Non-stationary Loading Research Articles

Methods of the terrain allowable slope determining for safe operation of specialized equipment under the non-stationary load action

The operation of modern high-tech equipment requires a clear delineation of safe conditions for its operation. To a large extent, this applies to machines that move and work on untreated soil surface: forestry machinery, agricultural machinery, road construction machinery, military equipment, and so on. Asymmetry of the location of the working bodies, work on surfaces with a lateral slope, non-stationary interaction with the working environment - these are the factors that increase operational risks. Objective of this study is to establish the limits of safe operation of specialized machines operating on a rough surface with a slope to the horizon. The methods of determining safe slopes for the above-described equipment in the conditions of its non-stationary interaction with the subject of work are considered in the work. In particular, dangerous slopes that can cause the car to overturn or roll sideways are identified. The realization of this goal is achieved by building a mathematical model and appropriate calculation schemes that cover both possibilities of loss of stability. Graphs are plotted to display the maximum slopes due to the overturning and sliding of the machine on the slope for the specified operating loads. The integral characteristic of the slope limit value covers both of the above risks. The application of the proposed methods is illustrated by the calculation of the safe slope for firing tanks for different angles of deviation of the gun from the surface of the movement on the slope and the type of ground surface of the movement. The following results were obtained: methods for calculating the allowable slopes for the possibility of operating specialized machines on them, taking into account soil conditions, and demonstrated the application of the approach to the case of military equipment. The use of these results is a necessary factor for the implementation in the design of technological processes for specialized machines in order to minimize operational risks.

Multilayer Structures under Non-Stationary Loading: Prediction of Damages and Further Operation Possibility

Mathematical model of the complex interaction of composite structures elements is developed. A half-strip composed of two various materials is considered as a case of the composite structure. For each layer the dynamic equations of the theory of elasticity are used. An impact-impulse load is applied at the end of the structure. During the complex interaction, the conjugation of layers is carried out by conditions that ensure joint deformation, slipping (with friction) or absence of contact. The area and the contact type are determined during the solving process. This approach requires the construction of the special numerical algorithm which allows to change the boundary conditions during the calculation depending on the fulfilment of the strength criterion. The problem is solved numerically using method of characteristics. The propagation of elastic waves in the two-layer half-strip is studied. The wave field characteristics are determined in the calculated point of the layer at a given time. The calculation results are analysed in order to identify areas of the contact surface that are most prone to damage. The geometric and mechanical parameters influence on the behaviour of the structure is studied.

Dynamics of Spherical Sandwich Shells with Discrete-Symmetrical Light Core Reinforced with Ribs Under Nonstationary Loads*

Dynamics of Spherical Sandwich Shells with Discrete-Symmetrical Light Core Reinforced with Ribs Under Nonstationary Loads*

Time-Dependent Resilience of Repairable Structures Subjected to Nonstationary Load and Deterioration for Analysis and Design

Civil structures and infrastructures are often subjected by design to the impacts of natural and human-caused hazardous events, and accordingly may suffer from damages, functionality loss, and failure. In order to quantitatively measure the associated likelihood and consequences for quantifying risks, an appropriate measure of structural reliability and resilience is essentially required. This paper presents an explicit measure for the time-dependent resilience of repairable structures as a natural extension of time-invariant and time-dependent structural reliability concepts, taking into account the effects of structural performance deterioration and nonstationary external loads. First, the resilience measure associated with a single load event is discussed, and an integral-free expression is developed for a special case of structural robustness and recovery. Subsequently, the resilience measure for a planning horizon, which is a function of the duration of considered service period, is proposed in a closed form. Remarkably, the time-dependent resilience can be treated as a generalized form of the time-dependent reliability. Motivated by this, the resilience-based design and cost optimization of structures are also discussed. A numerical example is presented to demonstrate the accuracy and applicability of the proposed resilience measure.

Subband Decomposition Based Output-Only Modal Analysis

AbstractOutput-only modal analysis (OMA) is an indispensable alternative to experimental modal analysis for engineering structures while in operation. Conventional OMA often fails to identify the underlying modal structure with insufficient modal energy contribution. Such low modal participation is expected when the sampled response is subjected to sensor nonlinearity or when specific modes are not directly excited. A novel subband decomposition (SBD) method that resolves modal parameters even with biased modal energy distribution is proposed. It isolates the system response within a narrow frequency subband through a finite impulse response analysis filter bank. Whenever the filter subband captures a resonance, the filtered system response is close-to-singular and contains mainly the resonant mode contribution. A modal cluster metric is defined to identify the resonant normal modes automatically. The modal parameters are also identified and extracted within the subband possessing the locally maximal clustering measure. The proposed method assumes no a priori knowledge of the structure under operation other than the system should have any repeated natural frequencies. Therefore, the SBD algorithm is entirely data-driven and requires minimal user intervention. To illustrate the concept and the accuracy of the proposed SBD, numerical experiments of a linear cantilevered beam with various stationary and non-stationary loading are conducted and compared to other OMA methods. Furthermore, physical experiments on an aluminum cantilever beam examine the method’s applicability in field modal testing. Compared to traditional OMA methods, the numerical and physical experiments show orders of magnitude improvement in modal identification error using the proposed SBD.

Dynamics of Sandwich Conical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading

Dynamics of Sandwich Conical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading

Experimental and theoretical assessment of the durability of machine elements and parts under cyclic unstationary loading

A statistical model of fatigue failure is proposed, which allows analytically determining the durability of a part operating under a cyclic complex inhomogeneous stress state and non-stationary loading mode. A comparative analysis of the test results of samples and parts of steel 45 was carried out in order to assess the effectiveness of the statistical model.

Bearing Fault Diagnosis under Time-Varying Speed and Load Conditions via Observer-Based Load Torque Analysis

Bearing fault is the most common failure in rotating machines, and bearing fault diagnosis (BFD) has been investigated using vibration, current, or acoustic signals. However, there are still challenges in some existing approaches. This study proposes a novel BFD method based on natural observer. Based on the analysis of the effects on the load torque signal caused by bearing faults in the permanent magnetic synchronous machine (PMSM), a modified natural observer was designed to reconstruct the load torque signal from electrical signals, acquiring a novel indicator without the additional sensor installed. Angular resampling was implemented to convert the non-stationary load torque signal into a stationary one to reduce the computational complexity. For full-auto diagnosis without human involvement, a threshold determination algorithm was also modified. Experimental validations were carried out under speed-varying and torque-varying conditions and were compared with phase current and q-axis current signals. The average signal-to-noise ratio (SNR) of the estimated load torque is about 8.65 times compared with the SNR of the traditional q-axis current. The effectiveness of the proposed method prior to the traditional PMSM bearing fault indicators is demonstrated by the order spectrum results.

Vibrations of a Layered Conical Shell Under Nonstationary Load*

Vibrations of a Layered Conical Shell Under Nonstationary Load*

МОДЕЛЮВАННЯ ПОВЕДІНКИ ЛОКАЛЬНО НАВАНТАЖЕНОЇ ПОЛОСИ З ПСЕВДО-ПРУЖНО-ПЛАСТИЧНОГО МАТЕРІАЛУ ПРИ ВЕЛИКИХ ПЛАСТИЧНИХ ДЕФОРМАЦІЯХ

Introduction. Currently, a number of models are known to describe the thermomechanical behavior of functionally inhomogeneous materials, in particular alloys with shape memory (SPF) [3; 4]. Most of them are based on classical ideas, ie aim to directly describe the experimental data obtained on different macrosamples under simple and complex loads. However, as established in experimental studies, the behavior of the material at a point in the body in the General case may be different from the behavior of the sample as a whole [5]. In the considered problems the numerical procedure of calculation of the diagram of material which represents a curve which surrounds a family of diagrams of the material constructed for certain laws of change of speed of a front of rupture of deformations is developed. Purpose. The aim of the work is to apply a nonlinear phenomenological model, which describes the properties of alloys with shape memory and thermo-pseudo-plastic behavior (TPPM) of the material at the point to the problem of modeling a locally loaded strip of pseudo-elastic-plastic material at large plastic deformations. Compare the results of modeling in geometrically linear and nonlinear formulations for large plastic deformations. Results. The behavior of the locally loaded weakened strip of pseudo-elastic-plastic material under its non-stationary loading is modeled in the work. The authors used a nonlinear phenomenological model of the material to solve the above problem, which allows to describe a number of experimental data on different samples under different conditions. A comparison of the results obtained in geometrically linear and nonlinear formulations with large plastic deformations. Conclusion. Modeling the behavior of pseudo-elastic-plastic material with large plastic deformations requires the use of nonlinear mathematical models that could more accurately describe and predict the behavior of such a body. The behavior of the locally loaded weakened strip of pseudo-elastic-plastic material under its non-stationary loading is modeled in the work. The authors used a nonlinear phenomenological model of the material to solve the above problem, which allows to describe a number of experimental data on different samples under different conditions. A comparison of the results obtained in geometrically linear and nonlinear formulations with large plastic deformations. Numerically compared intensity fields at symmetric and asymmetric loading It is established that at plastic deformations up to 6% (small deformations) the discrepancy of results in points of localization of deformation does not exceed 5%. With increasing values of plastic deformation (more than 7%, large deformations), the discrepancy of the results can increase significantly and in the vicinity of the possible creation of the neck to reach 20%.

Numerical modeling of deformation and fracture of constructions made of concrete composites under non-stationary loading

Numerical modeling of deformation and fracture of constructions made of concrete composites under non-stationary loading

Explosive and heating devices for strength testing thin-walled composite constructions for joint action of non-stationary heat and power loads having various physical nature

Explosive and heating devices for strength testing thin-walled composite constructions for joint action of non-stationary heat and power loads having various physical nature

Explosive technologies for testing composite constructions of aircraft for strength to heat-power non-stationary loading

Sets of explosive and heating devices for experimental study of strength of composite constructions of aircraft against complex thermal and mechanical action of radiation and particles fluxes of different physical nature are considered. Two new explosive devices for generating low-pulse loads of microsecond duration are proposed. Devices based on thermoelectric heating elements, conductive plates and pyrotechnic compositions applied to the surface of the tested structure have been developed to simulate thermal action of radiation and particles fluxes. A universal test bench using these sets of devices has been developed. This test bench allows testing the strength of composite constructions to the joint action of thermal and mechanical loads having given space-time distributions.

Investigation of the influence of an additional viscoelastic support mass-inertial characteristics on the rectangular plate non-stationary deformation

Modeling additional supports that affect the non-stationary deformation of lamellar structural elements is associated with a number of idealizations and assumptions. Many sources describe the deformation of supported structural elements using absolutely rigid additional supports or stiffeners. In reality, additional supports have viscoelastic properties (viscous and elastic components). When studying non-stationary vibrations, one should also take into account the mass-inertial properties of additional supports. Goal. The goal of the work is: 1) refinement of the existing mathematical model of an additional viscoelastic support by taking into account the influence of its mass-inertial characteristics; 2) study of the influence of these characteristics on the non-stationary deformation of a rectangular plate. Methodology. The non-stationary deformation of beams or plates is described by systems of partial differential equations. For these objects, good results are given by models based on the hypotheses of S.P. Timoshenko, taking into account the inertia of rotation and shear. Such systems of equations can be solved by expanding the sought functions (displacements and angles of rotation) in the corresponding series and using the direct and inverse integral Laplace transform. The determination of the unknown reaction of the additional viscoelastic support, taking into account its mass-inertial characteristics, is carried out on the basis of solving the Volterra integral equations. Results. In this work, an analytical and numerical solution in a general form is obtained, which makes it possible to determine the dependence of the change in time of reaction between the plate and the additional support for various parameters of the mechanical system. Originality. The solution to this problem is based on the further development by the authors of an approach to modeling additional supports in the form of additional unknown non-stationary loads, which are determined from the analysis of Volterra integral equations. Practical value. Examples of calculations for the considered mechanical system at three different values of mass are given. It is shown that the mass-inertial characteristics of the additional support cause a noticeable effect on the oscillatory process, and the changes concern both amplitude and phase characteristics.

The nonstationary thermoelectric elasticity problem for a long piezoceramic cylinder

А new closed-loop solution for the coupled nonstationary problem of thermoelectric elasticity is designed for a long piezoceramic radially polarized cylinder. The case of the nonstationary load acting on its inner cylindrical surface is considered as a function of temperature change at a given law of the convection heat exchange on the outer face wall (boundary conditions of heat conductivity of the 1st and 3rd types). Electrodynamic cylinder surfaces are connected to a measuring device with a high input resistance (electric idling). We investigate the problem where the rate of the temperature load changes does not affect the inertial characteristics of the elastic system. It makes it possible to expand the initial linear computational relations with the equilibrium, electrostatics and heat conductivity equations with respect to the radial component of the displacement vector, electric potential as well as the function of temperature field changes. Hyperbolic LS-theory of the thermal conductivity is used in the computations. The problem is solved with a generalized method of biorthogonal finite integral transformation based on a multicomponent ratio of eigen functions of two homogeneous boundary value problems. The structural algorithm of this approach allows identifying a conjugated operator, without which it is impossible to solve non-self-conjugated linear problems in mathematical physics. The resulted computational relations make it possible to determine the stress-strain state, temperature and electric fields induced in the piezoceramic element under an arbitrary external temperature effect. By connecting the electroelastic system to the measuring tool, we can find voltage. Firstly, the analysis of the numerical results allows identifying the rate of the temperature load changes, at which it is necessary to use the hyperbolic theory of thermal conductivity. Secondly, it allows determining the physical characteristics of the piezoceramic material for the case when the rate of changing the body volume leads to a redistribution of the temperature field. The developed computational algorithm can be used to design non-resonant piezoelectric temperature sensors.

A resource efficient and environmentally safe charge structure for mining in an open-pit

Purpose. The purpose is to reduce mineral losses during the explosive destruction of rocks and environmental pollution by harmful gases and fine particulate matter. Methods. To achieve the objectives of the study, methods of physicochemical analysis and mechanics of continuous media have been used. The method of physico-chemical analysis has been used to determine the quantitative and qualitative characteristics of the composition of the well stemming depending on the parameters of the well, the type of explosive, the amount and type of harmful gases formed during the explosion. Methods of solid medium mechanics have been used to establish the patterns of pressure waves during an explosion depending on the characteristics of the gap filler between the charge and the well wall. To solve the problem of the behavior of a two-layer medium during the loading of a cylindrical cavity by a nonstationary load, a numerical method based on the finite-difference McCormack predictor-corrector scheme has been used. Findings. A resource-saving and environmentally friendly charge structure for rock mining by explosion was developed. The design of the charge involves the formation of a gap between the charge and the wall of the borehole, and filling it with a suspension of calcium hydroxide or a suspension of calcium carbonate. Originality. SThe dependences of the volume of harmful gases (NO2, CO2, CO) formed during the explosive destruction of rocks and the magnitude of the pressure peak in the area close to the charge on the chemical composition of the filler of the radial gap between the charge and the well wall have been set. Practical implications. Developed charge design allows to neutralize the harmful gases formed during the explosion, to reduce the pressure peak in the area of the rock massif close to the charge, and can be widely used in non-metallic quarries that extract minerals for the production of crushed stone.

Time-dependent reliability analysis of fixed offshore structures under stochastic loadings

Fixed offshore structures under stochastic loadings usually have time-dependent reliability due to time-varying statistics of nonstationary load effects. Since closed-form solutions for such time-varying statistics are difficult to obtain, traditional methods cannot analytically evaluate reliability of structures. In this paper: (1) the explicit closed-form solutions for variances of nonstationary load effects at arbitrary time of linear structures are derived by a pole-residue method; and (2) the explicit solution of a time-dependent reliability index of the structure is then established. For computing displacement variances of offshore structures to waves using the pole-residue method in step (1), an innovative approach of writing the wave force power spectral density into its pole-residue form is developed. To verify the efficiency of the proposed method, a numerical example studies the time-dependent reliability index of the monopile foundation of offshore wind turbines under random waves. Furthermore, a hybrid numerical–experimental study of a jacket platform model to ground motions is conducted. The results indicate that reliability of structures at the nonstationary part is significantly smaller than that at the stationary part. This study provides a reference and advocates attention to structural failures generated by nonstationary responses to extreme loads, e.g., earthquakes.

Effect of the Asymmetry of Cylindrical Sandwich Shells on their Stress–Strain State under Non-Stationary Loading*

Effect of the Asymmetry of Cylindrical Sandwich Shells on their Stress–Strain State under Non-Stationary Loading*

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

Stress–Strain State of Three-Layer Cylindrical Shells with Reinforced Light Core Under Nonstationary Loading*

Aerodynamic Instability of Circular Slender Structures Due to Bistable Flow Activity

Slender structures with circular cylindrical cross-sections are very common in civil engineering, industrial equipment and bridge engineering. Such long cylinders subjected to wind are columns, piles, long cables, chimney, pylons and others. On long cables, an instability called dry galloping has been recently theorized to be linked to an unpredictable jump state occurring once the boundary layers of the circular cylinder changes from laminar to turbulent. With a non-stationary character, the force generated at the critical flow regime is named bi-stable activity. In this work, the birth of bi-stable flow activity around a circular cylinder made of high-density polyethylene is studied experimentally in a wind tunnel. The pressure pattern is linearly decomposed and geometric modes governing the bi-stable activity as a function of circularity defect are created. The results show that the energy of the non-stationary load observed at the critical flow regime depends strongly on the circularity defect. Furthermore, the inclination angle of 60° confers a significant increase in the energy of the bi-stable flow mode when an unsteady asymmetric reattachment event occurs. The paper also highlights the variability of the mean drag coefficient as a function of the macroscopic defect.