Nonlinear Assumptions Research Articles

Families of exact similaritons with flexible modulations in N-coupled homogeneous and inhomogeneous systems

In this paper, a family of exact solutions to N-coupled nonlinear Schrödinger (N-CNLS) equations including bright and dark solitons, Akhmediev breathers, Kuznetsov-Ma breathers, and rogue waves are derived with the aid of a generic nonlinear wave assumption. As an application of the solutions, we present a scheme to realize amplitude coding in an identical waveguide system. Furthermore, by a general self-similar transformation method, exact controllable similaritons of N-coupled inhomogeneous NLS (N-CINLS) equations are constructed under relaxed compatibility conditions. Flexible modulations of similaritons are investigated in a typical inhomogeneous system. Based on the general self-similar transformation, we further study various and novel modulations of composite similariton of 2-CINLS regimes. The various similaritons presented here may be expected to find application in the control and transmission of nonlinear waves in realizable complex systems including those based on optical fibers and Bose-Einstein condensates.

Numerical investigation of knee prosthesis stresses in daily activities: Insight into knee rehabilitation and Creation of a new optimal model

Total knee arthroplasty (TKA) is a cornerstone in addressing knee joint disorders, significantly enhancing patients' quality of life. However, despite technological advancements, a comprehensive understanding of the dynamic stresses experienced by knee prostheses during daily activities, particularly under rehabilitation interventions, remains elusive. This study aims to bridge this gap by employing numerical simulations and finite element analysis to elucidate these dynamic stresses and their interaction with rehabilitation protocols.A real-life knee replacement prosthesis model was meticulously constructed through coordinate measuring and 3D scanning, facilitating detailed finite element analysis in ANSYS Workbench version 17.1. Two distinct boundary conditions and loading scenarios were applied, with comparisons made between linear and nonlinear material assumptions. The simulation results using these different boundary condition methods revealed minimal differences. Specifically, at a knee angle of 0°, the relative stress error rate between the two boundary condition types was approximately 1 % (1.11 MPa and 1.099 MPa, respectively). At 15° and 90°, the error rates were 1.9 % and 0.56 %, respectively (10.275 MPa and 10.078 MPa at 15°; 10.275 MPa and 10.078 MPa at 90°). Given these minimal differences, the first type of boundary condition was adopted for the subsequent scenarios to enhance convergence efficiency in the analysis.Moreover, comparative analyses between linear and nonlinear material behaviors demonstrated acceptable agreement, offering insights into potential efficiency gains in simulation methodologies. Building on this foundation, an optimized tibial model was proposed, incorporating geometric alterations to the tray. Quantitative assessments revealed significant reductions, with von Mises stress decreasing by 23.35 % and equivalent strain by 17 % at a knee angle of 140°. Further evaluations at varying angles, including 60°, consistently showed positive influences on stress and strain. These quantitative findings not only contribute valuable insights into the mechanical behavior of knee prostheses but also provide tangible evidence for the efficacy of linear material behavior assumptions. The proposed optimized model exhibits promising potential for enhancing the design and performance of knee prostheses, particularly under critical loading conditions.In conclusion, these results underscore the importance of a nuanced understanding of knee prosthesis behavior during rehabilitation, offering a quantitative foundation for refining existing designs and informing the development of next-generation prostheses.

Localization of Beltrami fields: Global smooth solutions and vortex reconnection for the Navier-Stokes equations

We introduce a class of divergence-free vector fields on R3 obtained after a suitable localization of Beltrami fields. First, we use them as initial data to construct unique global smooth solutions of the three dimensional Navier-Stokes equations. The relevant fact here is that these initial data can be chosen to be large in any critical space for the Navier–Stokes problem, however they satisfy the nonlinear smallness assumption introduced in [10]. As a further application of the method, we use these vector fields to provide analytical example of vortex-reconnection for the three-dimensional Navier-Stokes equations on R3. To do so, we exploit the ideas developed in [13] but differently from this latter we cannot rely on the non-trivial homotopy of the three-dimensional torus. To overcome this obstacle we use a different topological invariant, i.e. the number of hyperbolic zeros of the vorticity field.

Thermal vibration analysis of bi-directionally stepped porous functionally graded plates with segment-specific material property variation supported by Kerr foundation

This paper presents a comprehensive analysis of the nonlinear dynamic response of stepped rectangular plates made of functionally graded porous material (FGPM), supported by the Kerr foundation, in a thermal environment. A novel analytical framework is developed to explore geometric and material variations. The study investigates structural variations in plate thickness with abrupt changes in uni- or bi-directional orientations, examining both single and double stepped thickness profiles. Material properties vary with thickness, featuring distinct horizontal discontinuities across plate segments. Porosity distributions, both even and uneven, are addressed using modified mixture rules. Nonlinear kinematic relationships are established using Reddy’s third-order shear deformation plate theory and von Kármán’s nonlinear geometric assumptions, with equations of motion solved via Galerkin’s technique. This improved model effectively addresses non-continuous thickness variation through integral calculus, enhancing computational efficiency. Validation is achieved by comparing outcomes with published literature and Finite Element Analysis (FEA). The study investigates the influence of material properties, elastic foundation, boundary conditions, and geometric parameters on the free vibration and nonlinear behaviors of the plates. Some of the key findings include: increasing the thickness of the stepped segment significantly heightens the fundamental frequency while reducing vibrational amplitudes; optimizing the location of the stepped segment directly impacts the plate’s fundamental frequency and vibrational amplitudes; and as the load factor increases, the difference between linear and nonlinear deflection becomes evident. Therefore, accurate FGPM stepped plate design requires incorporating nonlinear terms in the strain–displacement relationships. Suggestions for future model modifications are also discussed, contributing to advancements in structural design and analysis.

Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks

In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient uncertainty quantification for goal-oriented inverse problems. Contrary to standard inverse problems, these approaches are goal-oriented in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e. VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent and target spaces. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach.

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Nonlinear forced vibration of functionally graded hybrid three-phase nanocomposite toroidal shell segments reinforced by carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs)

This study proposes a unique three-phase functionally graded (FG) hybrid nanocomposite material reinforcing the toroidal shell segments to investigate the nonlinear forced vibration using Reddy's higher-order shear deformation theory, von Karman geometrical nonlinearity and Stein-McElman's assumption along with the Hamilton principle. The examined toroidal shell's material consists of polymeric resin, carbon nanotubes (CNTs), and graphene platelets (GPLs) as nanocomposites. The material properties have been derived based on a modified Halpin-Tsai micromechanical model. Four distribution patterns have been studied: uniform (UD), FG-X, FG-O, and FG-V. The continuous distribution of GPLs and CNTs leads to inhomogeneous position-dependent properties throughout the shell thickness. The obtained differential equations of motion have been reduced to ordinary equations using Galerkin's technique. A multi-scales method (MSM) is used to estimate a closed-form solution representing the frequency-amplitude relation, and the state space representation is used along with numerical fourth-order Runge Kutta method (RK4) to obtain the nonlinear dynamic response of the toroidal shell. The accuracy of the current results obtained has been verified by comparing them with the relevant literature and numerical results using (RK4). In addition, the influence of both GPLs and CNTs weight fractions, nanofillers’ distribution types, longitudinal and circumferential wave numbers, elastic foundation parameters, static axial compression load, transverse excitation load, damping ratio, geometrical characteristics of the toroidal shell on the dimensionless natural frequency, nonlinear primary resonance (frequency-amplitude curve), and nonlinear dynamic response are carefully studied. The results found that combining (GPLs & CNTs) into the shell's matrix improves performance, especially in concave shells compared to convex ones. The FG-X pattern reduces peak resonance amplitude and improves natural frequency. A reduction of 12.3 % is observed for convex shells, and 21.5 % for concave shells compared to FG-O.

Primary resonance analysis of hyperelastic doubly curved shallow shells subjected to external loading

In this paper, primary resonance analysis of stiffened shallow shells with doubly curved ones is evaluated employing an analytical method. The shell material is hyperelastic, and the system is under external loading. The shell's mathematical model is developed using the first-order shear deformation theory (FSDT), considering von-Kármán's non-linear shell assumptions, multiple scales, and the Galerkin method. The Neo-Hookean hyperelastic type has been selected to explain the non-linear elasticity of the material. The stiffened shell geometric can be changed to different forms such as hyperbolic, cylindrical, and spherical shells by curvature components set. Several material parameters, number of stiffeners, geometrical ratio, etc., that affect shell oscillations results are examined and investigated in detail. According to the numerical results, it is characterized by increasing and decreasing the stiffener's number, damping coefficients (µ), and force amplitude (K), leading to significant changes in fundamental frequencies of the stiffened doubly curved shallow shell. Also, increasing of parameter σ, causes to increase the peak of response amplitude.

Estimating the health effects of COVID-19-related immunisation disruptions in 112 countries during 2020–30: a modelling study

There have been declines in global immunisation coverage due to the COVID-19 pandemic. Recovery has begun but is geographically variable. This disruption has led to under-immunised cohorts and interrupted progress in reducing vaccine-preventable disease burden. There have, so far, been few studies of the effects of coverage disruption on vaccine effects. We aimed to quantify the effects of vaccine-coverage disruption on routine and campaign immunisation services, identify cohorts and regions that could particularly benefit from catch-up activities, and establish if losses in effect could be recovered. For this modelling study, we used modelling groups from the Vaccine Impact Modelling Consortium from 112 low-income and middle-income countries to estimate vaccine effect for 14 pathogens. One set of modelling estimates used vaccine-coverage data from 1937 to 2021 for a subset of vaccine-preventable, outbreak-prone or priority diseases (ie, measles, rubella, hepatitis B, human papillomavirus [HPV], meningitis A, and yellow fever) to examine mitigation measures, hereafter referred to as recovery runs. The second set of estimates were conducted with vaccine-coverage data from 1937 to 2020, used to calculate effect ratios (ie, the burden averted per dose) for all 14 included vaccines and diseases, hereafter referred to as full runs. Both runs were modelled from Jan 1, 2000, to Dec 31, 2100. Countries were included if they were in the Gavi, the Vaccine Alliance portfolio; had notable burden; or had notable strategic vaccination activities. These countries represented the majority of global vaccine-preventable disease burden. Vaccine coverage was informed by historical estimates from WHO-UNICEF Estimates of National Immunization Coverage and the immunisation repository of WHO for data up to and including 2021. From 2022 onwards, we estimated coverage on the basis of guidance about campaign frequency, non-linear assumptions about the recovery of routine immunisation to pre-disruption magnitude, and 2030 endpoints informed by the WHO Immunization Agenda 2030 aims and expert consultation. We examined three main scenarios: no disruption, baseline recovery, and baseline recovery and catch-up. We estimated that disruption to measles, rubella, HPV, hepatitis B, meningitis A, and yellow fever vaccination could lead to 49 119 additional deaths (95% credible interval [CrI] 17 248-134 941) during calendar years 2020-30, largely due to measles. For years of vaccination 2020-30 for all 14 pathogens, disruption could lead to a 2·66% (95% CrI 2·52-2·81) reduction in long-term effect from 37 378 194 deaths averted (34 450 249-40 241 202) to 36 410 559 deaths averted (33 515 397-39 241 799). We estimated that catch-up activities could avert 78·9% (40·4-151·4) of excess deaths between calendar years 2023 and 2030 (ie, 18 900 [7037-60 223] of 25 356 [9859-75 073]). Our results highlight the importance of the timing of catch-up activities, considering estimated burden to improve vaccine coverage in affected cohorts. We estimated that mitigation measures for measles and yellow fever were particularly effective at reducing excess burden in the short term. Additionally, the high long-term effect of HPV vaccine as an important cervical-cancer prevention tool warrants continued immunisation efforts after disruption. The Vaccine Impact Modelling Consortium, funded by Gavi, the Vaccine Alliance and the Bill & Melinda Gates Foundation. For the Arabic, Chinese, French, Portguese and Spanish translations of the abstract see Supplementary Materials section.

1/2 and 1/3 Subharmonic Resonance Behaviors of a Rotating FG-CNTRC Beam with Geometric Imperfections

This paper aims at investigating 1/2 and 1/3 subharmonic resonances of a rotating functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam in the presence of geometric imperfections. A general function is introduced to denote three types of imperfections containing sine, global, and local modes. At first, based on the von-Kármán geometric nonlinearity assumption, the forced vibration equation is set up. Then, the Galerkin method and multiple scale method are utilized to study subharmonic resonance behaviors. Finally, coupled effects of FG-CNTRCs, rotating motion, and geometric imperfections on subharmonic resonance responses are investigated. It is found that a specific range of the excitation amplitude and frequency motivates the subharmonic resonance behavior. The coupling of geometric imperfections and geometric nonlinearities generates the 1/2 resonance phenomena, and geometric nonlinearities result in the 1/3 resonance behavior. Both the imperfection mode and amplitude can affect the resonance response and resonance regions. Moreover, in contrast with the 1/3 subharmonic resonance, geometric imperfections produce greater influence on the 1/2 subharmonic resonance.

Causal association of blood lipids with all-cause and cause-specific mortality risk: a Mendelian randomization study

Dyslipidemia has long been implicated in elevating mortality risk; yet, the precise associations between lipid traits and mortality remained undisclosed. Our study aimed to explore the causal effects of lipid traits on both all-cause and cause-specific mortality. One-sample Mendelian randomization (MR) with linear and nonlinear assumptions was conducted in a cohort of 407,951 European participants from the UK Biobank. Six lipid traits, consisting of low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), triglycerides, apolipoprotein A1 (ApoA1), apolipoprotein B (ApoB), and lipoprotein(a), were included to investigate the causal associations with mortality. Two-sample MR was performed to replicate the association between each lipid trait and all-cause mortality. Univariable MR results showed that genetically predicted higher ApoA1 was significantly associated with a decreased all-cause mortality risk (HR[95% CI]:0.93 [0.89–0.97], P value = 0.001), which was validated by the two-sample MR analysis. Higher lipoprotein(a) was associated with an increased risk of all-cause mortality (1.03 [1.01–1.04], P value = 0.002). Multivariable MR confirmed the direct causal effects of ApoA1 and lipoprotein(a) on all-cause mortality. Meanwhile, nonlinear MR found no evidence for nonlinearity between lipids and all-cause mortality. Our examination into cause-specific mortality revealed a suggestive inverse association between ApoA1 and cancer mortality, a significant positive association between lipoprotein(a) and cardiovascular disease mortality, and a suggestive positive association between lipoprotein(a) and digestive disease mortality. High LDL-C was associated with an increased risk of cardiovascular disease mortality but a decreased risk of neurodegenerative disease mortality. The findings suggest that implementing interventions to raise ApoA1 and decrease lipoprotein(a) levels may improve overall health outcomes and mitigate cancer and digestive disease mortality.

New fixed point results for nonlinear Feng-Liu contractions with applications

In this paper we will extend the concept of multi-valued Feng-Liu contraction, by imposing a nonlinear assumption on the operator. Then, fixed point, strict fixed point and stability theorems for the fixed point inclusion with multi-valued nonlinear Feng-Liu contractions are given. An application illustrates the main theoretical results.

Non-linear behaviour of soil–pile interaction phenomena and its effect on the seismic response of OWT pile foundations. Validity range of a linear approach through non-degraded soil properties

The effect of non-linear and inelastic behaviour of the soil–pile interaction on the seismic response of offshore wind turbine pile foundations embedded in sandy soils is analysed. For this purpose, the responses obtained assuming three different Beam on Dynamic Winkler Foundation (BDWF) models are compared: a Plastic Non-Linear Model (PNLM), an Elastic Non-Linear Model (ENLM) and a simple elastic linear model with non-degraded properties of soil (NDLM). The influence of non-linearity and plasticity assumption is studied by evaluating the effects of the kinematic and inertial interaction within soil–pile interaction. Two soil stiffness levels are analysed: very loose and medium dense sand. The seismic response under ten earthquakes is computed in terms of mean envelopes of internal forces along the pile length. The non-linearity and inelastic influence of soil–pile interaction is quantified by means of relative differences with respect to the linear elastic model. Results show that the non-linear and inelastic models acquire relevance when the contribution of the inertial interaction dominates, leading to lower maximum responses than the linear elastic model. If the inertial interaction is not significantly activated, similar results between the three models are obtained, being the linear elastic model enough to reproduce the soil–pile dynamic interaction.

How does trade policy uncertainty affect green innovation in the USA and China? A nonlinear perspective.

Green innovations are the most critical factor in promoting environmental sustainability worldwide. Trade can speed up the adoption of green innovations by facilitating the transfer of information, skills, and technology. However, trade policy uncertainty can create significant challenges for businesses investing in eco-innovations, leading to increased risk, reduced investment, and slower progress toward sustainable technologies. Recently, a growing number of researchers have shown their interest in finding the factors that can impact green innovations, but none have investigated the influence of trade policy uncertainty on green innovations in the USA and China. In addition, none of the past studies has relied on the nonlinear assumption. This analysis fills these gaps by examining the nonlinear impacts of trade policy uncertainty on eco-innovations in China and the USA over 2000Q1-2021Q4 by employing a nonlinear ARDL model. The finding reveals that a positive shock in trade policy uncertainty results in a decrease in green innovation in the USA and China, while a negative shock in trade policy uncertainty leads to an increase in green innovation in the USA over the long run. The nonlinear models also indicate that a positive shock in trade policy uncertainty harms green innovation in both the USA and China in the short run. The robustness of these results is confirmed by the NQARDL model, which confirms that an upsurge in trade policy uncertainty lowers green innovation in most quantiles in the USA and China in the short and long run. Conversely, negative shocks in trade policy uncertainty stimulate green innovation at most quantiles in both China and the USA, in the short and long run. Thus, policymakers need to consider the potential impact of trade policies on eco-innovations and work to create stable and predictable trade environments that support the growth of renewable technologies and other sustainable solutions.

Savings and growth nexus in the context of Southern African Customs Union countries

Orientation: The primary goal of Southern African Customs Union (SACU) is to promote economic development through regional coordination. Consequently, SACU members have set economic growth targets through various medium- and long-term policies.Research purpose: The article investigates the savings-growth nexus among SACU countries.Motivation for the study: This study is motivated by low economic growth among SACU countries and the gap in the saving-growth literature. Specifically, previous studies assumed linear relationship, thereby ignoring the fact that savings may be related to economic growth in a nonlinear fashion.Research approach/design and method: The study utilised several panel estimation techniques with data over 1990–2021 for the SACU countries.Main findings: Firstly, there is a strong evidence of long run relationship between saving and economic growth in SACU countries. Secondly, domestic saving exhibits a positive and statistically significant effect on economic growth both in the short-and long-term. Thirdly, there is evidence of non-linear relationship between domestic saving and economic growth. Lastly, it is shown that 16% threshold level of domestic savings to gross domestic product (GDP) ratio is consistent with 6% GDP growth target aspired by SACU union.Practical/managerial implications: The findings of this article suggest that domestic saving is a prerequisite for economic growth provided the funds are channelled to productive investments. Consequently, there is a need to design appropriate policies that can help to promote and mobilise savings.Contribution/value-add: This article contributes to the ongoing debate on saving-growth in the context of developing countries. In addition, it addressed the linearity assumption of the previous studies by incorporating nonlinear assumption.

Numerical study of linear and nonlinear stability in double-diffusive Hadley-Prats flow through a horizontal porous layer with Soret and internal heat source effects

Numerical analysis is constructed to study the onset of the double-diffusion convection mechanism through an infinite parallel permeable channel with heat generation, mass flow and Soret impacts. Homogenous isotropic Darcy’s flow model is deployed to elucidate the porous features. The roll instabilities pertaining to longitudinal and transverse cases are examined through a linear and nonlinear stability analysis. The unit-less eigenvalue problem is constructed through linear and nonlinear stability assumptions and which is solved numerically using a fourth order Runge-Kutta scheme. The critical values of wave and thermal Rayleigh parameters are evaluated. Extended graphical and tabular visualization is presented to describe the onset of the convection mechanism. The results of this semi-numerical investigation may be useful in environmental, geothermal and chemical engineering processes. In addition, the critical R z value is also determined for a range of thermo-physical numbers. Significant modifications in the flow patterns are computed with mass flow parameter and vertical thermal and solutal Rayleigh number. With an increment in Soret (thermo-diffusive) parameter Sr the regime become more unstable. Based on the nonlinear stability analysis, an elevation in solutal Rayleigh number also induces earlier instability. The collective influence of the Lewis number and horizontal concentration parameter is observed to render the system more stable.

Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates

This paper presents an investigation into the free vibration and nonlinear dynamic analyses of new complex edge contour plate structures, known as single-variable-edge (SVE) plates. Cracks emerge at the center of the plate’s surface, and the effects of edge crack orientation and depth on the dynamical characteristics of the laminated nanocomposite SVE plates have been considered in this study. The functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) material was utilized for the edge-cracked plate that rests on a Winker-Pasternak elastic foundation. The Halpin-Tsai micromechanical model is used to predict the material characteristics, which are presumptively temperature-dependent. The rule of mixtures is employed to determine Poisson's ratio, density mass, and thermal expansion. The governing equations are established based on the theory of elasticity, and Von Karman-Donnell geometric nonlinearity assumption. To confirm the reliability and accuracy of this approach, the acquired findings are validated with those produced using Finite Element Analysis (FEA). Furthermore, the geometrical and material parameters, fracture properties, and environmental (temperature and elastic foundation) factors are also investigated in the study. The research findings hold significant implications for applications in aerospace and aeronautical, civil, and mechanical engineering.

The efficient data-driven solution to estimate the nonlinear bending of sandwich doubly curved panel subjected to transient loading

This paper investigates nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading which is extensively used in aerospace structures. Due to the lack of a dataset for the nonlinear transient bending of the sandwich doubly curved panel for the data-driven solution, mathematical modeling is used. The sandwich doubly curved panel is made of two graphene nanoplatelets (GPLs) reinforced face sheets, and a polymer core. In the mathematical modeling section, the effective Young's modulus is obtained via modified Halpin-Tsai methodology, and the role of the mixture is used to estimate other material properties of the composite face sheets. The presented structure is analyzed using Reddy's third-order shear deformation theory (RTSDT), which incorporates von Kármán nonlinear geometric assumptions and Hamilton's principle. The governing equations and associated boundary conditions are derived accurately by imposing shear stress-free conditions on the upper and lower surfaces of the panel. The meshfree radial point interpolation method (RPIM) with interpolation functions is utilized to determine the unknown degrees of freedom to numerically simulate the mid-plane of the sandwich doubly-curved panel. The Newton-Raphson approach is used to solve the nonlinear ordinary differential using the constant-average acceleration strategy from Newmark's time integration method. After obtaining the dataset, the data is collected, and using an efficient data-driven approach, the results are tested, validated, and trained. In future studies, the presented efficient data-driven approach can be used with low computational cost to simulate nonlinear transient bending characteristics of sandwich doubly curved panels under transient loading for related aerospace industries.

Nonlinear torsional vibration and dynamic post-buckling responses of spiral stiffened functionally graded porous cylindrical shells

This study employs a semi-analytical approach to investigate the nonlinear torsional vibration and dynamic torsional post-buckling (DTPB) responses of spiral stiffened functionally graded (FG) porous (SSFGP) cylindrical shells. These shells are resting on a generalized nonlinear viscoelastic foundation (GNVEF). This foundation consists of a dual-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model. The model includes nonlinear cubic stiffness and takes damping effects into consideration. Within the scope of this research, two variations of SSFGP cylindrical shells are examined: those characterized by non-uniform and uniform porosity distributions. Employing the Donnell shell theory, von-Kármán nonlinear geometric assumptions, and Galerkin’s method, a discretized nonlinear governing equation is derived to analyze the behaviors of the shells. Consequently, explicit formulations for dynamic torsional load are meticulously obtained. The findings of the present study are validated by comparing them with the outcomes documented in existing literature, as well as through alignment with the P-T method. This research delves into the system’s nonlinear behaviors, with scrutinization of the effects of diverse factors such as material and geometrical parameters. The researchers and engineers in this field may use the findings of this research as benchmarks for their design and research of SSFGP cylindrical shells.

Decentralized model reference adaptive control for interconnected systems with time‐varying delays and unknown dead‐zone inputs

AbstractIn this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time‐varying delay interconnect systems that comprise unknown system matrices and unknown dead‐zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time‐varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type‐B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed‐loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method.