International Journal of Non-Linear Mechanics最新文献

Glass laminates consist of stiff glass plies permanently shear-coupled by polymeric interposed layers. When an external temperature rise occurs, the interlayers undergo a dramatic stiffness decay. As a consequence, not only the sectional warping typical of alternating stiff/soft composites is intensified, but also the overall behavior may evolve counter-intuitively. When slender elements prone to geometric nonlinearities are involved, even small thermal variations in intensity or distribution may act as uncertainty factors, strongly affecting the outcome. This paper proposes an efficient, robust, and accurate numerical framework to perform the sensitivity analysis to thermo-mechanical actions in glass plates. A large deformation isogeometric Kirchhoff-Love shell model enriched with through-the-thickness warping is employed, together with a generalized arc-length method involving a suitable temperature parameter as an additional unknown, namely the thermal amplifier or a spatial distribution coefficient. Numerical experiments are presented to highlight the effects that even small temperature variations produce on the equilibrium paths and the influence of the stiffness loss in the interlayer on the structural behavior and the accuracy of the models.

High-fidelity simulations are increasingly called-upon to resolve the nucleation of instabilities such as crack initiation and propagation and fluid mixing. While multiscale modeling capabilities have progressed rapidly over recent decades, associated simulations still present a computational burden, thus often preempting a systematic statistical analysis of related problems. Given the paucity of data that relate micro-structure to macroscale behavior, and the unavoidable modeling errors at both scales, the lack of a probabilistic characterization significantly limits the value of highly-resolved numerical simulators. The goal of the present research is to develop a probabilistic model that encodes pathwise relationships between micro and macro scales. Specifically, we develop a switching diffusion model to relate damage evolution, characterized at the microscale, to system performance identified with a macroscale property. Microscale behavior is modeled as a Markov switching process with a finite state space while the macroscale counterpart is modeled as a continuous-state diffusion process. The interaction between macro and micro scales is captured by coupling these two processes. Calibrated by data, the switching diffusion model can generate, with minimal computational effort, sample paths with prescribed statistics. The proposed model contributes new capabilities and perspectives at the interface of multiscale simulation, uncertainty quantification, and stochastic modeling.

The optimization-oriented exponential-polynomial-closure (OEPC) method is extended and investigated to analyze stochastic nonlinear oscillators under multiple excitations, with the purpose of obtaining probabilistic solutions for the corresponding system. The presented method extends the original EPC projection procedure for solving the FPK equation by minimizing an objective function, which is defined as the spatial integration of the weighted square residual error. Using the exponential polynomial function, the parameters within it can be located by seeking the minimum of the objective function. In this paper, the novel method has been tested with four examples of strong nonlinearities raised by polynomial nonlinear terms and parametric excitations. The results provide adequate evidence that the OEPC approach delivers notably improved accuracy compared to the Gaussian closure method and demonstrates superior efficiency compared to Monte Carlo simulation. The OEPC method presents a viable alternative for investigating stochastic nonlinear oscillators.

Nonlinear asymmetric bi-stable composite laminates, characterized by multistable nature and rich dynamics, have seen increased application potential recently. This has necessitated a detailed dynamical analysis of bistable laminates. In this manuscript, the nonlinear behaviour of asymmetric $[0_n/90_n]$ bistable laminates with free–free boundary conditions is investigated through simulations and experimental observations. A refined 17 degrees of freedom (dofs) analytical model is developed, fusing Raleigh–Ritz with Hamilton’s principle to obtain the governing nonlinear equations of motion. A nonlinear finite element (FE) model is also developed using ABAQUS®. Experiments are conducted by clamping the midpoint of the plate with a shaker and then exciting it. The composite laminate shows many intricate dynamics, such as sub-harmonic and super-harmonic oscillations, intra-well oscillation (periodic and chaotic), and inter-well snap-through (periodic and chaotic snap-through) prominently. The primary focus of this paper is to highlight the potential of bistable laminates by elucidating the existence of large-amplitude vibrations over a broad frequency range under different input and system parameters. Further, it has been observed that attached mass plays a significant role in modifying the response bandwidth for cross-well oscillation for a given excitation frequency and amplitude. Hence fine-tuning of masses can excite different nonlinear dynamic characteristics of the laminate, making it applicable in different engineering fields.

A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is analyzed, and invariant manifolds are found. For the case of three platforms (links), a phase portrait for motion on an invariant manifold is shown and trajectories of the attachment points of the wheel pairs of the three-link vehicle are presented. In addition, an analysis is made of motion in the case where the leading platform has a rotor whose angular velocity is a periodic function of time. The existence of trajectories for which one of the velocity components increases without bound is established, and the asymptotics for it is found.

In this paper, a horizontal rotor with passive anisotropic asymmetric magnetic bearings nonlinear model is developed. The model is based on the experimental evidence of an educational demonstrator, a powerful benchmark which highlights features of rotordynamics systems. An experimental setup is developed using laser sensors to track the displacements of the rotor and tachometer to record the rotor angular speed. Several test campaigns are performed with different initial conditions to characterise the educational demonstrator. The first test campaign is oriented to identify the system structural properties, while the second one is focused on the nonlinearity identification. The rotor modelling is divided into three stages with progressive increase in complexity, starting from the overall linear structural behaviour to the nonlinear subharmonic resonance phenomenon. The model is developed with a generalised approach suitable for a wide range of operating conditions and rotor configurations. Progressively, the developed rotor models are compared to highlight their limitations and advantages. Finally, rotor trajectory analysis and time–frequency analysis are used in the numerical-to-experimental comparison.

In order to reveal the nonlinear dynamics of dual-rotor-support-casing system, a numerical procedure is proposed using the finite element method and the component mode synthesis method. Especially, the casing system is subdivided into the casings, struts and housings, which are modeled by shell elements, beam elements and rigid regions with mass elements, respectively. Furthermore, the inter-shaft rub-impact, which may occur in the aero-engine because of imbalance and other faulty, is considered in the dynamic model as a nonlinear excitation. The modal analysis verified the validity of the dual-rotor-support-casing system model. The motion equations are established using the reduced-order model and solved by Newmark-β method with Newton-Raphson iteration. The results show that larger rubbing stiffness will cause the rubbing to enter a self-excited vibration state, and the rotational speed ratio will change the speed region where the self-excited vibration occurs. Finally, the experiment is performed based on a real dual-rotor aeroengine under inter-shaft rub-impact and the results are consistent with the theoretical results, which proves the effectiveness of dual-rotor-support-casing system dynamic model.

In this paper, we proposed a new mechanical diode with non-smooth and nonlocal elastic, which support a backflow of the input mechanical energy. It is composed of a nonlinear converter connecting with nonlocal bilinear springs and linear phononic crystal. The asymmetrical stiffness of bilinear springs can be utilized to periodically modulate the stiffness of converter, generate non-reciprocal propagation of mechanical waves, thereby decompose the excitation frequency into multiple sub-bands. Utilizing this characteristic of converter, during the forward propagation of mechanical diodes, it is possible to effectively surpass the cutoff frequency of phononic crystals, ensuring higher energy transmission efficiency and achieving wideband performance of mechanical diodes. Nonlocal connections induce a roton-like dispersion in the wave propagation, resulting in negative group velocities and partial energy backflow. The Runge-Kutta method is utilized to simulate wave propagation and verified by experimental. It is shown that the low-frequency impinging wave is rectified and nearly 100% contrast ratio is observed. Our work provide a new platform for mechanical wave manipulation and energy harvesting.

Viscoelastic rubber materials are widely used in various vibration reduction structures of military and construction machinery. The complex driving and working conditions make the mechanical structure suffer severe impact, which leading to the damage or lose efficacy of the important viscoelastic elements. In order to reveal the dynamic mechanical properties of silicone rubber after impact, the Uniaxial compression tests of silicone rubber under different high strain rates were carried out with the separated Hopkinson pressure bar (SHPB) dynamic impact experiment, and the original Zhu-Wang-Tang (ZWT) constitutive model was modified by combining logarithmic law and power function law. The dynamic impact simulation model of silicone rubber was established using the modified ZWT-rate-dependent constitutive model, and the dynamic impact damage behavior of silicone rubber was studied under the condition of high strain rate, and the microscopic damage analysis was carried out on the experimental silicone rubber samples by scanning electron microscopy (SEM). The results show that the silicone rubber has obvious strain rate effect and strong deformation resistance at high strain rate. The modified ZWT-rate-dependent constitutive model can be used to obtain the constitutive expression of unified parameters, which can better describe the dynamic mechanical properties of silicone rubber at high strain rates. After dynamic impact compression, a damage line zone appears in the silicone rubber sample. There is a certain rule between the position of the line zone and the loading strain rate and the friction coefficient of the end face, and the silicone rubber is significantly affected by the friction effect of the end face.

Electromagnetic energy harvesting suspension (EMEHS) systems can convert mechanical energy into electrical energy, which has attracted much attention in the field of automotive energy harvesting. This paper aims to examine the stochastic dynamics of the EMEHS system with time-delayed feedback and fractional derivative damping under random road excitation. The equivalent system can be obtained by variable transformation, followed by the derivation of the steady-state probability density function using stochastic averaging method. The consistency between numerical simulation and analytical results verifies the effectiveness of the proposed method. Results indicate the existence of stochastic bifurcation phenomenon. The influences of fractional order, delayed time, fractional coefficient, and nonlinear damping coefficient on the stochastic P-bifurcation of the system are discussed individually in detail. Then the output performance of the EMEHS system is illustrated by presenting the mean square current and mean output power. The conclusions demonstrate that adjusting parameters such as fractional order, delayed time, and noise intensity can enhance the energy harvested from road vibrations. This article provides a theoretical reference for the future design of high-performance EMEHS.