International Journal of Non-Linear Mechanics最新文献

{"title":"Neural controller for targeting a desired stationary distribution in stochastic systems","authors":"Wantao Jia ,&nbsp;Zhe Jiao ,&nbsp;Zhengrong Jin","doi":"10.1016/j.ijnonlinmec.2025.105058","DOIUrl":"10.1016/j.ijnonlinmec.2025.105058","url":null,"abstract":"<div><div>One of the major missions in the field of stochastic control is to design efficient control policies that guarantee the stochastic systems stabilize within some specified stationary distribution. In this paper, we propose a neural controller based on the stochastic asymptotic stability theory and the condition of detailed balance. A novel physics-informed learning procedure is introduced to update the parameters in a multi-output neural network which is utilized to approximate the controller. We also prove rigorously that the proposed controller is unique if it exists, which is essential in applications. Furthermore, several representative stochastic systems are used to illustrate the usefulness of this neural controller for the stabilization of these dynamical systems in distribution.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105058"},"PeriodicalIF":2.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"In-plane simultaneous resonance instability behaviors of a fixed arch under a two-frequency radial uniformly distributed excitation","authors":"Fulin Shen ,&nbsp;Zilin Zhong ,&nbsp;Xiaobin Xu ,&nbsp;Jianhua Li ,&nbsp;Qinxi Dong ,&nbsp;Jian Deng","doi":"10.1016/j.ijnonlinmec.2025.105056","DOIUrl":"10.1016/j.ijnonlinmec.2025.105056","url":null,"abstract":"<div><div>This paper delves into a theoretical and numerical exploration of the in-plane simultaneous resonance instability behaviors exhibited by a fixed arch subjected to a two-frequency radial uniformly distributed excitation. An intriguing and previously overlooked phenomenon of simultaneous resonance instability in fixed arches has been identified—specifically, the coexistence of superharmonic resonance and combination subharmonic resonance. The in-plane governing equation of motion was derived using Hamilton's principle and subsequently decoupled through the application of the Galerkin method. Employing the method of multiple scales, boundary excitation frequencies at varying amplitudes were determined, establishing dynamic instability zones and distinguishing between stable and unstable regions of the arch. These findings were further validated using both the finite element method and the fourth-order Runge-Kutta technique. The investigation brought to light a fascinating phenomenon wherein the concurrent manifestation of both 2-order superharmonic resonance and 1/2-order combination subharmonic resonance occurs when the sum of two excitation frequencies approaches twice the natural frequency of the arch, with one of them being approximately half of the natural frequency.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105056"},"PeriodicalIF":2.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A magnetorheological elastomer-based hybrid vibration isolation system with semi-active control and quasi-zero stiffness performance","authors":"Yu Lin ,&nbsp;Guilin Wen ,&nbsp;Chengxiang Liu ,&nbsp;Junfeng He ,&nbsp;Jie Liu","doi":"10.1016/j.ijnonlinmec.2025.105063","DOIUrl":"10.1016/j.ijnonlinmec.2025.105063","url":null,"abstract":"<div><div>The quasi-zero stiffness (QZS) vibration isolation system suffers from conflicts between low-frequency and mid-to-high-frequency isolation, despite having outstanding low-frequency vibration isolation performance. Meanwhile, the semi-active control technology based on magnetorheological elastomers (MRE) can achieve good vibration isolation effects over a wide frequency range. However, its ability to isolate low-frequency vibrations is still restricted. To address the challenge, this paper proposes a hybrid vibration isolation system that combines QZS isolation technology with semi-active control technology based on MRE. The hybrid vibration isolation system consists of the QZS vibration isolation unit and the semi-active control unit. The inclined springs provide negative stiffness, while the MRE and linear vertical spring jointly provide positive stiffness. The magneto-mechanical properties of the MRE samples are analyzed, and a phenomenological constitutive model is established. The relationship between the magnetic field and control current in the hybrid system is determined through electromagnetic field simulation. The hybrid system's vibration isolation performance in passive mode as a QZS isolator with nonlinear damping properties is assessed using the harmonic method. The hybrid system's vibration isolation performance under random and harmonic excitations is then examined in semi-active control mode. The findings demonstrate that the hybrid system outperforms traditional QZS isolators in terms of vibration isolation performance in passive mode. Furthermore, it demonstrates excellent performance in the semi-active mode under both harmonic and random excitations, with good wideband low-frequency vibration isolation capabilities.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105063"},"PeriodicalIF":2.8,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143578508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-objective optimization of the asymmetric-grinding rail profile for sharply curved tracks on metro line","authors":"Fei Yang ,&nbsp;Liang Gao","doi":"10.1016/j.ijnonlinmec.2025.105065","DOIUrl":"10.1016/j.ijnonlinmec.2025.105065","url":null,"abstract":"<div><div>Rail grinding is an effective strategy to improve the curve negotiation performance of metro vehicles. This paper develops a multi-objective optimization model for the design of the asymmetric-grinding rail profiles. The root-mean-square value of the derailment coefficient and the mean value of the rail wear of high rail are taken as two optimization objectives. A surrogate model, established using the results of the vehicle-track coupled dynamics simulations and non-uniform rail wear predictions, is used to calculate the optimization objectives. The multi-objective particle swarm optimization (MOPSO) model is applied to solve the multi-objective optimization model. The asymmetric-grinding rail profile of a sharp metro line is optimized by using the developed model, and the Pareto front of the multi-objective optimization problem is obtained. The performance of three typical asymmetric-grinding rail profiles in vehicle dynamics and rail wear rate is analyzed by comparing them with those of the original rail profile. The simulation results show that the optimized asymmetric grinding of rail profiles achieves the optimization objectives of reducing both the derailment coefficient and the mean value of rail wear on high rail. Due to the conflicting relationship between the two objective functions, an optimized asymmetric-grinding of rail profiles in the Pareto front that could balance both the wheel-rail safety and rail wear is chosen as the best rail grinding strategy.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105065"},"PeriodicalIF":2.8,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis and control of coexisting attractor transitions in a class of rigid vibro-impact systems","authors":"Guofang Li ,&nbsp;Tao Liu ,&nbsp;Shaopei Wu ,&nbsp;Deyang Li ,&nbsp;Wangcai Ding ,&nbsp;Zonghong Feng","doi":"10.1016/j.ijnonlinmec.2025.105066","DOIUrl":"10.1016/j.ijnonlinmec.2025.105066","url":null,"abstract":"<div><div>In order to solve the problem that coexisting attractor transition control is not easy to achieve in rigid vibro-impact systems, the coexisting attractors and the transition control of a single-degree-of-freedom vibro-impact system with clearance is explored in this paper. Firstly, the Poincaré map of system and its Jacobi matrix are obtained by constructing the local map. Secondly, the coexistence and transition characteristics between stable and unstable periodic motions are studied by the cell mapping method, the shooting method, and parameter continuation algorithms. Finally, with the boundary point being whether a collision occurs between the controlled system and the target system, a piecewise controller based on Lyapunov stability theory and the backstepping method is proposed to adapt to the rigid vibro-impact system with clearance and multistability coexistence. The controller employs the impact occurrence between the controlled system and the target system as the boundary point. Numerical simulation results demonstrate that the designed controller can effectively control the transition of the attractors.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105066"},"PeriodicalIF":2.8,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel weighted averaging operator for frequency analysis of nonlinear free vibrations","authors":"Anh Tay Nguyen ,&nbsp;Nguyen Ngoc Linh ,&nbsp;Nguyen Cao Thang ,&nbsp;Nguyen Anh Ngoc ,&nbsp;Le Quang Vinh ,&nbsp;N.D. Anh","doi":"10.1016/j.ijnonlinmec.2025.105057","DOIUrl":"10.1016/j.ijnonlinmec.2025.105057","url":null,"abstract":"<div><div>The paper develops a weighted equivalent linearization (WEL) using a novel weighted averaging operator (WAO) for deterministic nonlinear oscillation problems. WAO is based on a linear combination of global and local integrations involving an embedding parameter. The main properties of WAO are systematically presented and proven. Further selecting the embedding parameter as a function of the local variable is implemented. WEL with the proposed weighted averaging operator is then applied to analyze frequency of nonlinear conservative oscillations, and some case studies are subsequently carried out in order to verify the accuracy of WEL. It is shown that WEL provides the lowest maximal errors among the approximate solutions obtained from several analytical methods for various nonlinearities considered, including strong nonlinear levels.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"173 ","pages":"Article 105057"},"PeriodicalIF":2.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Transitions to chaos, fractal basin boundaries, bursting and mixed modes oscillations in a cubic-quintic-septic duffing oscillator with four wells of equal depth","authors":"Pyrrhus Dior Landry Kamseu ,&nbsp;Hervé Simo ,&nbsp;Paul Woafo ,&nbsp;Jan Awrejcewicz","doi":"10.1016/j.ijnonlinmec.2025.105055","DOIUrl":"10.1016/j.ijnonlinmec.2025.105055","url":null,"abstract":"<div><div>This work analyses the various dynamical states that can be delivered by a sinusoidally excited cubic-quintic-septic Duffing oscillator with a potential having four wells of equal depth and three bumps of the same level using mathematical methods and numerical simulation based on the fourth order Runge-Kutta method. This special potential can be obtained in mechanics using magnets with appropriate magnetic inductions placed appropriately close to a line on which a magnetic body is moving. The frequency response curves are plotted for asymmetric oscillations around the stable equilibria. The transition routes to chaos are obtained through the bifurcation diagrams. Chaos appears through several routes. The signature of the four well potential on the phase portraits is clearly visible by the display of periodic or chaotic rounds near the equilibrium points. The horseshoes chaos is observed by plotting the attraction basins. The model shows four basins of attraction corresponding to each of the four wells which are regular for dynamics or fractal for chaos in the Melnikov sense. Bursting and mixed modes oscillations are obtained, some of which are chaotic. The justification of the appearance of bursting oscillations is conducted using the analysis of the equilibrium points in case of a slow variation of the excitation.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"173 ","pages":"Article 105055"},"PeriodicalIF":2.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3D finite element analysis of micromorphic hyperelastic structures considering finite deformations: Two-point formulation","authors":"F. Sadeghi,&nbsp;R. Ansari,&nbsp;A. Basti","doi":"10.1016/j.ijnonlinmec.2025.105054","DOIUrl":"10.1016/j.ijnonlinmec.2025.105054","url":null,"abstract":"<div><div>The purpose of this article is to introduce a novel finite element (FE) approach for investigating the large deformations of three-dimensional (3D) micromorphic hyperelastic continua that have an arbitrary geometry. The 3D micromorphic hyperelasticity formulation is initially presented in a general form. To facilitate the procedure of coding, the vector-matrix counterparts of the aforementioned relations are also provided, which can be conveniently employed in numerical methods. Afterwards, an FE approach is implemented to investigate the large deformations of micromorphic hyperelastic structures under static loading. This is achieved via the user element (UEL) subroutine utilized by the commercial ABAQUS software. Problems with complex domains can be solved using this FE approach. Solving some test problems, including bending of a beam, Cook's membrane under bending load, a cracked spherical shell under external pressure point load and a cracked cylindrical shell under stretching load, demonstrates the fast convergence rate, simple implementation, accuracy and efficiency of the method. In addition, the influences of internal length and scale-transition parameters and geometrical properties on the finite deformation of considered micromorphic hyperelastic structures are evaluated.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105054"},"PeriodicalIF":2.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The corotational stability postulate: Positive incremental Cauchy stress moduli for diagonal, homogeneous deformations in isotropic nonlinear elasticity","authors":"Patrizio Neff ,&nbsp;Nina J. Husemann ,&nbsp;Aurélien S. Nguetcho Tchakoutio ,&nbsp;Sergey N. Korobeynikov ,&nbsp;Robert J. Martin","doi":"10.1016/j.ijnonlinmec.2025.105033","DOIUrl":"10.1016/j.ijnonlinmec.2025.105033","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In isotropic nonlinear elasticity the corotational stability postulate (CSP) is the requirement that &lt;span&gt;&lt;span&gt;&lt;span&gt;(0.1)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;〉&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mtext&gt;Sym&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; is &lt;strong&gt;any&lt;/strong&gt; corotational stress rate, &lt;span&gt;&lt;math&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the Cauchy stress and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;sym&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the Eulerian rate of deformation tensor where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̇&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the spatial velocity gradient. For &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≔&lt;/mo&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; it is equivalent almost everywhere to the monotonicity (TSTS-M&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;) &lt;span&gt;&lt;span&gt;&lt;span&gt;(0.2)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;〈&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;log&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;〉&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mtext&gt;Sym&lt;/mtext&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;≠&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;For hyperelasticity, (CSP) is in general independent of convexity of the mapping &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;↦&lt;/mo&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"174 ","pages":"Article 105033"},"PeriodicalIF":2.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear analysis and response identification of tristable energy harvesters under wind and base excitations","authors":"Xiaoqing Ma ,&nbsp;He Ma ,&nbsp;Shengxi Zhou","doi":"10.1016/j.ijnonlinmec.2025.105052","DOIUrl":"10.1016/j.ijnonlinmec.2025.105052","url":null,"abstract":"<div><div>The excellent working performance of nonlinear vortex-induced vibration (VIV) energy harvesters has been verified by researchers. However, in practical working environments, the harvester is not only affected by wind excitation but also by base excitation. Analyzing the impact mechanism of base excitation on the nonlinear harvesters' working performance is very important for designing wind energy harvesters with high energy harvesting efficiency and strong robustness. This paper designs a VIV energy harvester based on the tristable structure, and the frequency spectrum, Poincaré maps, and phase diagrams are adopted to characterize the harvester's output response and dynamic characteristics. It is found that base excitation can adjust the working performance of the harvester. In addition, the complex response characteristics (chaotic, periodic and quasi-periodic responses) of the harvester is accurately identified by the analysis method of “0–1” test, and the parameter analysis are carried out. Overall, this paper provides theoretical framework for analyzing tristable VIV energy harvesters subjected to complex excitations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"173 ","pages":"Article 105052"},"PeriodicalIF":2.8,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}