spectral profile along the excitation wavelength mode and the offset mode do not allow the application of MCR-ALS analysis on augmented TSFS data set. Moreover, the augmentation procedure and chemical-mathematical rank of the subsequently obtained data sets were found to be ‘not independent’ of each other. Two-way array sample×(excitation wavelength×Δλ) obtained by unfolding TSFS-based three-way array along the sample mode was found to have symmetrical structure, i.e., both sample mode and spectral mode have equal mathematical and chemical rank making them highly attuned to MCR-ALS analysis.

Effect of strain rate and saturation on uniaxial dynamic compressive behaviours of mortar

The effect of moisture content on the compressive mechanical behaviours of cement mortar under different high strain rates is studied in this paper. The rapid impact testing, i.e. the strain rates of 80, 100, 150, 200 and 250 s− 1 by Split Hopkinson pressure bar, on number of specimens with special water/cement ratio of 0.50 and saturations as 0%, 25%, 50%, 75% and 100%, respectively, was executed. The dynamic compressive behaviours were analysed in terms of the maximum stresses, elastic modulus, critical strain at maximum stresses and ultimate strains at failure. Results indicated that similarity existed in the shape of strain–stress curves of mortars with different moisture subjected to different strain rates of impact loading, i.e. the upward section presented bilinear characteristics, while the descending stage was almost linear. As strain rate increases, the dynamic compressive strength, elastic modulus and critical strain at maximum stress increase which can be ascribed to the dynamic fracture effect and the microscope inertia effect. Besides, it was shown that desiccation provokes an increase in mortar strength and deformation behaviour of the studied mortar with different saturation caused by capillary depression and microcracking. Drying effect has to be considered in modelling of the coupling between desiccation and mechanical behaviour of the mortar. Finally, the multi-parametric statistical analysis of water content and strain rate on the mechanical behaviours of cement mortar subjected to dynamic loading is detailed.

Isolation Performance Analysis of a Porous Material Vibration Isolator

To explore the isolation mechanism and optimize the performance of the porous material in a dynamic viewpoint, a nonlinear porous material vibration isolator is modeled in this work. The stiffness of the isolator is regarded to be a piecewise linear, according to the stress–strain characteristics of porous material. Averaging method is employed to analyze the amplitude-frequency characteristics when the system excited by harmonic excitation. It is found that the vibration system represents linear, bilinear and tri-linear characteristics, when the porous material isolator works in linear-elastic phase, plateau phase and densification phase, respectively. The result shows that the amplitude response of the system in the plateau stage is much less than the linear isolator.

Bilinear electric-field characteristics in the problem of the galvanomagnetic properties of composite materials

Some general properties of the effective conductivity tensor \(\hat \sigma _e\) of a composite material placed in magnetic field H are considered. It is shown that the derivatives of the tensor \(\hat \sigma _e\) components with respect to their arguments can be expressed in terms of various bilinear characteristics, namely, the mean products of the electric fields in an initial system and the “transposed” system (which differs from the initial system in the substitution H → −H). At H → 0, the general formulas derived in this work yield the well-known expressions for the Hall coefficient and magnetoresistance that are valid for the case of weak magnetic fields.

INVESTIGATION OF DYNAMIC CHARACTERISTICS OF GONDOLA CARS ON PERSPECTIVE BOGIES

Purpose. In this paper, it is necessary to examine the dynamic properties of the gondola car with bogies, model 18-1711 when it moves on straight and curved sections of a track. Methodology. The calculations were performed using the object-oriented programming on the program "Dynamics of Rail Vehicles" ("DYNRAIL" Myamlin S.V. registered 20.03.2003). Mathematical models of a gondola car and bogies 18-100 and 18-711 were created for the calculations. Findings. Dynamic performances comparison of the gondola car with bogies 18-1711 and the gondola car with bogies 18-100, obtained by calculation method was carried out. Originality. Firstly calculations in order to determine the dynamic properties of the gondola car with bogies 18-1711 when it moves on straight and curved sections of track were performed. At the same time an assessment of the dynamic characteristics of the gondola car was made. The following dynamic standards were determined: the coefficient of vertical dynamics (Cdv), the coefficient of horizontal dynamics (Cdh), and the safety factor against derailment (SFd). Track irregularities in vertical and horizontal transverse planes were assigned as perturbations. They should be so that the dynamic indexes of the widely used in operation gondola car on bogies model 18-100 keep in admissible range of speeds up to 80km / h for the empty gondola car and at speeds up to 90km / h for the loaded gondola cars. Practical value. As a result of the calculations and comparisons of their results, we have findings that the use of bogies with bilinear characteristic of the central suspension will improve the dynamic performances of gondola cars, currently operating on bogies, model 18-100. And by improving the dynamic performances it is possible to increase the permissible speeds of these cars motion.

Numerical Simulation of Residual Stresses Induced from Shot Peening with Finite Element Method

Shot peening is a manufacturing process intended to give components the final shape and to introduce a compressive residual state of stress inside the material in order to increase fatigue life. The modeling and simulation of the residual stress field resulting from the shot peening process are proposed. The behaviour of the peened target material is supposed to be elastic plastic with bilinear characteristics. The results demonstrated the surface layer affected by compressive residual stresses is very thin and the peak is located on the surface.

Research on the Controlling Parameters of Creep-Thermal Fatigue Crack

The opening process of creep-thermal fatigue crack (CTFC) is studied by finite element method, considering the bilinear kinematic hardening and creep characteristic of the material. The crack is closed under the compressive thermal stress during the heating and insulating processes. The tensile stress during the late cooling process, which is normal to the crack face, makes the crack gradually open. At this time, the temperature of material around the crack has become lower than the creep temperature; therefore, the creep fracture mechanism parameter C* is not applicable. The CTFC is quite shallow, and comparatively the plastic zone is rather large; thus, the method of stress intensity factor is restricted. A modified J-integral method is put forward according to the stress analysis of CTFC, which has been proved to be path independent and valid. The method is used for not only the CTFC but also any unloading crack or the crack in the residual compressive plastic strain field. Experimental results show that the modified J-integral can be used as the controlling parameter of the CTFC propagation.

Approximate determination of vibrodiagnostic parameter of nonlinearity for an elastic body due to the presence of a breathing crack at a subharmonic resonance

The reliability of one of the simplest methods for calculating vibration parameters in the region of subharmonic resonance for an elastic body with a breathing crack, which is modeled by a single-degree-of-freedom system with a bilinear asymmetric characteristic of the restoring force is assessed. The method is based on the proposition that in a nonlinear system the subharmonic vibrations exist alongside with the fundamental forced ones and are the free vibrations maintained by a driving force.

Influence of free water content on the compressive mechanical behaviour of cement mortar under high strain rate

The effect of free water content upon the compressive mechanical behaviour of cement mortar under high loading rate was studied. The uniaxial rapid compressive loading testing of a total of 30 specimens, nominally 37 mm in diameter and 18.5 mm in height, with five different saturations (0%, 25%, 50%, 75% and 100%, respectively) were executed in this paper. The technique ‘Split Hopkinson pressure bar’ (SHPB) was used. The impact velocity was 10 m/s with the corresponding strain rate as 102/s. Water-cement ratio of 0.5 was used. The compressive behaviour of the materials was measured in terms of the maximum stress, Young’s modulus, critical strain at maximum stress and ultimate strain at failure. The data obtained from test indicates that the similarity exists in the shape of strain–stress curves of cement mortars with different water content, the upward section of the stress–strain curve shows bilinear characteristics, while the descending stage (softening state) is almost linear. The dynamic compressive strength of cement mortar increased with the decreasing of water content, the dynamic compressive strength of the saturated specimens was 23% lower than that of the totally dry specimens. With an increase in water content, the Young’s modulus first increases and then decreases, the Young’s modulus of the saturated specimens was 23% lower than that of the totally dry specimens. No significant changes occurred in the critical and ultimate strain value as the water content is changed.

Approximate analytical method for determining the vibration-diagnostic parameter indicating the presence of a crack in a distributed-parameter elastic system at super- and subharmonic resonances

An approximate method for calculating the vibration-diagnostic parameter indicating the presence of a crack in an elastic distributed-parameter system at super- and subharmonic resonances is considered. The method involves the finding of the non-linearity characteristic of an elastic system based on the analysis of its forced vibrations in the undamaged state and the use of results of the approximate analytical determination of parameters of nonlinearity for vibrations of an elastic body with a closing crack, which is simulated by a single-degree-of-freedom system with an asymmetric bilinear characteristic of the restoring force at the above-mentioned resonances.