Elastic Impact Research Articles

Complex response analysis of a non-smooth oscillator under harmonic and random excitations

It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.

Identification of acoustic emission sources for structural health monitoring applications based on convolutional neural networks and deep transfer learning

In the present work, different types of acoustic emission (AE) sources are identified by means of computational intelligence. The goal is to characterize the type of AE source and to successfully differentiate between sources that are related to an internal damage, such as a fracture initiation, or an external load represented by an elastic impact. A Hsu-Nielsen source (pencil-lead break) and two steel ball impacts of different diameters are selected for the excitation of an aluminum plate equipped with four piezoelectric transducers to record the acoustic emissions. Furthermore, 25 different areas for the AE sources are defined to collect a large database. Three different machine learning architectures are considered, which can predict the type of the AE source. Time domain signals of the acoustic emissions are used for the training of an artificial neural network and a 1D convolutional neural network. Additionally, the wavelet transformation is performed on the captured signals to generate RGB images of the sensor responses and to train a 2D convolutional neural network in combination with deep transfer learning. An error evaluation of each machine learning model is performed to discuss the classification results. The proposed methodology demonstrates that computational intelligence can be applied to accurately identify the type of AE source based on the captured acoustic emission signals.

Design of impact dampers for transporting cargoes by two-link vehicles

This paper considers the influence of the transitional modes of movement (acceleration, braking) of a multi-link vehicle on the vibration protection of transported non-fixed or partially fixed cargoes. The impact phenomenon, in this case, can be strengthened by the existence of coupling mechanisms between the links of a multi-link vehicle. To reduce such horizontal impact loads, it is advisable to use elements with viscoelastic damping in the coupling devices of a multi-link vehicle. To study the actual impact phenomena during the transportation of non-fixed or partially fixed cargoes under the extreme modes of movement of two-link vehicles, it is proposed to use a flat two- and three-mass dynamic model with viscoelastic damping. At the same time, the theory of elastic impact has been applied while the elastic-damping characteristics of vehicles' suspensions were not taken into consideration. It has been shown that the reported research results make it possible to estimate the approximate values of the mechanical parameters for restrictive devices that protect non-fixed or partially fixed cargoes from impact, during the transition modes of transportation, depending on the conditions of motion. This practically makes it possible to select the rational design parameters for the elements of viscoelastic restrictive devices, in particular elastic elements and dampers, in order to reduce impact loads on non-fixed heavy cargoes during transportation under extreme modes of movement. Based on this study, a procedure of vibration protection of non-fixed or partially fixed cargoes in the body of a two-link vehicle during its uneven movement has been proposed, which implies determining the maximum dynamic loads on these cargoes as well as the possibility of choosing the rational design parameters for restrictive devices in order to prevent or reduce the impact of these cargoes hitting the restrictive devices

Numerical Simulation of the Effects of Strain Hardening Exponent with and without Strain Rate Sensitivity of Material on Normal Elastic Plastic Impact

The material behavior selection is an important factor governing the structural response analysis of transverse impact problems, such as impact force, indentation and local elastic plastic deformation. In the present paper, the effects of strain hardening exponent (n) and strain rate sensitivity (m) on the transient response were investigated for low impact velocity by the aid of finite element simulation using the Abaqus Software. Investigated parameters are impact force histories, indentation and plastic strain (PEEQ). Results showed that the effect of n values on required parameters is more pronounced, unlike strain rate sensitivity which has not a significant influence. As well, material behavior selection is essential for an accurate local plastic strain analysis.

Effect of Temperature on the Mechanical Properties of Unsaturated Polyester Reinforced with Fibers and Nanoparticles

A composite material is a material that consists of a matrix (base phase) and a stiffener (reinforcement) that combined together to build up a structural unit. Reinforcement material form may be fibers, flakes or as a particle. In the current paper, unsaturated polyester resin (UP) was used as a base material, Sisal fibers (SF), glass fibers (GF) and Silica dioxide (SiO2) particles were performed as a reinforcing material. Three composite types were prepared: (C1) UP only, (C2) UP reinforced with 15% SF and 15% GF, and (C3) UP reinforced with 15% SF and 15% SiO2 to investigate the effect of reinforcement type on some mechanical properties such as elastic modulus, compressive strength, hardness and impact toughness with various temperatures. The experimental results showed that the mechanical properties of composite materials were improved by using reinforcement with fibers and nanoparticles. The high values of elasticity, hardness and toughness were obtained with the specimen C2 composite. While the highest values of compressive strength were obtained with the specimen C3. On the other hand, the modulus of elasticity, compressive strength and hardness were decreased with increasing of temperature values with various percentages. Other clockwise, the toughness values were increased

Контроль одноосных напряжений в сталях с учетом их магнитоупругой чувствительности

The magnetoelastic demagnetization of a number of steels in the state of delivery under longitudinal elastic tension, transverse compression and impact has been investigated. The estimation of the magnetoelastic sensitivity of the studied steel grades in the linear approximation is given. The possibility of determining the tensile and compressive stress in the mode of magnetoelastic memory is considered, taking into account the magnetoelastic sensitivity of the selected section of steel, and a method for its determination using dosed loading (impact or compression) is proposed. It is shown that the regression equation in the form of a polynomial is in satisfactory agreement with the experimental results.

Transient Impact Analysis of Elastic-plastic Beam with Strain-Rate Sensitivity

The impact response of an elastic-plastic beam is highly complicated in nonlinear transient dynamics especially when the material's plasticity is strain rate dependent. To reduce the efforts required for the computational analysis, an analytical-numerical model (hybrid model) is proposed for the analysis of the transient response of the beam to sphere impact. The model couples two sub-models, a combined discretization model and a refined contact model. Both the sub-models incorporate the material strain rate dependence. The combined discretization model discretizes the beam in length direction by a dynamic substructure technique and in thickness direction by a finite difference technique to capture the beam wave propagations along the length and the stress variations along the thickness. The refined contact model extends the BD model [1] to sphere-beam impacts by introducing a new representative contact strain rate and a new unloading law to avoided the force discontinuity at the inception of unloading. The hybrid model is validated by the laboratory test performed for low-velocity impacts and by the three-dimensional finite element (FE) analysis implemented for moderate-velocity and moderate high-velocity impacts. The validations show that the hybrid model is accurate, highly efficient and suitable for the parametric study, especially for the study of impact-induced wave effects. By using the hybrid model, tests and FE analyses, the influences of the material strain rate sensitivity are investigated by comparing to the results of elastic plastic impact simulations ignoring the effect of strain rate. It is found that the influence of the strain rate dependence on the contact force-indentation relation is significant even in the low-velocity impacts. The influences of the strain rate dependence on the contact duration and maximum contact force are small, even for the impact velocity up to 30 m/s. The influences of the strain rate dependence on other impact responses are small in the low-velocity impacts, and increase with increasing of the impact velocity. A parametric analysis is conducted to investigate the effects of the impact conditions on the contact duration and coefficient restitution. Their map structures are complicated, depending upon the mass ratio and the impact position. A jumping/falling phenomenon for the variations of the contact duration and coefficient of restitution is found, which are caused by the multiple impacts.

The Reaction of the Consumption of Fossil Fuels to Trade Openness in Latin America & the Caribbean Countries

This article investigates the impact of trade openness and renewable energy on the consumption of fossil fuels for a panel of fourteen LAC countries over the period from 1990 to 2014. To this end, a PARDL model in unrestricted error-correction form is estimated, and robustness checks are performed by estimating a PNARDL model. The results of the PARDL model point indicate that the impact of economic growth and elasticity of trade openness are statistically significant at the 1% level and contribute to increased consumption of fossil fuels in the LAC countries. However, the impact and elasticity of consumption of renewable energy are statistically significant at 1% and 5% levels and thus contribute to decreasing consumption of fossil fuels. Nevertheless, the asymmetry of the impact of consumption of renewable energy and its elasticity decrease the consumption of fossil fuels. Therefore, the positive impact of trade openness on the consumption of fossil fuels suggests that the process of globalisation by trade liberalisation in the LAC countries is not sufficient to bring more investment that encourages R&D in energy efficiency technologies, and equipment that reduces the consumption of energy from non-renewable energy sources by households and firms.

Dynamics of stochastically excited energy harvesting systems with impact

Focusing on rigid impact (RI) and elastic impact (EI) vibratory energy harvesting systems with the excitation of Gaussian white noise, the stochastic response characteristics, and energy harvesting performance of the systems are presented and compared. The stochastic averaging of the energy envelope is introduced with different processing methods in these systems to derive the theoretical probability density functions. Numerical simulation results verify the effectiveness of such theoretical methods. Effects of the coefficients and positions of impact barriers in the systems on the mean square voltage are analyzed. The analysis can help explain the physical mechanisms of the systems and provide ideas for optimizing energy harvesting performance by properly tuning the coefficients. Effects of the existence of three kinds of impact on the output energy are explored and compared. It is found that the existence of EI can help to enhance the energy harvesting performance of the system in most cases, and setting the impact barrier at the origin is more conducive to harvesting energy compared with other impact positions.

An Emerging Class of Hyperbolic Lattice Exhibiting Tunable Elastic Properties and Impact Absorption Through Chiral Twisting

An Emerging Class of Hyperbolic Lattice Exhibiting Tunable Elastic Properties and Impact Absorption Through Chiral Twisting

Improved prediction of litchi impact characteristics with an energy dissipation model

A model of elastic impact (EI) and a model that considers energy dissipation (CED model) were developed to describe the deformation behavior during litchi impact. In the CED model, dissipation energy is due to damping effect and the change of elastic modulus after impact. Drop tests of fruit onto a fixed plate were conducted with a pendulum device for three litchi cultivars (‘Nuomci’, ‘Guiwei’, and ‘Lvhebao’) to test the accuracy of the two models. The results show that the CED model better simulated the change of fruit velocity during impact and better predicted the occurrence time of maximum impact force and maximum deformation compared to the EI model. Both models accurately predicted the maximum impact force of ‘Guiwei’ litchi with all errors less than 5 %, but had errors up to 24.8 % for the prediction of the maximum impact force of ‘Nuomici’ and ‘Lvhebao’ litchis at high drop heights (drop height ≥ 400 mm). The CED model accurately predicted maximum deformation (errors less than 8 %) but the EI model over-predicted maximum deformation with errors range from 12.2 % to 39.2 % at all drop heights for the three tested cultivars. Both models predicted the contact time with low-level errors (<10 %). With a reliable theoretical model, the impact characteristics of litchis can be calculated and then applied to assess the fruit damage degree.

Impact of substrate elasticity on contact angle saturation in electrowetting.

The electrostatically assisted wettability enhancement of dielectric solid surfaces, commonly termed as electrowetting-on-dielectric (EWOD), facilitates many microfluidic applications due to simplicity and energy efficiency. The application of a voltage difference between a conductive droplet and an insulated electrode substrate, where the droplet sits, is enough for realizing a considerable contact angle change. The contact angle modification is fast and almost reversible; however it is limited by the well-known saturation phenomenon which sets in at sufficiently high voltages. In this work, we experimentally show and computationally support the effect of elasticity and thickness of the dielectric on the onset of contact angle saturation. We found that the effect of elasticity is important especially for dielectric thickness smaller than 10 μm and becomes negligible for thickness above 20 μm. We attribute our findings on the effect of the dielectric thickness on the electric field, as well as on the induced electric stresses distribution, in the vicinity of the three phase contact line. Electric field and electric stresses distribution are numerically computed and support our findings which are of significant importance for the design of soft materials based microfluidic devices.

Underground economy and GDP growth: Evidence from China’s tax reforms

Since 1991, China has implemented two significant tax reforms. The first reform, in 1994, was a large-scale adjustment of the tax distribution system between the central and local governments, and the second reform, in 2012, replaced business tax with value-added tax. Also, the size of China’s underground economy decreased from 13.55% in 1995 to 12.30% in 2016. The paper presents an evaluation of the effect of the two tax reforms and the existing underground economy on GDP growth in China. GDP is defined as explained variable, the explanatory variables include: the ratio of declared income to actual income, the change of concealed income, and the influence of tax rate change on declared income and concealed income. According to the tax reform in 1994 and 2012, two dummy variables are set respectively. In methodology, this paper uses Simultaneous equations model, SUR-OLSs and Slutsky identity. Our estimation is based on the official statistics of China National Bureau of Statistics in the period from 1991 to 2019. In empirical analysis, we decomposed tax changes into tax rate effect (change of budget constraint slope) and income effect (change of tax liability), then analyzed the impact of tax elasticity on GDP growth. The empirical results demonstrate that both the 1994 tax reform and 2012 tax reform have had a positive impact on GDP, with high statistical significance respectively. The results also confirm that the increase of tax rate leads to the increase of hidden income, which eventually leads to the decrease of GDP. The offered methodology can also be applied to most countries for time series analyses.

A semi-analytical model of hydroelastic slamming

A semi-analytical model of hydroelastic slamming for two-dimensional symmetric flexible bodies is presented in this paper. The hydrodynamic loads are computed using the analytical Modified Logvinovich Model (MLM) with account for elastic deflections of the body surface. The elastic deflections are described by the modal approach. The rigid and elastic motions of the body are computed at the same time together with the wetted part of the body surface. The coupled problem of elastic impact is reduced to a system of nonlinear ordinary differential equations, which is integrated in time by the implicit Newmark method with iterations at each time step. Both free fall and constant water entry cases are considered. The developed model is validated for flexible wedge and cylindrical shell water entry problems. Good agreements with existing experimental and numerical results are achieved. It is shown that the MLM significantly improves predictions of the deflections and stresses cause by the impact compared with the Wagner model of water impact. The developed model is suitable for efficient and accurate computations of water elastic impacts.

Housing supply elasticity and growth: evidence from Italian cities

Abstract This paper examines the impact of housing supply elasticity on urban development. Using data for a sample of roughly one hundred Italian main cities observed over 40 years, we first estimate housing supply elasticities at the city level, measured as the correlation between the changes in the housing stock and in the house prices. Second, we show that differences in the elasticity of housing supply may determine the extent to which a demand shock translates into more intense employment growth or more expensive houses. To address endogeneity of housing supply elasticity, we exploit a synthetic measure of physical constraints to residential development as instrumental variable. We find that an exogenous increase in labor demand determines a rise of employment and house prices; however, in cities with a less elastic housing supply, the impact on economic growth is significantly lessened while the effects on house prices are larger.

Experimental study on the dynamics and mass transfer of CO2 bubbles rising in viscoelastic fluids

Single CO2 bubbles rising in quiescent viscoelastic polyacrylamide (PAA) aqueous solutions of different weight percentages (wt. %) were studied to obtain insight into the impact of fluid elasticity on the rising dynamics of dissolving bubbles. A random abrupt fall and rise in velocity was observed as the bubble velocity gradually and progressively decreased throughout the journey. This is the first time this observation is reported. In the most viscoelastic medium in which this phenomenon occurred, CO2 bubbles decreased in diameter by at least 20% over 1m of height. Mass transfer analysis of the system indicated significant reduction of mass transfer coefficient with increase in weight percentage of the polymer solution. Comparison of experimental mass transfer coefficients with predictions for mobile and immobile gas-liquid interfaces were consistent with theoretical predictions from Higbie's and Frössling's equations respectively. The rising dynamics was correlated using dimensional analysis, and the prediction by a developed empirical correlation considering the combined effect of fluid elasticity and shear-thinning property showed a satisfactory agreement with experimental data in all liquids studied.

Elastic impact of a spherical particle with a long, stationary, fixed Timoshenko beam

This study presents an analysis of the transient response of a beam subjected to transverse impact by a spherical particle. The beam is modeled as a long Timoshenko beam with clamped boundaries. A numerically stable solution to the dispersion relation is developed, which allows the deflection to include the effects of high-frequency waves. Time history of contact force, transverse deflection, velocity and acceleration provide insight into the interactions between the two objects after impact. Comparison with the Euler-Bernoulli beam model demonstrates the advantage of the Timoshenko beam in capturing the dispersive features of wave propagation. The group and phase velocities of bending waves due to impact are presented and show a good correlation with the time-domain analysis. The dependence of the coefficient of restitution on the mass ratio of the particle and the beam is discussed. Results show that the mass ratio divides the contact behavior of the particle and beam to a single-contact regime and multiple-contact regime and influences the coefficient of restitution (COR) value in different ways.

Global dynamics of a non-smooth system with elastic and rigid impacts and dry friction

Global dynamics of a non-smooth dynamic model is discussed under the combined effects of three non-smooth factors of elastic impact, rigid impact and dry friction,which is a rarely discussed topic before.Six different basic phases, nine events and six segments of the system have been described. The stability of periodic motions in the system is analyzed theoretically. The motions distribution and the transition to the sticking-adhesion motions are studied. Influences of the sliding bifurcation and grazing bifurcation in the way to the transition to sticking-adhesion motions are demonstrated. The transition to sticking-adhesion motions composed of one or more of three basic routes is illustrated. The transition law of three kinds of fundamental periodic motions in the low-frequency and small-gap parameter domain is further analyzed so as to delineate the transition mechanism from fundamental periodic motions to sticking-adhesion motions. In high frequency region, the global motions distribution in the system is obtained through the global analysis method in parameter-state space. The transition and coexistence of the motions including stable and unstable periodic motions are further explored. In addition, the motions distribution and transition of large friction force versus forcing amplitude from the static state are discussed. The results will be beneficial for the motions control of the system.

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues

The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems.

The effect of impact velocity on rebound height after impact interaction

Using the mechanorheological viscoelastic plastic model, the effect of impact velocity of a spherical body on rebound height after impact interaction was studied. With an increase in impact velocity, the energy losses of impact interaction increase. Under the elastic deformations, energy dissipation depends on the deformation rate and increases with increasing impact velocity. During plastic deformations, energy dissipation increases with increasing deformations. Plasticity of the material significantly reduces rebound height. The more ductile the material, the lower the rebound height due to large plastic deformations. In case of an elastic impact, a decrease in elasticity leads to a decrease in the rebound height, since the viscoelastic model becomes more viscous, and the viscous resistance to deformations increases compared to the elastic resistance. This increases energy losses and decreases the rebound height. For the elastic-plastic model, the relationship is reverse. A decrease in elasticity leads to an increase in the rebound height. This is due to the fact that an increase in elasticity of the material leads to an increase in its stiffness. Elastic deformation resistance increases. An increase in the force causes an increase in plastic deformations and an increase in energy losses. An increase in the viscous resistance to deformations leads to an increase in energy losses and a decrease in the rebound height. Thus, the rebound height depends on impact interaction velocity. To improve reliability of dynamic process simulation, it is necessary to take into account these factors when studying the operation of equipment in the conditions of impact interaction of structural elements.