Nonlinear Behavior Research Articles

A subbands study on the resistivity of field-effect CNT-based piezoresistive nanocomposites.

In this paper, an analytical model based on the percolation theory has been developed to predict the subbands effect on the effective electrical resistivity of carbon nanotubes (CNT)-based polymer nanocomposites. The CNTs are considered as randomly distributed or aligned channel material in the polymer transmitting electrons through tunneling. The tunneling effect takes into account the electron transmission between each connected pair of CNTs to evaluate electrical resistivity. The modeling approach contains two steps of primary prediction of resistivity and further calculation of CNTs' displacements and subsequent change of the resistance. A good agreement is found between the analytical model predictions and experimental data when the tunneling behavior was considered in the percolation transition region. The effect of CNT diameter, orientation state, and subbands on the resistivity has been investigated. The results depict that subbands increment is a collateral benefit to the aspect ratio in decreasing the resistivity. The analytical results demonstrate that a random CNT dispersion leads to a decreased piezoresistivity, while an increased strain range depicts a more non-linear behavior.

Feasibility Study of Scanning Spectral Imaging Based on a Birefringence Flat Plate

Hyper-spectral imaging (HSI) systems can be divided into two main types as follows: a group of systems that includes a dedicated dispersion/filtering component whose role is to physically separate the different wavelengths and a group of systems that sample all wavelengths in parallel, so that the separation into wavelengths is performed by signal processing (interferometric method). There is a significant advantage to systems of the second type in terms of the integration time required to obtain a signal with a high signal-to-noise ratio since the signal-to-noise ratio of methods based on scanning interferometry (Windowing method) is better compared to methods based on dispersion. The current research deals with the feasibility study of a new concept for an HSI system that is based on scanning interferometry using the “push-broom” method. In this study, we investigated the viability of incorporating a simple birefringent plate into a scanning optical system. By exploiting the motion of the platform on which the system is mounted, we extracted the spectral information of the scanned region. This approach combines the benefits of scanning interferometry with the simplicity of the setup. According to the theory, a chirped cosine-shaped interferogram is obtained for each wavelength due to the nonlinear behavior of the optical path difference of light in the birefringent plate as a function of the angle. An algorithm converts the signal from a superposition of chirped cosine signals to a scaled interferogram such that Fourier transforming (FT) the interferogram retrieves the spectral information. This innovative idea can turn a simple monochrome camera into a hyperspectral camera by adding a relief lens and a birefringent plate.

Development and Characterization of Heparin-Containing Hydrogel/3D-Printed Scaffold Composites for Craniofacial Reconstruction.

Regeneration of cartilage and bone tissues remains challenging in tissue engineering due to their complex structures, and the need for both mechanical support and delivery of biological repair stimuli. Therefore, the goal of this study was to develop a composite scaffold platform for anatomic chondral and osteochondral repair using heparin-based hydrogels to deliver small molecules within 3D-printed porous scaffolds that provide structure, stiffness, and controlled biologic delivery. We designed a mold-injection system to combine hydrolytically degradable hydrogels and 3D-printed scaffolds that could be employed rapidly (<30min) in operating room settings (~23°C). Micro-CT analysis demonstrated the effectiveness of our injection system through homogeneously distributed hydrogel within the pores of the scaffolds. Hydrogels and composite scaffolds exhibited efficient loading (~94%) of a small positively charged heparin-binding molecule (crystal violet) with sustained release over 14days and showed high viability of encapsulated porcine chondrocytes over 7days. Compression testing demonstrated nonlinear viscoelastic behavior where tangent stiffness decreased with scaffold porosity (porous scaffold tangent stiffness: 70%: 4.9MPa, 80%: 1.5MPa, and 90%: 0.20MPa) but relaxation was not affected. Lower-porosity scaffolds (70%) showed stiffness similar to lower ranges of trabecular bone (4-8MPa) while higher-porosity scaffolds (80% and 90%) showed stiffness similar to auricular cartilage (0.16-2MPa). Ultimately, this rapid composite scaffold fabrication method may be employed in the operating room and utilized to control biologic delivery within load-bearing scaffolds.

Efficient Deformation Learning of Varied Garments with a Structure-Preserving Multilevel Framework

Due to the highly nonlinear behavior of clothing, modelling fine-scale garment deformation on arbitrary meshes under varied conditions within a unified network poses a significant challenge. Existing methods often compromise on either model generalization, deformation quality, or runtime speed, making them less suitable for real-world applications. To address it, we propose to incorporate multi-source graph construction and pooling to achieve a novel graph learning scheme. We first introduce methods for extracting cues from different deformation correlations and transform the garment mesh into a comprehensive graph enriched with deformation-related information. To enhance the learning capability and generalizability of the model, we present structure-preserving pooling and unpooling strategies for the mesh deformation task, thereby improving information propagation across the mesh and enhancing the realism of deformation. Lastly, we conduct an attribution analysis and visualize the contribution of various vertices in the graph to the output, providing insights into the deformation behavior. The experimental results demonstrate superior performance against state-of-the-art methods.

First principles investigation of Li[formula omitted]Si and Li[formula omitted]Sn alloys: Unraveling atomic-scale influences on material properties

Commercial batteries have currently reached their peak specific capacity, which proves insufficient for the ongoing global energy transition. Consequently, there has been a surge of interest in developing new materials over the last decade, especially those based on silicon (Si) and tin (Sn), known for their high capacity. Despite numerous publications highlighting the advantages of these materials, crucial questions remain regarding volume expansion that must be addressed to propose effective solutions and facilitate their widespread commercial application. In this study, density functional theory was employed to investigate the formation of LixM (M = Si, Sn). Our analysis delves into crystal (c-LixM), amorphous (a-LixM), and amorphous slab (s-LixM) configurations during structural optimization calculations, with the aim of comparing and contrasting relevant findings. The exploration encompasses energetic aspects, volume expansion, and electronic properties. The obtained data enables the simulation of lithiation potential curves for each structural type, directly comparable with experimental results of these materials functioning as anodes in lithium-ion batteries. Notably, the volume expansion of a-LixM exhibits non-linear behavior, correlating with characteristic plateaus in the voltage profile curves.

Development and Calibration of a Phenomenological Material Model for Steel-Fiber-Reinforced High-Performance Concrete Based on Unit Cell Calculations

A phenomenological material model has been developed to facilitate the efficient numerical analysis of fiber-reinforced high-performance concrete (HPC). The formulation integrates an elasto-plastic phase-field model for simulating fractures within the HPC matrix, along with a superimposed one-dimensional elasto-plasticity model that represents the behavior of the embedded fibers. The Drucker–Prager plasticity and one-dimensional von-Mises plasticity formulations are incorporated to describe the nonlinear material behavior of both the HPC matrix and the fibers, respectively. Specific steps are undertaken during the development and calibration of the phenomenological material model. In the initial step, an experimental and numerical analysis of the pullout test of steel fibers embedded in an HPC matrix is conducted. This process is used to calibrate the micro-mechanical model based on the elasto-plastic phase-field formulation for fracture. In the subsequent step, virtual experiments based on an ellipsoidal unit cell, also with the resolution of fibers (used as a representative volume element, RVE), are simulated to analyze the impact of fiber–matrix interactions and their physical properties on the effective material behavior of fiber-reinforced HPC. In the final step, macroscopic boundary value problems (BVPs) based on a cuboid are simulated on a single scale using the developed phenomenological material model. The resulting macroscopic stress–strain characteristics obtained from both types of simulations, namely simulations of virtual experiments and macroscopic BVPs, are compared. This comparison is utilized for the calibration of material parameters to obtain a regularized solution and to assess the effectiveness of the presented phenomenological material model.

On the aeroelastic bifurcation of a flexible panel subjected to cavity pressure and inviscid oblique shock

The aeroelasticity of a panel in the presence of a shock is a fundamental issue of great significance in the development of hypersonic vehicles. In practical engineering, cavity pressure emerges as a crucial factor that influences the nonlinear dynamical characteristics of the panel. This study focuses on the aeroelastic bifurcation of a flexible panel subjected to both cavity pressure and oblique shock. To this end, a computational method is devised, coupling a high-fidelity reduced-order model for unsteady aerodynamic loads with nonlinear structural equations. The solution is meticulously tracked by continuous calculations. The obtained results indicate that cavity pressure plays a pivotal role in determining the bifurcation and stability characteristics of the system. First, the system exhibits hysteresis behaviour in response to the ascending and descending dynamic pressures. The evolution of hysteresis behaviour originates from the phenomenon of cusp catastrophe. Second, variations in cavity pressure induce three types of bifurcation phenomena, exhibiting characteristics akin to supercritical Hopf bifurcation, subcritical Hopf bifurcation and saddle-node bifurcation of cycles. The system's response at the critical points of these bifurcations manifests as long-period asymptotic flutter or explosive flutter. Lastly, the evolution of the dynamical system among these three types of bifurcations is an important factor contributing to the discrepancies observed in certain research results. This study enhances the understanding of the nonlinear dynamical behaviour of panel aeroelasticity in complex practical environments and provides new explanations for the discrepancies observed in certain research results.

Military Expenditures and Economic Growth: Evidence from NATO and Non-NATO Alliances

ABSTRACT Given its significant socioeconomic implications, the nexus between military expenditures and economic growth has been the subject of an extensive theoretical and empirical debate. The present study focuses on NATO vs. non-NATO member countries (i.e. 141 countries) as a case study to empirically examine the aforementioned complex relationship during the period 1992–2020. Using annual data, we employ a panel model, as well as spectral preliminary analysis that takes into account the nonlinear behaviour of our series, positive or negative causal relationships and their coherence characteristics across both time and frequency domains. Findings reported herein from an extended panel of several states suggest that military expenditure enhances economic growth under the NATO alliance case, whereas it becomes harmful for growth in the case of non-NATO alliances such as the SCO & CSTO. Our study contributes to the understanding on the crucial role of a military alliance membership in the formation of the economic growth and military spending relationship. Hence, our findings can be beneficial for policymakers to account for the existence of possible spillovers that may arise from country participation in a military alliance.

Adaptive neuro fuzzy technology to enhance PID performances within VCA for grid-connected wind system under nonlinear behaviors: FPGA hardware implementation

Wind Energy Conversion Systems (WECSs) exhibit nonlinear behavior due to internal and external disturbances, which can significantly impact the control performance. Firstly, this paper proposes a Vector Control Approach (VCA) based on Adaptive Neuro Fuzzy (ANF) of Proportional Integral Derivative (PID) controllers for a variable speed Permanent Magnet Synchronous Generator (PMSG)-based WECS connected to the grid to address these issues. The proposed ANF-PID controller combines the robustness of the fuzzy logic with the neural network's performance to ensure high accuracy, excellent tracking, and robustness against the WECS's nonlinear behavior. The neural network automates the placement of fuzzy logic membership functions. Secondly, this paper suggests a real-time hardware implementation of the VCA based on ANF-PID using a Field Programmable Gate Array (FPGA) to reduce the processing time and the WECS's sampling period. The effectiveness of the VCA based on ANF-PID controllers is validated by conducting a numerical simulation within the Matlab-Simulink using the Xilinx System Generator tool, alongside an experimental in-the-loop hardware implementation using FPGA board. Different scenarios are conducted to validate the robustness and stability of the proposed VCA based on ANF-PID control schemes, which is compared to Conventional Fuzzy PID (C-FPID) and PID controllers. The results exhibit that the VCA based on ANF-PID controllers outperforms VCA-C-FPID and VCA-PID controllers in terms of precision, tracking accuracy, and robustness against the WECS's nonlinear behavior and the PMSG parameter variations. The performances of the proposed controllers are tested under some criteria. In fact, the proposed ANF-PID controller provides a Mean Absolute Error (MAE), a Mean Squared Error (MSE) and a Root Mean Squared Error (RMSE) of 8.1911 × 10−04, 8.4181 × 10−05 and 0.0092, respectively. Compared to the C-FPID controller, the proposed controller offers an improvement gain of 98.96 %, 99.61 %, and 93.79 % of MAE, MSE, and RMSE, respectively. When compared to the PID controller, its improvement is even more significant, with a reduction of 99.9919 %, 99.9999 %, and 99.9288 % of MAE, MSE, and RMSE, respectively. In addition, the ANF-PID-based VCA utilizes hardware resources on the FPGA efficiently, requiring only 65.60 % slices LUT, 0.28 % LUTRAM, and 22.99 % FF. This makes it a more cost-effective option compared to the VCA-C-FPID controller for diverse control systems.

Magnetic enhancement of the electrical asymmetry effect in capacitively coupled plasmas

The development of real-time control strategies for key discharge parameters, such as densities, fluxes, and energy distributions, is of fundamental interest to many plasma sources. Over the last decade, multi-harmonic ‘tailored’ voltage waveforms have been successfully employed to achieve enhanced control of key parameters in a wide range of radio-frequency (RF) plasma sources through application of the electrical asymmetry effect (EAE). More recently, the analogous magnetic asymmetry effect (MAE) has been numerically and experimentally demonstrated to achieve a notable degree of control in parallel plate RF plasma sources. The MAE is achieved via selectively magnetising the charged species adjacent to one electrode, altering the charge flux to the surface and enforcing a DC self-bias to maintain quasineutrality. This study addresses the degree of control achieved by the MAE in a non-planar geometry via 2D fluid/kinetic simulations of a magnetised RF capacitively coupled plasma source employing two different magnetic topologies. The simultaneous application of the EAE and MAE is then presented for the same geometry, demonstrating a degree of non-linear behaviour dependant upon the applied magnetic topology. Control of the DC self-bias voltage ηdc is demonstrated for a single 600 Vpp , 13.56 MHz discharge in both ‘convergent’ (maximum on-axis field strength) and ‘divergent’ (minimum on-axis field strength) magnetic topolgies. MAE induced modulations of ηdc = 0.13 Vpp and ηdc = 0.03 Vpp are achieved for each magnetic topology, respectively, for magnetic field strengths between 50 and 1000 G. Simultaneous application of an EAE and MAE is achieved through a multi-harmonic ‘peak’-type tailored voltage waveform employing varying harmonic phase offsets between 0∘ ⩽ θ ⩽ 360∘ . The degree to which the DC self-bias voltage is modulated by the applied EAE is mediated by the orientation and magnitude of the applied magnetic field. The EAE induced DC self-bias modulations exhibit non-linear behaviour in response to a superimposed MAE, such that the resulting DC self-bias differs from an additive combination of the two effects alone Simultaneous application of the electrical and MAEs offers the possibility of further decoupling ion and electron dynamics in RF plasma sources, and represents an improvement over each approach in isolation.

Sliced chaotic encrypted transmission scheme based on key masked distribution in a W-band millimeter-wave system

In order to guarantee the information of the W-band wireless communication system from the physical layer, this paper proposes the sliced chaotic encrypted (SCE) transmission scheme based on key masked distribution (KMD). The scheme improves the security of free space communication in the W-band millimeter-wave wireless data transmission system. In this scheme, the key information is embedded into the random position of the ciphertext information, and then the ciphertext carrying the key information is encrypted by multi-dimensional chaos. Chaotic system 1 constructs a three-dimensional discrete chaotic map for implementing KMD. Chaotic system 2 constructs complex nonlinear dynamic behavior through the coupling of two neurons, and the masking factor generated is used to realize SCE. In this paper, the transmission of 16QAM signals in a 4.5 m W-band millimeter-wave wireless communication system with a rate of 40 Gb/s is proved by experiments, and the performance of the system is analyzed. When the input optical power is 5 dBm, the bit error rate (BER) of the legitimate encrypted receiver is 1.23 × 10−3. When the offset of chaotic sequence x and chaotic sequence y is 100, their BERs are more than 0.21. The key space of the chaotic system reaches 10192, which can effectively prevent illegal attacks and improve the security performance of the system. The experimental results show that the scheme can effectively distribute the keys and improve the security of the system. It has great application potential in the future of W-band millimeter-wave wireless secure communication.

Multi-mechanical frequency locking mechanism and robustness analysis of MDOF coupled resonator

Mechanical frequency locking can overcome the dependence of peak frequency on the driving amplitude and improve the frequency stability in nonlinear resonant systems. Most research focuses on the single mechanical frequency locking phenomenon, but few studies focus on multi-mechanical frequency locking phenomenon. In this study, the multi-mechanical frequency locking mechanism and robustness analysis of the peak frequency is proposed through multi-mode coupled vibration. Firstly, a multi-degree-of-freedom (MDOF) coupled resonator consisting of a low-frequency resonant element and multiple high-frequency resonant elements is designed, and the vibration energy of the resonant system can be transferred from the low-frequency resonant element driven by a harmonic excitation to the high-frequency resonant elements via the 1:3 internal resonance. Through perturbation and bifurcation analysis, the nonlinear dynamic behaviors of MDOF coupled resonator are analyzed in detail. It is found that the peak frequency of the low-frequency resonant element can remain stable in multiple drive intervals, leading to multi-mechanical frequency locking phenomenon. Then, a 3-DOF magnetic coupled resonant system is experimentally designed to demonstrate the physical conditions and influencing factors of the double mechanical frequency locking phenomenon. Typically, introducing external disturbances, the frequency locking is experimentally demonstrated to improve the robustness of peak frequency. The experimental results show that when the mechanical frequency locking phenomenon occurs, the influence of small external noise disturbance on the peak frequency can be ignored, which greatly improves the frequency stability of nonlinear resonant systems.

Study on Nonlinear Behavior of Variable Thickness Plates

The analysis of variable-thickness plates is much more complicated than that of uniform-thickness plates because variable coefficients occur in the equations. In reality, this analysis is of great interest in various engineering disciplines, such as civil engineering, aerospace engineering, machine design, and so on. Although there is extensive literature on analyses of plates with constant thickness, a rather limited amount of technical literature is available on the solutions to problems dealing with plates with nonuniform thickness. The reason is that the analytical solutions meet insurmountable difficulties. Besides, the nonlinear analysis process also faces more difficulties than the linear analysis of structures. For these reasons, the nonlinear behavior of variable-thickness plates based on a finite element procedure is presented in this study. Although the topic is not special, it will help the engineer have a specific view of the nonlinear bending of the plate with variable thickness. This survey will be based on the change in geometrical parameters. Numerical solutions are then presented to verify the simplicity of this proposed procedure.

Nonlinear behaviors and chaos control of a fluid-conveying piezoelectric pipe in supercritical regime

The study investigated the steady state response of a piezoelectric pipe conveying fluid under external and internal resonances in the supercritical regime of fluid velocity. Internal resonance conditions between the first and second frequency modes were studied at a specific flow velocity in the supercritical regime. The Galerkin method and the multiple scale method were used to extract the vibration amplitude versus the excitation frequency and amplitude. The steady state solutions lost stability through saddle-node and Hopf bifurcations, leading to periodic, double periodic, multi-periodic, and chaotic behaviors in the forced and frequency response curves. Time response, FFT, phase portrait, and Lyapunov exponents were presented to predict the unstable regions of the piezo-pipe system between the Hopf points. The Wolf algorithm was utilized to evaluate the Lyapunov exponents. Additionally, a fuzzy terminal sliding mode controller was designed in the chaotic region of the piezoelectric pipe conveying fluid, and its parameters were optimized using the genetic algorithm. The controller effectively stabilized the chaotic motion of the system, demonstrating better performance than the sliding mode control in numerical results.

Initial load factor adjustment through genetic algorithm for the generalized displacement control method: Implementation on non-rigid origami analysis

The nonlinear analysis of structural systems relies on effective nonlinear solution schemes, known as nonlinear solvers or path-following methods. This paper explores the challenge of determining the initial load factor in such analyses, with a particular focus on complex origami structures. This study presents a novel approach that leverages genetic algorithms (GA) to efficiently determine the initial load factor for the generalized displacement method. Building upon the concept of stiffness parameters, our method offers a systematic solution. In this work, GA serves as a tool to discover the appropriate initial load factor based on changes in the stiffness parameter, providing a more rational and user-friendly approach. To demonstrate the practical applicability of our approach, we apply it to a range of complex origami problems, including the folding of Miura-ori, folding of an egg-box origami, bending of an egg-box origami, and folding of an arc Miura-ori. These examples, along with a truss example, encompass highly nonlinear behaviors, including limit points, extreme stiffness fluctuations, snap-through, and snap-back. Our results showcase the effectiveness of our method in accurately tuning the initial load factor to capture and track intricate nonlinear behaviors. Furthermore, it offers the flexibility to fine-tune the distribution of points along the path and manage the resolution of the depicted equilibrium path. This versatility underscores its potential applications in fields such as deployable structures and complex large deformation structural analysis.

Experimental study on the pseudo threshold pressure gradient of supported fractures in shale reservoirs

AbstractPseudo threshold pressure gradient (PTPG) exists in the propped fractured reservoir, but its nonlinear flow law remains unclear. The effects of the mineral composition of shale and microstructure of fracturing fluid on PTPG were analyzed by X-ray diffraction and liquid nitrogen quick-freezing method. The results demonstrate that a proppant with a large particle size is more likely to form an effective flow channel and reduce liquid flow resistance, thus decreasing PTPG and increasing conductivity. The polymer fracturing fluid with rectangular microstructures significantly increased the PTPG supporting the fractured core. Experimental results show that the PTPG of the resin-coated sand-supported core in the fracturing fluid with a concentration of 1.2% is 245 times higher than that in the fracturing fluid with a concentration of 0.1% when the confining pressure is 5 MPa. Wetting hysteresis and the Jamin effect are responsible for the rise of PTPG in two-phase flow. The equivalent fracture width shows a good power function relationship with the PTPG. Thus, this study further explains the nonlinear flow behavior of reservoirs with fully propped fractures.

Air-Water Flow Properties In Highly Unsteady Flows

Recent catastrophic events caused by tsunamis, storm surges, flood waves, and the failure of dams (e.g. in Ukraine and Libya) have shown to be a significant threat to densely populated coastal communities. Interactions with built environments can lead to violent wave impacts that may have severe consequences, including significant infrastructural damage and potential loss of life. The frequency of these water-related disasters is increasing globally due to climate change and sea level rise, resulting in a rising demand for deeper knowledge related to the physical processes of such hazards. The dynamic behaviour of these type of wave phenomena is described by long-period, high translatory waves, where the on-shore propagation or inland inundation is associated with sudden free-surface deformations. This results in a steeping of the slope at the leading edge, causing non-linear flow behaviour to prevail and inducing the wave to collapse. The breaking process generates a breaking roller at the wave front, containing a rapidly fluctuating mixture of air and water, associated with a strong recirculation. The high degree of air-water interaction in these unsteady flows has a significant impact on the flow properties as it influences many dynamic processes, including viscous and surface tension effects at air-bubble level, as well as larger scale gravitational effects associated with the turbulent flow and eddy formation (Brocchini and Peregrine, 2001). New innovative measurement techniques have allowed experimental studies to more precisely quantify the air-water interactions in multiphase flows. However, most experimental research focused on air-water flow properties in hydraulic jumps and other steady flows (e.g. spillway flows, plunging jets). Currently, limited research is available for unsteady flows and mostly based on small datasets and limited flow conditions. This lack of availability and diversity of experimental data restricts the understanding of how these multi-phase flows behave under different conditions, hence the need for future research.

Fracture toughness evolution and failure mechanisms of two-dimensional SiCf/SiC composites at temperatures up to 1500 °C in air

Silicon carbide fiber reinforced silicon carbide composites (SiCf/SiC) are of the few most promising materials for high-temperature structural applications. In this study, two-dimensional (2D) plain-woven SiCf/SiC composites were prepared by chemical vapor infiltration process and subjected to single-sided notched beam three-point bending tests from room temperature (RT) to 1500 °C in air. The temperature-dependent bending load–deflection curves and fracture toughness were obtained. The results show that the SiCf/SiC composites exhibit linear deformation characteristics initially, followed by nonlinear deformation behavior which become more pronounced with increasing temperature. The fracture toughness decreases in the range of RT to 1000 °C due to the evolution of components properties, and increases at 1200 °C due to the interface property degradation and fiber pull-out. Above 1200 °C, it decreases with increasing temperature owing to the serious high-temperature oxidation. Further, the failure mechanisms of the 2D plain-woven SiCf/SiC composites at different temperatures was analyzed through macro and micro analysis. The evolution of components properties affected by high temperature and oxidation as well as fiber pull-out play a leading role in fracture toughness of composites. The findings of this study provide important support for the mechanical behavior and failure mechanisms of SiCf/SiC composites at ultra-high temperatures in air.

Studying the mode shape participation factor of wave loads for offshore wind turbine structures

This paper introduces a method for analyzing resonance between Offshore Wind Turbine (OWT) structures and wave loads using Wave Participation Factor ratios (WPFs). Despite temporal fluctuations in WPFs due to wave loads, they prove effective for identifying key modes influencing wave load behavior in both fixed and floating OWT structures. For fixed OWT foundations, nonlinear soil behavior causes some natural frequency variations under wave forces, but they typically remain within a limited range. Lower natural frequency modes show minor WPFs, reducing the risk of resonance with wave loads. Modes with higher natural frequencies have substantial WPFs and are less prone to resonance. However, precautions are needed to avoid rotor-induced wind load resonance. Floating OWT structures have large WPFs in their first six near-rigid body motion modes, while mooring line stiffness leads to substantial variations in these modes. It's crucial to control the first six nonlinear frequencies outside the dominant wave load range. Beyond these six modes, natural frequencies significantly exceed wave load frequencies, reducing resonance concerns. In summary, this study presents an effective method for assessing resonance between OWT structures and loads, providing valuable insights for structural design and operational safety.

Stability of arches with internal hinge

The in-plane stability of internally hinged, end-fixed shallow arches is in the spotlight. The non-linear model accounts for the coupled effect of the bending moment and axial force on the membrane strain. The model itself can handle homogeneous or non-homogeneous material distributions along the thickness of the uniform arch. Analytical findings reveal how the typical geometrical data, like arch length, radius of gyration, and arch angle, affect the lowest buckling loads. The typical non-linear behaviour of arches is also assessed including the equilibrium path and the internal force system.