Amplitude Loading Research Articles

Topology optimization of multi-material structures subjected to dynamic loads

Traditional designs for multi-material structures are mostly based on static loads. However, engineering structures are often subjected to dynamic loads. This paper firstly and systematically conducts an in-depth study on the topological design of multi-material structures under dynamic loads. In this method, the definition of design variable adopts the ordered solid isotropic material with penalization (ordered-SIMP) method to normalize the design variable, without introducing any additional variables, the HHT-α method is employed to solve the dynamic optimization problem. To address the dynamic optimization problems with constraints on mass and cost, a convex optimization method based on the concept of sensitivity separation is used to update the design variables, and search for the structural topologies. Finally, this paper provides some numerical examples with respect to time-varying, material parameters, load amplitude, load direction and multiple loads, to discuss in depth the topological and numerical results of these examples.

Impact of early-age vibration on the permeability and microstructure of mature-age concrete

Dynamic excitation in early-age significantly impacts the performances of mature concrete in underground structures, such as tunnels beneath railways supported by cast-in-place concrete. This study explores the impact of early dynamic excitation on properties of mature concrete. Vibration tests at a fundamental frequency of 114Hz, with peak acceleration levels ranging from 0.1g to 0.4g, were conducted using shaking table. Specimens underwent 33seconds of dynamic excitation every 15minutes over the initial 48hours, excluding a night break from 0-6am, totaling 114 vibration cycles. Various lab tests were employed to assess the properties and microstructure of mature concrete post-vibration, including water penetration resistance, capillary water absorption, Coulomb electric flux, scanning electron microscopy (SEM), mercury intrusion porosimetry (MIP) and Nitrogen adsorption-desorption measurement (NAM). The results proves that vibration causes water secretion and air bubbles discharge before the initial setting of concrete, thereby enhancing the hydration reaction. The relationship between vibration loads with varying peak accelerations and the cohesion resulting from hydration reaction influences the microstructural evolution of concrete, leading to the weakening and strengthening of permeability of mature concrete. Under the vibration spectrum and test conditions described in this paper, vibration loads with peak values less than 0.234g decrease the total volume of large and middle pores (>20nm) by up to 50% and increase the total volume of small pores (<20nm) by up to 200%. Due to these changes in pore structure, the permeability coefficient (Sk), cumulative capillary water height (i) and Coulomb electric flux decrease by up to 47.84%, 39.5% and 31.6%, respectively. However, when the amplitudes of vibration loads exceed 0.234g, the total volume of large and medium pores (>20nm) increases, and that of small pores (<20nm) decreases, leading to a reduction of the impermeability of mature concrete. Additionally, the SEM analysis corroborates these microstructural variations.

A Higher-Order Theory for Nonlinear Dynamic of an FG Porous Piezoelectric Microtube Exposed to a Periodic Load

This paper investigates the nonlinear dynamic deflection, natural frequency, and wave propagation in functionally graded (FG) porous piezoelectric microscale tubes under periodic load, hygrothermal conditions, and an external electric field. The piezoelectric material used to make the smart microtubes has pores that may be smoothly changed or uniformly distributed over the tube wall. Here, three types of porosity distribution are taken into consideration. The nonlinear motion equations are constructed using a novel shear deformation beam theory and the modified couple stress theory (MCST). The nonlinear motion equations are solved using the fourth-order Runge–Kutta technique and the Galerkin approach. The effects of various geometric parameters, porosity distribution type, porosity factor, periodic load amplitude and frequency, material length scale parameter, moisture, and temperature on the nonlinear dynamic deflection, natural frequency, and wave frequency of FG porous piezoelectric microtubes are explored through a number of parametric investigations.

Research on Multi-Parameter Error Model of Backcalculated Modulus Using Abaqus Finite Element Batch Modeling Based on Python Language

The error in modulus backcalculation is a crucial component in validating the rationality and reliability of results for engineering applications. The objective of this study is to identify the theoretical limitations associated with backcalculated modulus errors under typical parameter uncertainties and to determine the primary factors contributing to these errors. Firstly, using the actual measurements or data from the Long-Term Pavement Performance (LTPP) project, the statistical distributions of errors for typical parameters in the modulus backcalculation model were determined. Subsequently, a factor level table for orthogonal experimental design was developed, leading to the construction of 81 orthogonal design experimental schemes and their corresponding theoretical pavement structure models based on the actual error distributions. The deflection responses of 81 theoretical pavement structure models were then computed using an ABAQUS finite element batch analysis method devised in Python. Furthermore, a multi-parameter error model for modulus was established using multiple linear regression and variance analysis. Finally, the theoretical limitations of modulus errors under actual errors were analyzed. The results show that the errors of thickness, load amplitude and load frequency follow a normal distribution, while the distribution of backcalculated modulus errors follows an approximate mixed Gaussian distribution. When the errors of multiple parameters are combined randomly, the modulus errors range from −100% to 595%, and the probability of the modulus errors being less than 15% is highest in the asphalt surface layer, followed by the subgrade, and then the base and subbase layers. Within the same error range, the modulus error is random. However, with different error ranges, the overall level of modulus error increases in proportion to the size of those ranges. Compared to factors such as thickness, load amplitude, and load frequency, the errors in deflections have a highly contribution rate on the modulus errors exceeding 99%.

Complex High‐Cyclic Loading in an Accumulation Model for Sand

ABSTRACTExperimental evidence indicates that multidimensional cyclic loading of soils causes larger accumulation of deformations than equivalent one‐dimensional loading. The response of sand to high‐cyclic loading with 10,000 cycles and up to four‐dimensional stress paths (i.e., four independent oscillating components) is examined in 120 triaxial and hollow cylinder tests in this work to extend these findings. With increasing number of oscillating stress components, the accumulation of permanent strains tends to increase. It is demonstrated that the definition of the multidimensional strain amplitude incorporated in the high‐cycle accumulation (HCA) model can account for this. The validation of the HCA model for complex cyclic loading is complemented by the simulation of model tests on monopile foundations of offshore wind turbines subjected to multidirectional cyclic loading, for which the consideration of spatially variable cyclic loading with nonconstant load amplitudes in the HCA model is discussed. For this purpose, an extension of the HCA model considering multiple strain amplitudes is presented.

Experimental study on the cyclic performance of innovative self-centering three-dimensional isolation bearing

To improve vertical seismic isolation and seismic resilience in isolation bearings, this paper introduces an innovative three-dimensional isolation bearing combining a disc-spring system (DSS), a high-damping rubber bearing (HDR), and a horizontal spring system (HSS). The DSS is designed with low vertical stiffness to enhance vertical isolation, while the HSS provides self-centering force to improve the seismic resilience of the HDR. This study first presents a comprehensive theoretical analysis of the horizontal and vertical stiffness composition. The vertical performance of this three-dimensional isolation bearing is attributed to the DSS, while the HSS and HDR jointly contribute to its horizontal performance. Seven specimens were designed and subjected to shear-compression cyclic tests to assess the horizontal and vertical cyclic performance. Experimental parameters included loading amplitude, loading frequency, vertical pre-load, and DSS combinations for vertical tests, and axial compression force, loading frequency, shear strain, and HSS function in horizontal tests. The cyclic performance parameters for the three-dimensional isolation bearing, including equivalent damping ratio, equivalent stiffness, and energy dissipation, was evaluated. In general, the proposed three-dimensional isolation bearing exhibits stable cyclic performance and advantageous seismic resilience, warranting its promotion to practical engineering applications.

Study on mechanical properties and vibration reduction effect of a novel mesh-type elastic cushion plate with orifice: Theory, simulation and test

Elastic cushion plates in fastener systems play a critical role in controlling vibrations and noise, yet enhancing their damping capacity while maintaining cost-efficiency remains a persistent challenge. This paper presents a Novel Mesh-Type Elastic Cushion Plate with Orifices (NMTECPO), featuring innovative structural modifications that leverage air-damping mechanisms to achieve superior performance. Unlike conventional elastic cushions, NMTECPO incorporates a unique mesh structure with variable orifices and chamber volumes, significantly boosting its damping properties. Key structural parameters influencing the stiffness and damping characteristics of the NMTECPO such as orifice aperture, chamber volume, loading frequency, and loading amplitude, are identified through theoretical derivation and validated by extensive comparative tests. A fluid–structure interaction finite element model further demonstrates enhanced damping performance by optimizing the orifice aperture and chamber volume. Dynamic simulations also reveal that NMTECPO exhibits superior vibration attenuation compared to traditional cushion plates. The proposed NMTECPO offers a novel approach by effectively integrating structural innovations and parameter optimization to improve vibration damping, providing a cost-efficient solution with potential for future engineering applications and structural refinement.

A Novel Method for Analyzing Global Bifurcation and Global Hysteresis of FGM Truncated Conical Shell Structure

In the dynamic bifurcation and dynamic hysteresis of a system, our first consideration is the tiny changes in time that can lead to variations in the vector field, potentially causing the occurrence of system dynamic bifurcation and dynamic hysteresis. This paper presents a novel method for analyzing the global bifurcation and hysteresis of Functionally Graded Material (FGM) truncated conical shell structure under aerodynamics and in-plane force along meridian near internal resonances. This method involves introducing the ratio of vector fields as a periodic perturbation parameter in the system’s nonlinear second-order ordinary differential governing equations. This allows for the analysis of the nonlinear ordinary differential equations as algebraic equations, yielding algebraic expressions that only involve parameters and do not contain state variables. Subsequently, the global bifurcation set and global hysteresis set of FGM truncated conical shell structure are obtained, providing the parameters interval ranges for the stability and instability of FGM truncated conical shell structure. By utilizing MAPLE software for numerical simulation, the images of the global bifurcation set and global hysteresis set about the amplitude of in-plane load are first simulated numerically. Subsequently, the amplitude graphs of the equilibrium points are numerically simulated for validation. The results demonstrate a perfect alignment between the images of the global bifurcation set and global hysteresis set and the data from the amplitude graphs of the equilibrium point. Due to the periodicity of the periodic perturbation parameter, it shuttles between different persistent regions as other parameters change, leading to the generation of chaotic solutions in the governing equations. The validity of the obtained results is confirmed through comparisons with existing literature.

A study on the fretting corrosion of 316L in static lead-bismuth eutectic (LBE): The role of slip amplitude and normal force on damage mechanism at 350 °C

Fretting corrosion of stainless steel in the LBE affects the safety of lead-cooled fast reactors. Slip amplitude and normal load are the main mechanical factors affecting fretting wear behavior. Thus, the damage mechanism of 316L stainless steel at 350 °C LBE influenced by slip amplitude and normal load was investigated by jointly utilizing multiple characterization methods. The results indicate that the normal load and slip amplitude essentially affect the tangential stress and relative sliding value in the contact area, leading to different slip regions and damage mechanisms. In the mixed slip region, the damage mechanism is adhesion and delamination cracks. The increase in tangential stress leads to decrease in relative sliding. The thick wear debris layer attached to the worn surface can protect the substrate from being attacked by the LBE. In the gross slip region, the damage mechanism is abrasive wear and dissolution corrosion. The increase in relative sliding causes more damage and Ni dissolution, leading to the transformation from austenite to ferrite and internal strain, making the substrate more susceptible to damage and increasing the risk of liquid metal embrittlement (LME) of austenitic stainless steel at 350 °C. Accordingly, a model for different damage mechanisms was proposed. These results can provide important information on the fretting damage related to the LBE environment.

Shear Strengthening of RC Beams Incorporating Post-Tensioned Bars and Engineered Cementitious Composite Reinforced with Palm Fronds

This paper investigates, experimentally and numerically, the shear strengthening of Normal Concrete (NC) beams using post-tensioning steel bars and Engineered Cementitious Composite (ECC) reinforced with chemically cured Palm Fronds (PFs). The benefits of strain-hardening ECC and the tensile strength of PFs cured with 6% wt Alkali NaOH solution beside post-tensioned bars have been employed herein. Seven full-scale Reinforced Concrete (RC) beams were fabricated and experimented with under three-point loading until failure. The test parameters include the strengthening technique, type, and configuration of the material used for strengthening. The strengthening process has been implemented through two techniques: Externally Bonded Reinforcement (EBR) and Near-Surface Mounted (NSM) Reinforcement. The strengthening materials have been configured and placed in horizontal, vertical, and inclined positions. The effectiveness of the strengthening methods has been evaluated by examining their cracking propagations, load-deflection responses, collapse modes, elastic stiffness, and absorbed energy. It was found that the proposed strengthening systems could significantly control the crack pattern and failure mode, and they could enhance the ultimate load amplitude up to 37% and 50% for NSM ECC with PFs and EBR post-tensioning steel bars, respectively. Nonlinear three-dimensional finite element models of the tested beams were developed and validated with the test data, where it was found that finite element models predict the structural performance of tested beams with a maximum error of only 2%.

Research on the mechanism of impact of vibrational loads on the bearing capacity of drilling surface conductor

The surface conductor is the first structural pipe in the development of deep-water oil and gas resources, bearing the top load and suspending various casing layers. Vibrational loads can cause soil structural damage and increase pore pressure, reducing the bearing capacity of the surface conductor and threatening the safety and stability of the subsea wellhead. Based on the vertical force analysis of the surface conductor and considering the impact of vibrational loads on soil strength, a model for the vertical bearing capacity of the surface conductor was established. Utilizing the dynamic Winkler model for pile foundation horizontal dynamic response, the surface conductor was simplified as a bending beam subjected to harmonic vibration, and a control equation for lateral deformation of the surface conductor was established. The effects of vibration load amplitude and frequency on the vertical bearing capacity of surface conductors were analyzed through simulation experiments, resulting in an equivalent bearing capacity coefficient for surface conductors ranging from 0.88 to 0.97. Combining the engineering data from a deep-water block in the South China Sea, the reliability of the theoretical calculation model was validated. The analysis indicates that the maximum bending moment of the surface conductor is approximately 6m below the mudline; low-frequency(0.05Hz–0.2Hz) vibrational loads can reduce the ultimate bearing capacity of the surface conductor by 3%–11%, with the effect gradually diminishing over time. This research provides a theoretical basis for the design of surface conductor in deep-water oil and gas wells.

Effects of Fatigue Load Amplitude on the Mechanical and Energy Evolution Characteristics of Stratified Rock Mass under Triaxial Cyclic Loading and Unloading Conditions

Effects of Fatigue Load Amplitude on the Mechanical and Energy Evolution Characteristics of Stratified Rock Mass under Triaxial Cyclic Loading and Unloading Conditions

Bearing Performance of a Helical Pile for Offshore Photovoltaic under Horizontal Cyclic Loading

For an offshore photovoltaic helical pile foundation, significant horizontal cyclic loading is imposed by wind and waves. To study a fixed offshore PV helical pile’s horizontal cyclic bearing performance, a numerical model of the helical pile under horizontal cyclic loading was established using an elastic–plastic boundary interface constitutive model of the clay soil. This model was compared with a monopile of the same diameter under similar conditions. The study examined the effects of horizontal cyclic loading amplitude, period, and vertical loads on the horizontal cyclic bearing performance. The results show that under horizontal monotonic loading, the bearing capacities of a helical pile and monopile in a serviceability limit state are quite similar. However, as the amplitude of horizontal cyclic loading increases, soil stiffness deteriorates significantly, leading to greater horizontal displacement accumulation for both types of piles. The helical pile’s bearing capacity under horizontal cyclic loadings is approximately 60% of that under monotonic loading. With shorter cyclic loading periods, horizontal displacement accumulates rapidly in the initial stage and stabilizes over a shorter duration. In contrast, longer cyclic loading periods lead to slower initial displacement accumulation, but the total accumulated displacement at stabilization is greater. When vertical loads are applied, the helical pile exhibits more stable horizontal cyclic bearing performance than the monopile.

Investigation on internal evolution process of slope under seismic loading: insights from a transparent soil test and shaking table test

Earthquakes are a primary factor in triggering slope instability and pose a serious threat to transportation. However, current research on the internal deformation of slopes under seismic loading remains limited. To investigate the effects of different seismic loadings on the evolution process and failure mode of slopes, a novel experiment combining transparent soil materials and shaking table tests was proposed in this study. Using a self-designed shaking table system, sine waves with amplitudes of 0.10 g, 0.15 g, and 0.20 g and frequencies of 3 Hz, 5 Hz, and 8 Hz were applied. Based on Particle Image Velocimetry (PIV) technology and non-intrusive monitoring techniques, displacement and velocity contour maps, whole-field average displacement and failure mechanism of the slope were analyzed. The results show that, as the vibration persists, the slope transitions from initial shallow linear sliding to overall circular arc sliding, exhibiting an obvious progressive traction failure mode. The evolution process of the slope could be divided into three phases: shallow low-speed sliding phase, overall rapid sliding phase, and overall low-speed sliding phase. Furthermore, the amplitude of seismic loading has a greater influence on slope deformation compared to its frequency. This novel experiment offers important insights into the internal evolution process of slopes under seismic loading.

Stiffness Hardening Effect of Wire Rope Isolators under Small Cyclic Loads for Vibration Isolation

Wire rope isolator (WRI) devices are widely used in vibration reduction industrial equipment, and stiffness is the key parameter that determines isolation effectiveness. WRI devices show slight nonlinearity under small loads, and the manufacturers generally only provide the initial parameters. To investigate the mechanical behavior changes in the WRI devices under repeated loads, five types of WRI specimens were tested under various amplitudes, loading speeds, and preloads. The test results of large symmetrical compression and tension loads showed that the WRI devices demonstrated stable hysteresis curves under repeated loads, while the hysteresis curves were independent of the loading speed. The test results of small cyclic loads with large preloads show that the stiffness of the WRI specimen follows the logarithmic law, with the cycle number under various loading conditions. Particularly, the stiffness of the specimen increases by about 10–30% after 50 cycles. The initial stiffness Ka decreases linearly with the preloads, while the decrease is quadratic in relation to the cyclic load. The hardening coefficient Ca shows a positive correlation with the loading capacity of the WRI devices, while it shows a negative correlation with the preload and cyclic load amplitudes. It is recommended to consider the stiffness increase in the WRI devices during the evaluation of isolation effectiveness.

Numerical Simulation for Durability of a Viscoelastic Polymer Material Subjected to Variable Loadings Fatigue Based on Entropy Damage Criterion.

This study aims to explore the impact of load history on the premature failure of the viscoelastic polymer matrix in carbon-fiber-reinforced plastics (CFRPs) using a method based on the concept of fracture fatigue entropy (FFE). A user-defined subroutine (UMAT) developed by the authors in previous studies was incorporated to apply the FFE damage criterion using ABAQUS software. Several variable-amplitude load modes, including frequent load amplitude changes and intermittent interruptions, were designed based on the conventional linear damage accumulation method (Palmgren-Miner rule), and the fatigue life under these loadings was obtained via numerical simulations. The results show that both frequent amplitude changes and even brief pauses in loading can accelerate damage accumulation, leading to premature failure of the polymer matrix. In these scenarios, the fatigue life ranged from 33.6% to 91.9% of the predictions made using the Palmgren-Miner rule, which shows significant variation and highlights cases in which the predicted fatigue life falls far short of expectations. This study offers a more practical and reliable approach for predicting fatigue life under complex loading conditions. Since the accuracy of the FFE criterion has been comprehensively validated in previous studies, this research focuses on its application to predict failure under variable loading conditions.

Fatigue Life Assessment of Corroded AlSi10MgMn Specimens

This study investigates the influence of pre-corrosion damage on the fatigue behavior of AlSi10MgMn high-pressure die-cast specimens, using the statistical distribution of corrosion depths. The analysis is conducted on two different surface conditions: an unmachined rough surface (Ra=5.05μm) and a machined, polished surface (Ra=0.25μm). For the unmachined specimens, the corrosive damage manifests as homogeneously spread localized corrosion, whereas the polished specimens exhibit less uniform but deeper corrosion. The average corrosion depth of the polished specimens is found to be slightly higher (313 μm compared to 267 μm) with a broader depth distribution. Specimens are tested under a constant bending load amplitude in laboratory conditions at a stress ratio of R=0 until fracture. A fracture mechanics-based methodology is developed to assess the remaining fatigue life of corroded specimens, utilizing short and long crack fracture mechanical parameters derived from SENB specimens. This model incorporates a thickness reduction of the critical specimen cross-section based on the corrosion depth distribution and combines it with a small initial crack of the intrinsic defect size (aeff=14μm). Regardless of the surface condition, using the most frequent corrosion depth for thickness reduction provides a good estimate of the long-life fatigue strength, while using the 90th percentile depth allows for a conservative assessment.

Identification of the Payne effect in a viscoelastic material coupling Bayesian identification and digital twin

The Payne or Fletcher-Gent effect is a particular behavior occurring in viscoelastic materials containing fillers. It induces a nonlinear dependency of the viscoelastic storage modulus on the amplitude of the applied strain. This amplitude dependency must be taken into account in engineering applications as it does change the elastodynamic behavior of the overall structure integrating the material. A methodology is developed in the proposed work to identify this nonlinear effect. The approach first starts with the identification by Bayesian inference of the frequency and damping properties of a viscoelastic sample. The input data are obtained from a modified Oberst test, conducted for different displacement load amplitudes. A digital twin of the experimental set-up is then used to evaluate the stiffness behavior, and in particular the Young's modulus of the material, at the measured frequencies, and to deduce the strain level within the sample. This work shows that the Payne effect, which leads to the decrease with the amplitude of the Young's modulus, can thus be estimated in terms of mean and standard deviation by combining experiments and numerical simulations.

S–N curves established from limiting energy in the case of specimens additively manufactured from AlSi10Mg

AbstractThis study investigates the varying thermal response of additively manufactured specimens made of AlSi10Mg and subjected to cyclic loading. It is well known that the thermal response is driven primarily by the self‐heating effect. The paper explores the possibility of employing thermographic methods to establish an S–N curve for fatigue life prediction with the use of fewer specimens than are traditionally required for an S–N curve established from constant‐amplitude fatigue tests. Specific self‐heating step tests are conducted by gradually increasing the loading amplitude while monitoring the temperature of the specimen. A new approach is introduced to assess the lower limitation of the existing Fargione method, which addresses the absence of the fatigue limit threshold in previously published works. The validity of this approach is compared with our own experimental data. This new dataset concerns additively manufactured (AM) specimens made from AlSi10Mg powder, which were all printed on a single platform. To observe the sensitivity of the updated approach, four groups with different heat treatments were evaluated.

Advancements in electrohydraulic fatigue testing: Innovations in variable resonance frequency control and comprehensive characterization

This study addresses the challenge in electro-hydraulic fatigue testing machines where increasing excitation frequency leads to reduced output load amplitude, making it difficult to optimize both frequency and amplitude simultaneously. A new approach is introduced with the variable resonance fatigue testing machine controlled with 2D excitation valves. This technique involves adjusting the system’s intrinsic frequency by altering its mass, aligning the excitation frequency with the intrinsic frequency, and leveraging resonance energy to enhance excitation amplitude for broad-range resonance near the resonance point. The relationship between the system’s intrinsic frequency, the equivalent mass of the upper connector, and the upper fixture is explored, yielding analytical solutions. Experimental research validates these simulations, in the resonance condition, the fatigue testing machine energy efficiency can reach 94 %, to further verify the fatigue testing machine in the resonance condition to realize the High energy efficiency. Demonstrating that the system’s intrinsic frequency decreases with increasing mass, allowing for a broad frequency resonance between 200 and 300 Hz. Operating in a broadband resonance region, the output load force is increased by 60 %–95 % and the system flow is reduced by 20 %–30 %. This mass-adjustment technique effectively alters the system’s intrinsic frequency, expanding the electro-hydraulic fatigue testing machine’s application scope.