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Effect of Heat Treatments and Carbon Content on the Damping Properties of Structural Steel

Low- and medium-carbon structural steel components face random vibration and dynamic loads (like earthquakes) in many applications. Thus a modification to improve their mechanical properties, essentially damping properties, is required. The present study focuses on improving and developing these properties, significantly dampening properties, without losing the other mechanical properties. The specimens used in the present study are structural steel ribbed bar ISO 6935 subjected to heating temperatures of (850, 950, and 1050) ˚C, and cooling schemes of annealing, normalizing, sand, and quenching was selected. The damping properties of the specimens were measured experimentally with the area under the curve for the loading and unloading paths experienced from the tensile test. Considering the effect of different parameters on the damping properties, such as heat treatment temperatures, cooling rates, and carbon content, the results show that the damping properties in the annealing process at different temperatures have interesting damping properties, among other processes. Also, the highest damping energy for the annealing cooling scheme was attained at a heating temperature of 1050 ˚C, irrespective of the carbon content. Finally, better damping properties for the medium carbon content of (0.299%C) is achieved for all types of heat treatment process compared with a low carbon content of (0.188% C); and, in general, with increasing carbon content from medium to low, steel response to heat treatment increases and better damping properties are obtained.

IDENTIFICATION OF THE NATURAL FREQUENCY OF THE OFFSHORE TRUSS STRUCTURE FROM MULTIPLE SIMULATED MEASURED DATA

This article presents identification methods of the natural frequency of structures from single or multiple measurements in the frequency domain and its application to identify the natural frequencies of the offshore truss structure. The simulated measurements of structural vibrations in the time domain are determined by analyzing the finite element model of the offshore truss structure subjected to random dynamic loads using SAP2000 software. The frequency domain measurements are obtained by the fast Fourier transform of time domain measurements using MATLAB software. The identification method from the multiple combined frequency response function measurements can estimate more natural frequencies than using a single measurement. A study of the considered frequency range was also performed showing the accuracy of the identification methods compared with the finite element model. By subdividing the considered frequency range, it is possible to improve the accuracy of the obtained natural frequencies.

Solving elastodynamics via physics-informed neural network frequency domain method

Despite the fact that physics-informed neural networks (PINN) have been developed rapidly in recent years, their inherent spectral bias makes it difficult to approximate multi-frequency target functions such as the solutions to elastodynamics problems. To address this challenge, this paper proposes a new PINN frequency domain (PINNFD) method on the basis of frequency domain inputs. Fourier features for all frequencies can thus be constructed and embedded in the model, which provides essential support for the PINNFD method to accurately approximate multi-frequency target functions. To validate the effectiveness of the proposed PINNFD method, the proposed method and the traditional method are applied to solve the elastodynamics problem in infinite media under various dynamic point loads, including single-frequency harmonic load, multi-frequency harmonic load, and multi-frequency random load. The results show that although the PINN with embedded Fourier features is able to achieve the simulation of elastodynamics problems under harmonic loads, it fails to solve the problems under multi-frequency random loads. Whereas the proposed PINNFD method achieves better results in all cases of loading conditions, which demonstrates the advancement of the proposed method in solving multi-frequency problems in engineering applications.

Random vibration analysis of composite laminated conical–cylindrical cabin structures of air vehicles considering thermal load

This study proposes a novel semi-analytical random dynamic model using the meshless method to precisely predict and quickly analyze the frequency-domain random response properties of composite laminated conical–cylindrical cabin structures (CL-CCCSs) of air vehicles under stationary random loads. In addition, thermal load is considered in the analysis. The first-order shear deformation theory (FSDT) is used to develop a random dynamic theoretical model for CL-CCCSs based on the spectro-geometric method (SGM) and pseudo-excitation method (PEM). Variable stiffness springs are employed to handle diverse boundary cases and compatibility conditions in the current model. Also, the displacement admissible functions for laminated conical shell and cylindrical shell are uniformly depicted with SGM, which depends on sine and cosine functions. After that, the PEM is employed to transform stationary random loads into pseudo harmonic loads. Subsequently, the energy variation principle is used to derive theoretical discrete random dynamic equations for vibration model of CL-CCCSs considering the thermal effect. The results of numerical vibration analyses are compared to confirm the reliability of the established model. Finally, the effect of certain parameters, such as the lamination scheme, layer number, and temperature, on the random vibration response of a CL-CCCS is thoroughly explained.

A probabilistic fatigue life prediction method under random combined high and low cycle fatigue load history

In this paper, a probabilistic high and low cycle fatigue (H-LCF) life prediction framework is proposed to consider random load history into fatigue life prediction of structures. First, the random load history is generated and quantified by finite element analysis (FEA) and Monte Carlo simulation (MCS). Subsequently, based on the quantification approach and an improved H-LCF damage curve, the framework of probabilistic H-LCF life prediction is then established. A turbine shaft is analyzed by the proposed method, which confirms the superior accuracy of the proposed method than the existing ones. Overall, the proposed method provides an effective way for structures’ fatigue life and reliability assessment.

Multiaxial Fatigue Analysis of Jacket-Type Offshore Wind Turbine Based on Multi-Scale Finite Element Model.

The fatigue damage of a local joint is the key factor accounting for the structural failure of a jacket-type offshore wind turbine. Meanwhile, the structure experiences a complex multiaxial stress state under wind and wave random loading. This paper aims to develop a multi-scale modeling method for a jacket-type offshore wind turbine, in which local joints of the jacket are modeled in a detail by using solid elements, and other components are modeled via the common beam element. Considering the multiaxial stress state of the local joint, multi-axial fatigue damage analysis based on the multiaxial S-N curve is performed using equivalent Mises and Lemaitre methods. The uniaxial fatigue damage data of the jacket model calculated using the multi-scale finite element model are compared with those of the conventional beam model. The results show that the tubular joint of jacket leg and brace connections can be modeled using the multi-scale method, since the uniaxial fatigue damage degree can reach a 15% difference. The comparison of uniaxial and multiaxial fatigue results obtained using the multi-scale finite element model shows that the difference can be about 15% larger. It is suggested that the multi-scale finite element model should be used for better accuracy in the multiaxial fatigue analysis of the jacket-type offshore wind turbine under wind and wave random loading.

Formulation and selection of composite biomaterials for acetabular cup of hip prosthesis with wear analysis

The study of tribological performance of metal-on-plastic type of hip prostheses has drawn the attention of researchers since the last few decades. These studies mainly focus on the friction and wear behaviour of acetabular cups made of different polymer biomaterials with a view to enhance the prostheses life. In this study, a novel biomaterial coded as LHHA has been prepared for the acetabular cup in three different blends with help of bioprocess engineering by mixing low-density polyethylene and high-density polyethylene with10, 20 and 30 percent of hydroxyapatite to improve the mechanical properties. A popular decision-making method was applied to select the best alternative from these three blends on the basis of hardness, roughness and ultimate strength and LHHA-30 is found to be the best. Furthermore, experimental wear investigation was carried out in a well-designed hip simulator to control such biological system under a series of random loads, within 600N and 1500N acting at different points on prosthesis for 10 million gait cycles run followed by theoretical wear analysis. Wear rates are found to be 12.651 and 26.247 mg per million cycle with marginal differences of 0.1 and 0.6 for LHHA-30 and ultrahigh molecular weight polyethylene (UHMWPE) acetabular cups against cobalt–chromium (Co–Cr) alloy femoral head, respectively. Morphological studies carried out by scanning electron microscope revealed that LHHA-30 scored less compared to UHMWPE surface.

Random vibration-based virtual fatigue test for large-scale welded structures using frequency-domain structural stress method and its application to traction transformers

PurposeThis paper aims to present an engineering computational method for fatigue life evaluation of welded structures on large-scale equipment under random vibration load.Design/methodology/approachBased on a case study of the traction transformers, virtual fatigue test (VFT) was proposed via numerical simulation approach. Static analysis was conducted to identify the risky zone and then dynamic response of the risky welds under random vibration load was calculated based on frequency-domain structural stress method (FDSSM) theory, life distribution and associated survivability at various locations of the structure were obtained. Structural modification was finally performed according to the evaluation results. Moreover, experimental test was carried out and compared with the virtual test result.FindingsBy applying the virtual test, fatigue life of the complex welded structures on large-scale equipment can be accurately and efficiently obtained considering dynamic effect under random vibration load. Meanwhile, risky welds can be directly determined and targeted modification scheme can be accordingly concluded. Validity of the VFT result was proved by comparing with the experimental test.Originality/valueThe proposed method can help obtain equivalent structural stress and fatigue life distribution of the welded structure at any position with various survivability and make quantitative evaluation on the life-extending effect of the structural modification. This method shows significant cost and efficiency advantages over experimental test during design stage of the large-scale structures in numerous manufacturing industries.

Study on multidimensional and multipoint seafloor spatial ground motion simulation under an ice-water layer and the dynamic response of a cross-sea bridge

A combined ice-water reflection coefficient is developed to measure the effect of saltwater and floating ice on seabed ground motions to explore the effect of floating ice on seafloor ground motions. The combined reflection coefficient is made up of three parts: the reflection coefficient of the seawater layer, the transmission coefficient of the water layer, and the reflection coefficient of the ice layer. The combined reflection coefficient analyzes the reflection, transmission, and refraction pathways of seismic waves from the soil layer to the water layer, then to the ice layer and air, and then reflects the attenuation principle of seismic waves in an ice-water layer based on the mechanical parameters of the soil layer, water layer, ice layer, and air. The spatial coherence effect, traveling wave effect, and local site effect are then addressed using the trigonometric series method, and the ice-water layer combined reflection coefficient is utilized to analyze the influence of offshore complex sites on seafloor spatial ground motion. Under the floating ice and seawater layer, an artificial synthetic approach of multidimensional multipoint spatial ground motion is described. The random ice load time history was artificially produced using the ice load spectrum theory and the recorded sea ice parameters. The random response of a long-span cable-stayed bridge is investigated under the combined action of seafloor spatial ground motion and random ice load, and the structural responses of the bridge and tower vary substantially under the combined action of ground motion and ice load.

The vibration mitigation of jacket offshore platform based on inerter nonlinear energy sink

The application of the traditional passive vibration control system is limited by the demand for large mass. To ameliorate this situation, the inerter nonlinear energy sink (NES) is introduced and applied, as the substitute for the traditional passive vibration control system, to vibration mitigation of jacket offshore platform under random wave loading, since it has the clear advantage of obtaining apparent vibration control effect through low amounts of added mass. For one thing, the equation of jacket offshore platform including inerter NES is developed considering wave loads. For another, the optimal parameters of inerter NES are obtained through Particle Swarm Optimization (PSO) using numerical simulations. Both analytical and numerical results strongly support that the inerter NES contributes greatly to vibration suppression, compared with traditionally tuned mass dampers (TMD). To explore more practical benefits, further comparison between the vibration mitigation of inerter NES and the optimal TMD system, considering different masses and stiffness, is made right after, which verifies the effectiveness and robustness of inerter NES. Based on the above study and results, it proves valid to conclude that the inerter NES system allows practical application of vibration mitigation for marine structures.

Random vibrations of laminated planar frames

In this study, the normal mode method is used to determine the response of a generalized laminated planar frame structure subjected to random loading conditions. The model, which is based on the Timoshenko–Ehrenfest beam theory, accounts for the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy. The free vibration analysis of the frame is formulated and solved, and the orthogonality condition derived. Following this, the normal mode method is applied to determine expressions for the mean square longitudinal, transverse and rotational displacements in terms of the excitation spectral density. Although the proposed model is capable of analyzing a wide range of problems, the numerical analysis conducted in this paper is centered on investigating the response of inclined two-member and three-member frames excited by a point force, whose spectrum is band-limited white noise. It is shown that in cases where the modal cross-correlation is negligible and the boundary conditions are symmetric, the spatial response of the mean square displacements are nearly symmetric about the center point of the frame. Contrarily, as the influence of the modal cross-correlation on the overall response increases, the featured spatial symmetry vanishes. An interesting characteristic of frame structures, is that the spacing between the natural frequencies is dependent on the frame angle. Consequently, modal cross-correlations can have a much greater effect on certain frame angles compared to others, even when the damping is fairly low. The study also investigates the effects of bending-extension material coupling on the random response of asymmetrically laminated cross-ply frames. The numerical results presented in this work are verified with independent finite element simulations conducted in the software package, Ansys® Parametric Design Language (APDL).

A spectral method for accurate evaluation of fatigue damage induced by wide-band non-Gaussian random processes

Evaluating the fatigue damage of marine structures subjected to random environmental loadings is of great practical significance at the design stage. In many situations, the structural responses of marine structures exhibit wide-band non-Gaussian properties. This study presents the fatigue damage assessment of wide-band softening non-Gaussian random processes by a spectral method proposed by Benasciutti and Tovo (2005b). Following this spectral method, the rainflow fatigue damage is approximated by a linear combination of its upper and lower bounds. A refined formulation of the weighting factor is proposed, which depends on the bandwidth parameters, slope parameter of the S‒N curve, and skewness and kurtosis of non-Gaussian processes. By introducing a suitable transformation function, the simulated non-Gaussian process is generated from its underlying Gaussian process. Through case studies, the effectiveness and accuracy of the present method for wide-band non-Gaussian processes are verified by comparisons with the results from the time-domain rainflow counting method and the other existing spectral methods.

Effects of size and location of magnetorheological segments on random vibration response of laminated composite beams using an N-layer of layerwise theory

Laminated composite beams are widely used in engineering applications, including wind turbine blades and automobile, where the structures are highly subjected to non-deterministic random loadings, requiring a reliable technique to ensure the stability of the structure during operation. Recently, to mitigate the effects of random loadings on the structural stability of the structure, segments of magnetorheological (MR) fluids have been embedded in the laminated beams (MR-laminated beams). In this work, the effects of the size and location of MR-fluid segments on random vibration characteristics are investigated. A laminated beam is considered in which several layers/segments are filled with MR fluids and are subjected to several random loads. An N-layer model of layerwise theory (LWT) developed by the present authors in previous work is considered for computational purposes. A finite element model based on LWT is developed to study the numerical examples. MR-laminated beams consist of five sections; two MR-fluid sections and three composite sections have been studied using LWT. To justify the numerical results, the first three natural frequencies of a laminated beam without an MR layer are solved using a 3D model in COMSOL software which shows a close match with the results of LWT. An in-house experimental setup has been developed to verify the simulation results. The simulation results are then compared with the first-order shear deformation theory (FSDT) and verified by several experimental tests. The effects of MR fluid segments on the dynamic response of MR-laminated beams for six different configurations have been investigated. In addition, the effects of thicknesses of MR fluid section on the dynamic behavior of structures have been investigated. Effects of magnetic fields on statistical properties, correlation, and autocorrelation on MR-laminated beams made of E-glass and fiber-carbon have been investigated. As a case study, the vibration response of a wind turbine blade made of an MR-laminated beam has been investigated using a narrow band process.

Random fatigue life analysis of carbon fiber‐reinforced plastic for automotive drive shaft with environment temperature data

AbstractAutomotive drive shaft is an indispensable key component of the transmission system, and the use of composite drive shafts has shown great promise. The epoxy matrix of the shaft is susceptible to the effects of temperature in comparison to carbon fiber. To investigate the influence of the environmental temperature on the fatigue life of a carbon fiber‐reinforced plastic drive shaft, a temperature‐based property curve and performance fraction model for the shaft are established. The temperature coefficient is calculated and introduced by combining the collected temperature data with the property fraction function. A generalized S‐N surface of the composite drive shaft is proposed based on experimental data. The fatigue life under collected and processed random loads of the carbon fiber‐reinforced plastic drive shaft is predicted by modified Miner's law. The effect of mean, amplitude of load and ambient temperature on fatigue life are taken into account.

Development and seismic behavior of an assembly composite damping self‐centering brace

AbstractA new type of assembly composite damping self‐centering brace is proposed to simplify the configuration, reduce the manufacturing cost, and improve its energy dissipation capacity, which is assembled by several modules in parallel with different functions. A brace specimen with a total length of 1.843 m was designed and numerically analyzed. The brace exhibits stable and full flag‐shaped hysteretic responses, and dissipates adequate energy during cyclic motion, with a high bearing capacity. When the brace is unloaded, the viscous damping force disappears, and the residual displacement can be basically eliminated. The hysteretic envelope area increases with the increase in loading frequency. When the frequency is 0.5 Hz and the target displacement is 30 mm, the activation force, ultimate bearing capacity, residual displacement, energy dissipation during one cycle, and equivalent viscous damping ratio are 622.5 kN, 1018.7 kN, 9.11 mm, 41.10 kJ, and 0.214, respectively. Under random loading, the damping force provided by the viscous module ensures a fuller hysteretic loop than the existing displacement‐type energy dissipation self‐centering brace. The influences of design parameters on the hysteretic performances of the brace were studied. When the disc spring stiffness increases from 3.27 to 9.80 kN/mm, the ultimate bearing capacity, residual displacement, and equivalent viscous damping ratio change by 18%, −24%, and −15%, respectively. The viscous damping coefficient and flow index of the viscous module should be increased, and the prepressed force and stiffness of disc springs in recentering module should also be appropriately increased.

Random vibration fatigue behavior of directionally solidified superalloy: Experiments and evaluation of life prediction methods

Vibration is closely related to structural dynamics, and the study of random vibration fatigue loads is typically conducted in the frequency domain. In this study, various frequency domain methods were employed to predict the random vibration fatigue life of DZ125L directionally solidified superalloy under different vibration signal intensities. Experimental analysis was used to examine the fatigue life and random vibration response of DZ125L alloy specimens under different vibration signal intensities. The S-N curve derived from sinusoidal vibration tests was used to replace the traditional S-N curve obtained from tension-compression tests in random vibration fatigue analysis, leading to improved life prediction accuracy. Additionally, an intensity function fξ was established using the spectral width parameters α1 and α2 of the random process and the vibration signal intensity ξ, which was used to modify the traditional Rayleigh method. A new vibration fatigue life prediction model based on frequency domain method is obtained. The results indicate that the intensity function fξ emphasizes the elastic or plastic stage of the specimen during the random process, leading to highly accurate life prediction values using the Modified Rayleigh method across different vibration signal intensities, with all prediction points are within 1.5 times the scatter band.

Reliability Analysis of Mining Machinery Pick Subject to Competing Failure Processes With Continuous Shock and Changing Rate Degradation

Efficient mining machinery operation is essential for coal mining enterprises to reduce production costs, improve production efficiency, and maximize profits. As a key consumable part of mining machinery, the reliability of the pick directly determines the operational performance and service life of the machinery. During the mining process, the pick can be affected by natural wear and tear caused by the coal and rock and load shocks caused by the gangue and faults—that is, the result of the competing influence of soft failure caused by natural wear and tear and hard failure caused by random load shocks. At the same time, because the gangue and faults have a certain volume and hardness, a random load shock may last for a certain period of time, producing different acceleration effects on the pick wear under different hardness conditions. In this article, the reliability modeling of the pick competing failure process under random load shocks was studied by considering the influence of continuous shocks and the accelerated degradation at changing rates for different shock durations on the pick wear. First, the pick degradation model under random load shocks was established by considering the natural wear degradation, instantaneous shock degradation, and accelerated degradation at changing rates for different shock durations. Second, the pick reliability model under the competing failure mode was established on this basis. Finally, a numerical experiment and an effectiveness analysis of the pick reliability model were conducted based on the engineering data. The results showed that the competing failure reliability model of the pick considering continuous shocks and a changing degradation rate was more in line with engineering practice, which is of great significance for pick design optimization and improved reliability.

Response prediction and fatigue life estimation of thin-walled structures under random excitation using the modified equivalent linearization method

This paper proposes a fast estimation method for the high-cycle fatigue of geometrically nonlinear thin-walled structures under random loading. The core idea of this method is utilizing a modified equivalent linearization method to obtain the statistical properties of the modal displacement response of the thin-walled structures, which is used to generate samples and then transform them into stress samples to determine the peak probability density function of the von Mises stress for fatigue life estimation. There are three critical issues addressed in implementing the method: (1) Using the implicit condensation technique to introduce the membrane softening effect in the regulated equivalent linearization method to improve the computational accuracy of the displacement statistical properties and convert the higher order moments into easily computable second order moments by separating the displacement mean values, so the regulated equations of motion for non-zero mean systems are derived, and fix the problem that the regulated equivalent linearization method does not apply to the prediction of the dynamic response of general thin-walled structures. (2) A nonlinear relationship between modal displacement and stress is derived with the implicit condensation and expansion method to transform the generated displacement samples to stress samples, which are used to determine probability density functions of stress and their derivatives. (3) Simplifying the probability density function of the three-dimensional joint distribution to the probability density function of the two-dimensional joint distribution by taking advantage of the Bayes rule, thus deriving a fast formula for the probability density function of the peak Mises stress.

Analytical prediction method of power system frequency deviation under uncertain power fluctuations

AbstractIn modern power systems, the impact of random power sources and loads on power systems is increasing, resulting in threatened system frequency security. However, traditional methods are often not comprehensive in modelling randomness, and there is no analytical method to assess the frequency response of power systems under uncertain power fluctuations. Here, the power fluctuation in a power system is regarded as an interval random quantity. An analytical prediction method of the power system frequency deviation under uncertain power fluctuation is proposed. Through further deduction, the allowable range of power fluctuation under the premise of secure frequency deviation can also be defined, which provides a reference for frequency security and accident prevention in power systems. Numerical simulations with the model of the East China Power Grid demonstrate that the proposed analytical method can delimit the response interval of system frequency deviation well, and the backstepping calculation can also delimit the allowable range of power fluctuation to ensure the secure operation of the system.

Pseudo‐dynamic hybrid simulations of steel eccentrically braced frames equipped with cast steel replaceable modular yielding links

AbstractPrevious studies have underlined the importance of establishing a database of high‐fidelity benchmark experimental test results under random loading histories such as earthquake excitations for both existing structural systems as well as newly proposed ones. Such experimental results are useful for understanding the limitations of previously developed numerical models, proposing new numerical models for more recently developed structural systems, better assessing the ultra‐low cycle fatigue (ULCF) life of energy dissipative components, and improving the loading protocols used for element assessments or developments of numerical model. This paper presents experimental results from pseudo‐dynamic hybrid simulations on steel eccentrically braced frames (EBF) equipped with novel cast steel replaceable modular yielding links. The first set of experiments are carried out on a four‐story EBF, with the first‐floor yielding link physically tested in the laboratory. The second set of experiments are performed on a two‐story EBF where the second‐floor link is physically tested in the laboratory, while considering axial loads due to the imbalanced distribution of the seismic weight in the building. Each building structure is subjected to three Maximum Credible Event (MCE) level earthquakes. A framework for performing hybrid simulations on EBFs is proposed where the response of the yielding link is physically captured in a single degree of freedom control system, with or without axial loads. A substructuring strategy is proposed in conjunction with a modeling approach in the integration module. The results confirm the effectiveness of the hybrid simulation framework, which can be adopted in similar studies. Two numerical models are proposed for capturing the response of cast steel links using a simplified and a more advanced approach. The models are first calibrated using incremental reversed‐cyclic experimental test results, and then refined using the hybrid simulation test results. The effects of this calibration improvement are quantified through critically comparing the response prediction for different response parameters before and after improving the calibration with the experimental results. The numerical model which captures the physical mechanism of the cast steel links provides a more accurate response prediction compared to the simplified numerical model using a phenomenological truss with calibrated force‐deformation. The remaining ULCF life of the tested yielding links is experimentally investigated after having sustained three MCE level earthquakes, which indicates a large reserve ductility capacity which is more than twice the required plastic rotation capacity for cast steel links after seismic events.