A survey of Hopf bifurcation analysis in nonlinear railway wheelset dynamics

This article attempts to analyze the Hopf bifurcation behavior of a railway wheelset in the presence of dead-zone and yaw damper nonlinearities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov-Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideration. To solve these nonlinear equations analytically, the integration interval has been divided into three sub-domains. Two-dimensional bifurcation diagrams are provided to illustrate the mechanism of formation of Hopf bifurcation. These diagrams can be used for design of stable wheelset systems

Analytical approximation of nonlinear frequency of cantilever beam vibrations

This research presents the application of modern analytical approaches for the nonlinear vibrations of cantilever beams. These methods are Homotopy Analysis Method, Parameter Expansion Method and Bubnov-Galerkin Weighted Residual Method. Powerful analytical methods are used to obtain frequency-amplitude relationship of dynamic behavior of the mentioned system. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a comparison with numerical methods is provided in order to confirm the soundness of the obtained results

Dynamic analysis of preload nonlinearity in nonlinear beam vibration

The objective of this paper is to propose a novel exact equivalent function (EF) for preload nonlinearity. The nonlinear preloaded spring force, which is exerted on the cantilever beam has been rewritten with a definite force-displacement relationship using new EF. This approach permits us to overcome severe computational issues that are encountered in the analytical investigations of nonlinear problems. Highly nonlinear equation of beam vibration under the influence of preloaded spring at its end with cubic nonlinearity is considered and the related analytical solution is obtained through Parameter-expansion Method (PEM). Finally, the soundness of the introduced EF would be verified by comparison of the results with the obtained solutions using numerical method

Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model

This article proposes a photothermal model to reveal the thermo-magneto-mechanical properties of semiconductor materials, including coupled diffusion equations for thermal conductivity, elasticity, and excess carrier density. The proposed model is developed to account for the optical heating that occurs through the semiconductor medium. The Moore–Gibson–Thompson (MGT) equation of the fourth-order serves as the theoretical framework to establish the photothermal model. It is well-known that the optical and heat transfer properties of such materials behave as random functions of photoexcited-carrier density; therefore, the current model is remarkably more reliable compared to the earlier closed-form theories which are limited to a single form. The constructed theoretical framework is able to investigate the magneto-photo-thermoelastic problems in a semiconductor medium due to laser pulse excitation as a case study. Some parametric studies are used to exhibit the impact of thermal parameters, electromagnetic fields, laser pulses and thermoelectric coupling factors on the thermomagnetic behavior of physical variables. Finally, several numerical examples have been presented to draw the distributions of the examined field variables

On a 3D material modelling of smart nanocomposite structures

Smart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity and flexomagneticity. The recently discovered flexomagneticity in smart composites has been investigated under limited conditions. A review of the existing literature indicates a lack of evaluation in three-dimensional (3D) elasticity analysis of SCs when the flexomagnetic effect (FM) exists. To address this issue, the governing equations will incorporate the term ∂/∂z, where z represents the thickness coordinate. The variational technique will guide us in further developing these governing equations. By using hypotheses and theories such as a 3D beam model, von Kármán's strain nonlinearity, Hamilton's principle, and well-established direct and converse FM models, we will derive the constitutive equations for a thick composite beam. Conducting a 3D analysis implies that the strain and strain gradient tensors must be expressed in 3D forms. The inclusion of the term ∂/∂z necessitates the construction of a different model. It should be noted that current commercial finite element codes are not equipped to accurately and adequately handle micro- and nano-sized solids, thus making it impractical to model a flexomagnetic composite structure using these programs. Therefore, we will transform the derived characteristic linear three-dimensional bending equations into a 3D semi-analytical Polynomial domain to obtain numerical results. This study demonstrates the importance of conducting 3D mechanical analyses to explore the coupling effects of multiple physical phenomena in smart structures

Strain-Rate Dependency of a Unidirectional Filament Wound Composite under Compression

This article presents the results of experimental studies concerning the dynamic deformation and failure of a unidirectional carbon fiber reinforced plastic (T700/LY113) under compression. The test samples were manufactured through the filament winding of flat plates. To establish the strain rate dependencies of the strength and elastic modulus of the material, dynamic tests were carried out using a drop tower, the Split Hopkinson Pressure Bar method, and standard static tests. The samples were loaded both along and perpendicular to the direction of the reinforcing fiber. The applicability of the obtained samples for static and dynamic tests was confirmed through finite element modeling and the high-speed imaging of the deformation and failure of samples during testing. As a result of the conducted experimental studies, static and dynamic stress-strain curves, time dependencies of deformation and the stress and strain rates of the samples during compression were obtained. Based on these results, the strain rate dependencies of the strength and elasticity modulus in the strain rate range of 0.001–600 1/s are constructed. It is shown that the strain rate significantly affects the strength and deformation characteristics of the unidirectional carbon fiber composites under compression. An increase in the strain rate by 5 orders of magnitude increased the strength and elastic modulus along the fiber direction by 42% and 50%, respectively. Perpendicular loading resulted in a strength and elastic modulus increase by 58% and 50%, respectively. The average strength along the fibers at the largest studied strain rate was about 1000 MPa. The obtained results can be used to design structural elements made of polymer composite materials operating under dynamic shock loads, as well as to build models of mechanical behavior and failure criteria of such materials, taking into account the strain rate effects

Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)-Substrate Medium Systems

This paper proposes a novel nanobar-substrate medium model for static and free vibration analyses of single-walled carbon nanotube (SWCNT) systems embedded in the elastic substrate medium. The modified strain-gradient elasticity theory is utilized to account for the material small-scale effect while the Gurtin-Murdoch surface theory is employed to represent the sur-face-energy effect. The Winkler-foundation model is assigned to consider interactive mechanism between the nanobar and its surrounding substrate medium. Hamilton’s principle is called for to consistently derive the system governing equation, initial conditions, and classical as well as non-classical boundary conditions. Two numerical simulations are employed to demonstrate the essence of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on static and free vibration responses of single-walled carbon nanotube (SWCNT)-substrate medium systems. The simulation results show that the material small-scale effect, the surface-energy effect, and the interaction between the substrate and the structure lead to a system-stiffness enhancement both in static and free vibration analyses

Global incidence, prevalence, years lived with disability (YLDs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Detailed, comprehensive, and timely reporting on population health by underlying causes of disability and premature death is crucial to understanding and responding to complex patterns of disease and injury burden over time and across age groups, sexes, and locations. The availability of disease burden estimates can promote evidence-based interventions that enable public health researchers, policy makers, and other professionals to implement strategies that can mitigate diseases. It can also facilitate more rigorous monitoring of progress towards national and international health targets, such as the Sustainable Development Goals. For three decades, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) has filled that need. A global network of collaborators contributed to the production of GBD 2021 by providing, reviewing, and analysing all available data. GBD estimates are updated routinely with additional data and refined analytical methods. GBD 2021 presents, for the first time, estimates of health loss due to the COVID-19 pandemic. Methods: The GBD 2021 disease and injury burden analysis estimated years lived with disability (YLDs), years of life lost (YLLs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries using 100 983 data sources. Data were extracted from vital registration systems, verbal autopsies, censuses, household surveys, disease-specific registries, health service contact data, and other sources. YLDs were calculated by multiplying cause-age-sex-location-year-specific prevalence of sequelae by their respective disability weights, for each disease and injury. YLLs were calculated by multiplying cause-age-sex-location-year-specific deaths by the standard life expectancy at the age that death occurred. DALYs were calculated by summing YLDs and YLLs. HALE estimates were produced using YLDs per capita and age-specific mortality rates by location, age, sex, year, and cause. 95% uncertainty intervals (UIs) were generated for all final estimates as the 2·5th and 97·5th percentiles values of 500 draws. Uncertainty was propagated at each step of the estimation process. Counts and age-standardised rates were calculated globally, for seven super-regions, 21 regions, 204 countries and territories (including 21 countries with subnational locations), and 811 subnational locations, from 1990 to 2021. Here we report data for 2010 to 2021 to highlight trends in disease burden over the past decade and through the first 2 years of the COVID-19 pandemic. Findings: Global DALYs increased from 2·63 billion (95% UI 2·44–2·85) in 2010 to 2·88 billion (2·64–3·15) in 2021 for all causes combined. Much of this increase in the number of DALYs was due to population growth and ageing, as indicated by a decrease in global age-standardised all-cause DALY rates of 14·2% (95% UI 10·7–17·3) between 2010 and 2019. Notably, however, this decrease in rates reversed during the first 2 years of the COVID-19 pandemic, with increases in global age-standardised all-cause DALY rates since 2019 of 4·1% (1·8–6·3) in 2020 and 7·2% (4·7–10·0) in 2021. In 2021, COVID-19 was the leading cause of DALYs globally (212·0 million [198·0–234·5] DALYs), followed by ischaemic heart disease (188·3 million [176·7–198·3]), neonatal disorders (186·3 million [162·3–214·9]), and stroke (160·4 million [148·0–171·7]). However, notable health gains were seen among other leading communicable, maternal, neonatal, and nutritional (CMNN) diseases. Globally between 2010 and 2021, the age-standardised DALY rates for HIV/AIDS decreased by 47·8% (43·3–51·7) and for diarrhoeal diseases decreased by 47·0% (39·9–52·9). Non-communicable diseases contributed 1·73 billion (95% UI 1·54–1·94) DALYs in 2021, with a decrease in age-standardised DALY rates since 2010 of 6·4% (95% UI 3·5–9·5). Between 2010 and 2021, among the 25 leading Level 3 causes, age-standardised DALY rates increased most substantially for anxiety disorders (16·7% [14·0–19·8]), depressive disorders (16·4% [11·9–21·3]), and diabetes (14·0% [10·0–17·4]). Age-standardised DALY rates due to injuries decreased globally by 24·0% (20·7–27·2) between 2010 and 2021, although improvements were not uniform across locations, ages, and sexes. Globally, HALE at birth improved slightly, from 61·3 years (58·6–63·6) in 2010 to 62·2 years (59·4–64·7) in 2021. However, despite this overall increase, HALE decreased by 2·2% (1·6–2·9) between 2019 and 2021. Interpretation: Putting the COVID-19 pandemic in the context of a mutually exclusive and collectively exhaustive list of causes of health loss is crucial to understanding its impact and ensuring that health funding and policy address needs at both local and global levels through cost-effective and evidence-based interventions. A global epidemiological transition remains underway. Our findings suggest that prioritising non-communicable disease prevention and treatment policies, as well as strengthening health systems, continues to be crucially important. The progress on reducing the burden of CMNN diseases must not stall; although global trends are improving, the burden of CMNN diseases remains unacceptably high. Evidence-based interventions will help save the lives of young children and mothers and improve the overall health and economic conditions of societies across the world. Governments and multilateral organisations should prioritise pandemic preparedness planning alongside efforts to reduce the burden of diseases and injuries that will strain resources in the coming decades. Funding: Bill & Melinda Gates Foundation

Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term

This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the proposed asymptotic approach. It is demonstrated that two terms in series expansions are sufficient to obtain a highly accurate periodic solutions. The integrity of the analytical solutions is verified by numerical results. It is clearly demonstrated that this asymptotic approach is very effective and straightforward to study the nonlinear oscillator systems include odd and even nonlinear terms