Acta Mechanica最新文献

{"title":"Nonlinear normal modes and bifurcations of geometrically nonlinear vibrations of beams with breathing cracks","authors":"S. Malyshev,&nbsp;K. Avramov","doi":"10.1007/s00707-024-04191-8","DOIUrl":"10.1007/s00707-024-04191-8","url":null,"abstract":"<div><p>Two types of partial differential equations, which describe geometrically nonlinear vibrations of flexible beams with breathing cracks, are considered. The mechanical vibrations with two kinds of nonlinearities are considered. The first type of the partial differential equation uses crack function to describe the vibrations of the beams with one crank. The second model can be used to describe the vibrations of beams with several cranks. This approach uses delta function to simulate every crack. A contact parameter is used to describe nonlinearity due to crack breathing. The Galerkin technique is applied to derive the system of the ordinary differential equations with polynomial nonlinearity and piecewise-linear functions of the generalized coordinates. The combination of the collocation method and arc length continuation technique is applied to analyze numerically the nonlinear vibrations, their stability and bifurcations. The nonlinear normal modes of the geometrically nonlinear free vibrations of the beam with the breathing crack are analyzed numerically. The backbone curve of these nonlinear modes contains two loops, saddle-node bifurcations and Neimark–Sacker bifurcations. As follows from the numerical analysis, the nonlinear normal modes modal lines are curved essentially in configuration space. The frequency responses of the forced vibrations contain loops and saddle-node bifurcations. Moreover, the frequency responses of the forced vibrations contain Neimark–Sacker bifurcations, which result in steady quasi-periodic vibrations. The properties of the quasi-periodic vibrations are analyzed numerically.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1317 - 1337"},"PeriodicalIF":2.3,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513376","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":"Reflection of plane waves in a microelongated thermoelastic porous medium with Hall current under modified Green–Lindsay model","authors":"Komal Yadav,&nbsp;Devender Sheoran,&nbsp;Kapil Kumar Kalkal","doi":"10.1007/s00707-025-04222-y","DOIUrl":"10.1007/s00707-025-04222-y","url":null,"abstract":"<div><p>In this article, a model of two-dimensional problem of generalized thermoelasticity for a homogeneous, isotropic, microelongated thermoelastic medium with voids and Hall current is established. The enunciation is applied to generalized thermoelasticity theory based on modified Green–Lindsay model. Five coupled waves are found to exist in the medium, namely longitudinal displacement wave (PI), transverse displacement wave (PII), thermal wave (PT), microelongation wave (PM) and volume fraction wave (PV). In order to calculate reflection coefficients, appropriate boundary conditions are taken into account. The numerical calculations have been carried out with the use of MATLAB programming, and reflection coefficients and energy ratios for these reflected waves have been calculated. Graphical representations show how Hall parameters, voids and microelongation affect reflection coefficients and phase velocities. Comparisons are done between the results when certain parameters are present and absent. Variation of attenuation coefficients with frequency is also shown in a plot. Energy ratio expressions have been obtained in explicit form and are represented graphically as functions of incidence angle. It has been established that the sum of the energy ratios at each angle of incidence during the reflection phenomena equals unity. Existing findings are reduced as particular cases for the validation of this study.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1359 - 1380"},"PeriodicalIF":2.3,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513347","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":"Effect of non-Fourier heat transfer on the thermoporoelastic response of a borehole","authors":"Zhiqiang Fan","doi":"10.1007/s00707-024-04213-5","DOIUrl":"10.1007/s00707-024-04213-5","url":null,"abstract":"<div><p>In the framework of classical thermoporoelasticity, heat conduction is generally assumed to follow Fourier’s law, resulting in an infinite speed of heat propagation. Recent laboratory experiments on porous rocks revealed a significant time delay between the heat flux and the temperature gradient. To address this observation, I have formulated a modified thermoporoelasticity model by integrating hyperbolic heat conduction theory and accounting for the time of thermal relaxation. This non-Fourier thermoporoelasticity model is then applied to analyze a wellbore exposed to cooling fluid and non-hydrostatic in situ stresses. I utilize the Laplace transform and load decomposition approaches concurrently to derive solutions in the Laplace domain. The Stehfest inversion algorithm is employed to convert these solutions into the time domain. Our numerical findings demonstrate that during early stages, non-Fourier heat conduction notably impacts temperature, pore pressure, and stresses, particularly in the immediate vicinity of the borehole.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1299 - 1315"},"PeriodicalIF":2.3,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513297","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":"Free vibration and buckling analysis of FG graphene origami-enabled auxetic metamaterial beams in a thermal environment","authors":"Xiang-Yu Gao,&nbsp;Zhuang-Zhuang Wang,&nbsp;Lian-Sheng Ma","doi":"10.1007/s00707-024-04197-2","DOIUrl":"10.1007/s00707-024-04197-2","url":null,"abstract":"<div><p>Functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterials (FG-GOEAM) have received much attention due to their excellent mechanical properties. In this study, the buckling and free vibration behaviours of FG-GOEAM beams supported by elastic foundations in a thermal environment are investigated. Three temperature distributions were considered: uniform temperature profile (UTP), linear temperature profile (LTP), and sinusoidal temperature profile (STP). By assuming that the temperature at the geometrical neutral planes of any layer in an FG-GOEAM beam represents the temperature of the entire layer, this study determines the correction function for the material parameters associated with FG-GOEAM beams under LTP and STP. Mechanical response analysis of FG-GOEAM beams under LTP and STP was not reported. The effect of the thermal environment is described in the form of thermal strain energy. The control equations were derived based on refined beam theory (RBT) and Lagrange equations. Numerical results were obtained using the Chebyshev-Ritz method. The accuracy of the study in this paper was verified by comparing the results with the existing literature. It should be noted that bifurcation buckling does not occur for FG-GOEAM beams that exhibit asymmetric material distribution and temperature profiles in the thickness direction. Therefore, these asymmetric distributions are not considered in the buckling analysis. Emphasis was placed on the effects of temperature profiles, weight fraction, and degree of folding of Gori on the buckling and vibrational behaviour of FG-GOEAM beams under various boundary conditions. These numerical results provide important insights for the further design and development of FG-GOEAM beams.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1265 - 1287"},"PeriodicalIF":2.3,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513294","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":"Multiple super-transmission angle and Klein tunneling of elastic wave","authors":"Hongzhu Li,&nbsp;Xiaofei Lyu,&nbsp;Qian Ding,&nbsp;Tianzhi Yang","doi":"10.1007/s00707-024-04211-7","DOIUrl":"10.1007/s00707-024-04211-7","url":null,"abstract":"<div><p>Klein tunneling is a fascinating phenomenon in quantum mechanics, which has been discovered in acoustic metamaterials. However, most of the present theory and experiments are limited in normal impinging elastic wave. In this letter, we explore the possibilities for oblique tunneling for elastic wave. We introduce a unique approach by constructing a kind of one-dimensional tunneling model with two similar phononic crystals, extending tunneling beyond normal incidence. Supported by the quantum potential barrier model and pseudospin conservation principle, we demonstrate the super-transmission caused by tunneling at various angles, influenced by the thickness of potential barrier and Klein-like tunneling independent on thickness of that. Our results, confirmed through simulations and experiments, open avenues for constructing superlattices and exhibit potential applications in wave control and covert communications, emphasizing new dimensions in quantum tunneling research.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1289 - 1298"},"PeriodicalIF":2.3,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513295","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":"Optimum design, nonlinear dynamic response and vibration of graphene-reinforced laminated composite with negative Poisson’s ratio under dynamic load in thermal environment","authors":"Vu Minh Anh,&nbsp;Nguyen Dinh Duc","doi":"10.1007/s00707-025-04218-8","DOIUrl":"10.1007/s00707-025-04218-8","url":null,"abstract":"<div><p>Material with a negative Poisson’s ratio, also known as auxetic materials with honeycomb and zigzag structures, is useful for reinforcing and protecting buildings, military structures, etc. However, the use of composite materials combining graphene-reinforced fibers and adjusting the laminated angle to create a material with a negative Poisson coefficient is a new problem. Thus, analysis of the nonlinear dynamic response and vibration of graphene-reinforced composite laminated (GRCL) plates with a negative Poisson’s ratio in a thermal environment that is supported by elastic foundations under moving loads is very valuable. To evaluate the effect of the misalignment angle, volume ratio, distribution of graphene, temperature, and geometry parameters, the third-order shear deformation theory is proposed with a Vor-Karman term. Based on the theory used, the deformation compatibility equation and motion equation are listed in detail. Besides, the natural frequency values of the graphene-reinforced laminated composite are also investigated in detail and highlighted. Furthermore, by utilizing the differential evolutionary optimization technique, we can identify the highest possible value of the natural frequency while also adhering to the limitations of the problem. These constraints involve a laminated plates with a negative Poisson's ratio, and the optimization is performed using angle variables.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1217 - 1243"},"PeriodicalIF":2.3,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513255","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":"Vibration analysis of composite beams integrated with graphene nanoplatelets reinforced piezoelectric layer","authors":"Rui Ma,&nbsp;Qingrui Wang,&nbsp;Mingran Zhang,&nbsp;Yuanxiang Zhang,&nbsp;Tianchen Zhao,&nbsp;Qilin Jin","doi":"10.1007/s00707-025-04226-8","DOIUrl":"10.1007/s00707-025-04226-8","url":null,"abstract":"<div><p>Graphene nanoplatelets (GNP) possess distinctive physical properties, making them a remarkable material for a wide range of engineering applications. Nonetheless, the existing higher-order theories documented in the literature may not effectively predict the natural frequencies of composite beams that incorporate GNP-reinforced piezoelectric layers. This limitation arises from the electromechanical coupling effects and the pronounced variability in material properties at the interfaces between layers. To overcome these limitations, this study proposes a refined beam theory specifically designed to examine the vibrational behavior of composite beams embedded with GNP-reinforced piezoelectric layers. By enforcing the continuity of interlaminar stresses and incorporating the free-surface conditions for interlaminar shear stresses, the formulation eliminates the dependence on layer-specific unknown variables, leading to a simplified yet accurate displacement field. In contrast to earlier higher-order theories, the current model introduces a refined interlaminar shear stress field incorporating the effects of electromechanical coupling. By utilizing Hamilton's principle, the enhanced shear stress field is incorporated into the governing equations of motion, which leads to a notable improvement in the prediction of natural frequencies for piezoelectric sandwich and laminated beams. Key results show that the proposed model achieves deviations below 3% compared to exact solutions, while existing models exhibit errors exceeding 280%. Additionally, geometric parameters such as the length-to-thickness ratio and layer thickness significantly influence natural frequencies, whereas the GNP volume fraction and electrical boundary conditions have minimal impact. The proposed theory's effectiveness is demonstrated through exact solutions and comparative studies with other models. The results reveal that the proposed theory offers superior accuracy in predicting natural frequencies compared to conventional higher-order models for composite beams. Moreover, a parametric analysis is performed to explore the influences of various key parameters on the vibration properties of smart composite beams with GNP reinforcements.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1245 - 1263"},"PeriodicalIF":2.3,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513254","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":"Kinematic numerical analysis of bending plate bearing capacity under cyclic loads","authors":"Phuc L. H. Ho,&nbsp;Dung T. Tran","doi":"10.1007/s00707-024-04199-0","DOIUrl":"10.1007/s00707-024-04199-0","url":null,"abstract":"<div><p>This study introduces a robust approach for determining safety factors and elucidating failure mechanisms in bending plates under cyclic loading conditions. The kinematic shakedown formulation is established by integrating the Hsieh–Clough–Tocher element with second-order cone programming. The resulting optimization problems, characterized by a multitude of variables and constraints, are efficiently solved using the MOSEK optimizer, a highly effective primal–dual interior-point algorithm-based solver. The proposed method’s efficacy is validated by investigating various metal plates with diverse geometries, loading, and boundary conditions.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1179 - 1193"},"PeriodicalIF":2.3,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513185","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":"Analytical analysis of a circular tunnel with the segmental lining under harmonic plane waves","authors":"Yong-Hong Miao,&nbsp;Jian-Fei Lu","doi":"10.1007/s00707-024-04215-3","DOIUrl":"10.1007/s00707-024-04215-3","url":null,"abstract":"<div><p>In this study, based on the Fourier series expansion and wave function expansion methods, an analytical method for a circular tunnel with segmental lining under seismic waves is established. The surrounding soil of the tunnel is assumed to be a linear elastic medium. The lining of the tunnel is assumed to be composed of several segments and joints. Each joint is simplified as a portion of a cylindrical shell with a small central angle. The segments and joints together thus constitute an equivalent continuous shell (ECS) lining which is described by the cylindrical shell theory. To develop the analytical method, the wave function expansion method is employed to establish the representation for the scattered wave field in the soil. Using the cylindrical shell theory and expanding the quantities and parameters of the ECS lining into Fourier series along the circumferential direction together with introducing the Fourier space convolution-type constitutive relation for the ECS lining, the differential equations for the ECS displacements with variable coefficients are reduced to a linear system of equations for the Fourier components of the ECS displacements. Combining the linear system of equations for the ECS displacements with the representation for the wave field in the soil yields the coupled linear system of equations for the ECS lining and soil. With the proposed analytical method, some results for the response of the tunnel to harmonic seismic waves are presented.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1195 - 1216"},"PeriodicalIF":2.3,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513186","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":"Mechanical manipulation of electromechanical fields in multi-tunnel piezoelectric semiconductor thin film devices by creating localized transverse mechanical field excitations","authors":"Wenjun Wang,&nbsp;Miaomiao Li,&nbsp;Luke Zhao,&nbsp;Feng Jin,&nbsp;Tianhu He,&nbsp;Yongbin Ma,&nbsp;Tao Hou","doi":"10.1007/s00707-025-04225-9","DOIUrl":"10.1007/s00707-025-04225-9","url":null,"abstract":"<div><p>Piezotronics that couples piezoelectricity and semiconducting electronics of piezoelectric semiconductor (PS) materials through stress/strain is emerging field. To accurately depict physical and mechanical properties of two-dimensional (2D) PS thin film devices and comprehensively reveal underlying mechanisms from the perspective of device research, development, and applied science, a general theoretical framework called 2D higher-order phenomenological theory is established for the first time based on three-dimensional (3D) phenomenological theory and Mindlin plate theory, which is viewed as the basis for theoretically analyzing piezotronic effect and working mechanism in novel electronic devices. As the fundamental building blocks of novel piezotronic devices and a particular application example, the Kirchhoff bending deformation-dependent electromechanical fields about PS thin film bimorph devices have been solved successfully from static characteristic analysis viewpoint based on the established 2D phenomenological theory. Subsequently, a systematic investigation about local modulation and evolution of electromechanical fields has been carried out by creating localized external stimuli fields. To some extent, when there are local transverse mechanical load fluctuations within PS thin film devices, various physical fields alter because of deformation–polarization–carrier coupling effects, which affect the interaction between the mechanical deformations, polarization, and mobile charges in PS devices. A greater local transverse mechanical load yields a higher potential barrier and a deeper potential well, impeding the flow of charge carriers with low energy. Additionally, the potential barriers/wells (including their locations, heights/depths, distribution characteristics, and evolution laws) induced by local transverse mechanical loads are also influenced by other numerous physical and geometric parameters, e.g., load intensity, initial state electron and hole concentrations, thin film thickness, and rectangular element center coordinates. For piezotronic applications, the present research results not only provide a theoretical basis and tuning methodology for mechanically manipulating mobile charges related to potential barriers/wells, but also offer more flexibility for developing novel PS thin film devices with flexural deformations and transverse mechanical field excitations.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 2","pages":"1151 - 1177"},"PeriodicalIF":2.3,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143513393","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}