Archive of Applied Mechanics最新文献

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Nonlinear analysis of a wind turbine tower with a tuned liquid column damper (TLCD) 带调谐液柱阻尼器 (TLCD) 的风力涡轮机塔架的非线性分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-17 DOI: 10.1007/s00419-024-02645-y
Zenon J. G. del Prado, Marcus V. G. Morais, Yuri L. D. Martins, Suzana M. Avila
{"title":"Nonlinear analysis of a wind turbine tower with a tuned liquid column damper (TLCD)","authors":"Zenon J. G. del Prado,&nbsp;Marcus V. G. Morais,&nbsp;Yuri L. D. Martins,&nbsp;Suzana M. Avila","doi":"10.1007/s00419-024-02645-y","DOIUrl":"10.1007/s00419-024-02645-y","url":null,"abstract":"<div><p>Tall wind turbines are structures susceptible to high vibration levels, which may affect their optimal functioning and, ultimately, their overall structural stability. One alternative to minimize undesirable vibrations is to install vibration control devices. Various such devices are documented in the literature, with one noteworthy example being the tuned liquid column damper (TLCD), which is a vertical column filled with a liquid mounted at the top of the structure. When the main structure is dynamically excited, the appropriate TLCD vibrates out of phase with the structure, controlling its dynamic response. In this work, the nonlinear vibrations and control of a wind tower-nacelle-blade system subjected to an external harmonic force are studied. Nonlinear Euler–Bernoulli beam theory, together with the Rayleigh–Ritz method and Hamilton’s principle, are used to obtain a set of nonlinear equations of motion, which are, in turn, solved by the Runge–Kutta method. A TLCD device located at the top of the tower is used to control vibrations. First, the effect of blade rotation on the natural frequencies of the system is studied. Second, resonance curves are obtained to study the effect of blade rotation and the frequency of the external force on the nonlinear vibrations of the tower, and the effect of the TLCD on vibration control is also analyzed. This study provides valuable perspectives on the dynamics of offshore wind turbines, contributing to the development of wind energy systems that are more robust and adaptable.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 9","pages":"2417 - 2430"},"PeriodicalIF":2.2,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717646","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}
引用次数: 0
High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems 带耗散控制的双曲问题高阶精确多子步隐式积分算法
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-15 DOI: 10.1007/s00419-024-02637-y
Jinze Li, Hua Li, Kaiping Yu, Rui Zhao
{"title":"High-order accurate multi-sub-step implicit integration algorithms with dissipation control for hyperbolic problems","authors":"Jinze Li,&nbsp;Hua Li,&nbsp;Kaiping Yu,&nbsp;Rui Zhao","doi":"10.1007/s00419-024-02637-y","DOIUrl":"10.1007/s00419-024-02637-y","url":null,"abstract":"<div><p>This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge–Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step, and thus, the trapezoidal rule is always employed in the first sub-step. This paper demonstrates for the first time that the proposed <i>s</i>-sub-step implicit method with <span>( sle 6 )</span> can reach <i>s</i>th-order accuracy when achieving dissipation control and unconditional stability simultaneously. Hence, this paper develops, analyzes, and compares four cost-optimal high-order implicit algorithms within the present <i>s</i>-sub-step method using three, four, five, and six sub-steps. Each high-order implicit algorithm shares identical effective stiffness matrices to achieve optimal spectral properties. Unlike the published algorithms, the proposed high-order methods do not suffer from the order reduction for solving forced vibrations. Moreover, the novel methods overcome the defect that the authors’ previous algorithms require an additional solution to obtain accurate accelerations. Linear and nonlinear examples are solved to confirm the numerical performance and superiority of four novel high-order algorithms.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 8","pages":"2285 - 2334"},"PeriodicalIF":2.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141648176","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}
引用次数: 0
Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions 非连续边界条件下旋转 FGP-GPLRC 阶梯圆柱壳行波振动特性的半解析建模与分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-14 DOI: 10.1007/s00419-024-02654-x
Ying Zhang, Hongda Xu, Yu Wang, Haoran Liu, Yufan Zhang
{"title":"Semi-analytical modeling and analysis on traveling wave vibration characteristics of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions","authors":"Ying Zhang,&nbsp;Hongda Xu,&nbsp;Yu Wang,&nbsp;Haoran Liu,&nbsp;Yufan Zhang","doi":"10.1007/s00419-024-02654-x","DOIUrl":"10.1007/s00419-024-02654-x","url":null,"abstract":"<div><p>A semi-analytical modeling approach is introduced for investigating the traveling wave vibration characteristics of spinning functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) stepped cylindrical shells under discontinuous boundary conditions. The equivalent material properties of the stepped shell are generated based on the open cell body theory and the Halpin–Tsai micromechanical model. Then, the arc connection approach is introduced, and the artificial spring method is used to model the continuous coupling relationship between the shell segments and discontinuous boundary conditions at the ends of the shell. Based on the first-order shear deformation theory (FSDT), the traveling wave frequency of the shell under discontinuous boundary conditions is solved by the Gegenbauer–Ritz method and the state space method. Finally, the correctness of the semi-analytical modeling approach is confirmed by comparison of the results with the literature and the finite element method. In addition, the effects of various parameters on the frequency of spinning FGP-GPLRC stepped cylindrical shells under discontinuous boundary conditions are discussed.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 10","pages":"2989 - 3015"},"PeriodicalIF":2.2,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141649527","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}
引用次数: 0
Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification 通过机器学习辅助参数识别,加强大块金属成型过程中的损伤预测
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-12 DOI: 10.1007/s00419-024-02634-1
Jan Gerlach, Robin Schulte, Alexander Schowtjak, Till Clausmeyer, Richard Ostwald, A. Erman Tekkaya, Andreas Menzel
{"title":"Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification","authors":"Jan Gerlach,&nbsp;Robin Schulte,&nbsp;Alexander Schowtjak,&nbsp;Till Clausmeyer,&nbsp;Richard Ostwald,&nbsp;A. Erman Tekkaya,&nbsp;Andreas Menzel","doi":"10.1007/s00419-024-02634-1","DOIUrl":"10.1007/s00419-024-02634-1","url":null,"abstract":"<div><p>The open-source parameter identification tool ADAPT (A diversely applicable parameter identification Tool) is integrated with a machine learning-based approach for start value prediction in order to calibrate a Gurson–Tvergaard–Needleman (GTN) and a Lemaitre damage model. As representative example case-hardened steel 16MnCrS5 is elaborated. An artificial neural network (ANN) is initially trained by using load–displacement curves derived from simulations of a boundary value problem—instead of using data generated for homogeneous states of deformation at material point or one-element level—with varying material parameter combinations. The ANN is then employed so as to predict sets of material parameters that already provide close solutions to the experiment. These predicted parameter sets serve as starting values for a subsequent multi-objective parameter identification by using ADAPT. ADAPT allows for the consideration of input data from multiple scales, including integral data such as load–displacement curves, full-field data such as displacement and strain fields, and high-resolution experimental void data at the micro-scale. The influence of each data set on prediction quality is analyzed. Using various types of input data introduces additional information, enhancing prediction accuracy. The validation is carried out with respect to experimental void measurements of forward rod extruded parts. The results demonstrate, by incorporating void measurements in the optimization process, that it is possible to improve the quantitative prediction of ductile damage in the sense of void area fractions by factor 28 in forward rod extrusion.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 8","pages":"2217 - 2242"},"PeriodicalIF":2.2,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-024-02634-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609089","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}
引用次数: 0
Energy finite element model for predicting high frequency dynamic response of taper beams 用于预测锥形梁高频动态响应的能量有限元模型
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-12 DOI: 10.1007/s00419-024-02638-x
Miaoxia Xie, Junhong Han, Xintao Ren, Qianlang Huang, Ling Li, Lixia Li
{"title":"Energy finite element model for predicting high frequency dynamic response of taper beams","authors":"Miaoxia Xie,&nbsp;Junhong Han,&nbsp;Xintao Ren,&nbsp;Qianlang Huang,&nbsp;Ling Li,&nbsp;Lixia Li","doi":"10.1007/s00419-024-02638-x","DOIUrl":"10.1007/s00419-024-02638-x","url":null,"abstract":"<div><p>Taper beams are widely used due to its good damping properties in vibration and noise control field. For dynamic response analysis of taper beams in the high frequency, the energy finite element analysis (EFEA) based on wave theory is the most promising method. However, there is no energy finite element model for taper beams. In this paper, energy finite element model for taper beam is built though two steps. Firstly, the approximate displacement solution of the vibration equation of the taper beam is expressed by the geometry-acoustics approximation method. The expression of the relationship between energy density and power flow of the taper beam is obtained by utilizing the displacement solution. Based on the principle of conservation of energy, the governing equation taken energy density as a variable was derived. Secondly, the stiffness matrix of taper beam element and the solution format of this governing equation are obtained using the Galerkin weighting method, which led to the energy finite element model of the taper beam. Taking a taper beam as an example, the energy finite element model presented in this paper is used to calculate the energy density distribution on the taper beam, and the calculation results are consistent with the finite element calculation results, which proving the correctness of the energy finite element model of the taper beam established in this paper. In order to show the advantages of the EFEA model presented in this paper, a comparison with approximate EFEA model based on constant cross-section elements is performed. The results shown that the EFEA model presented in this paper have higher accuracy and less time consumption, which can reflect the dynamic response characteristics of the taper beam better.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 8","pages":"2335 - 2353"},"PeriodicalIF":2.2,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609166","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}
引用次数: 0
Traveling wave vibration control of rotating functionally graded conical shells via piezoelectric sensor/actuator pairs 通过压电传感器/执行器对旋转功能分级锥壳进行行波振动控制
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-09 DOI: 10.1007/s00419-024-02614-5
Shupeng Sun, Changying Zhao, Dengqing Cao
{"title":"Traveling wave vibration control of rotating functionally graded conical shells via piezoelectric sensor/actuator pairs","authors":"Shupeng Sun,&nbsp;Changying Zhao,&nbsp;Dengqing Cao","doi":"10.1007/s00419-024-02614-5","DOIUrl":"10.1007/s00419-024-02614-5","url":null,"abstract":"<div><p>This paper addresses the traveling wave vibration control of rotating functionally graded material (FGM) conical shells via piezoelectric actuator and sensor pairs. Considering the circumferential initial stresses and Coriolis forces induced by rotation, as well as arbitrary boundary conditions, the electromechanically coupled governing equations of the rotating FGM conical shell with piezoelectric patches are established using the Lagrange equation. The model validation is carried out through a comparative analysis with existing literature. Base on the model, the linear–quadratic regulator controller is designed to suppress the traveling wave vibrations of rotating FGM conical shells considering the participation of multi-vibration modes in the dynamic responses. To evaluate the performance of the controller, free and forced vibrations of rotating FGM conical shells with different rotational speeds, material compositions and excitation positions are investigated in detail. Additionally, five typical piezoelectric sensors/actuators distributions are presented and the effects of piezoelectric patch layout on the control efficiency are discussed.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 10","pages":"2769 - 2791"},"PeriodicalIF":2.2,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570228","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}
引用次数: 0
A novel model on studying the interactions varying thermal and electrical conductivity with two-temperature theory in generalized thermoelastic process 用双温理论研究广义热弹性过程中热导率和电导率相互作用的新模型
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-08 DOI: 10.1007/s00419-024-02643-0
Alwaleed Kamel, Kh. Lotfy, M. H. Raddadi, E. S. Elidy
{"title":"A novel model on studying the interactions varying thermal and electrical conductivity with two-temperature theory in generalized thermoelastic process","authors":"Alwaleed Kamel,&nbsp;Kh. Lotfy,&nbsp;M. H. Raddadi,&nbsp;E. S. Elidy","doi":"10.1007/s00419-024-02643-0","DOIUrl":"10.1007/s00419-024-02643-0","url":null,"abstract":"<div><p>This article investigates the influence of an electromagnetic field on the surface of an elastic semiconductor material in a scenario where deformation occurs in just one dimension. The problem is solved by employing the two-temperature theory to examine the interactions between plasma and thermoelastic waves in a generalized thermoelastic half-space. The study examines the impacts of changing thermal and electrical conductivity. We examine the influence of the initial hydrostatic stress and a small mechanical strain on a photothermal transfer mechanism. The Laplace transform (LT) technique is employed to compute the constitutive relationships, governing equations, and various parameters of the thermo-electro-magnetic medium. To determine the principal physical parameters in the Laplace domain, the interface close to the vacuum is subjected to mechanical forces, temperature constraints, and plasma boundary conditions. The numerical method is employed to inverse the LT and offer comprehensive solutions in the time domain for the primarily investigated physical phenomena. We have performed a visual examination of how the thermoelectric and thermoelastic properties, as well as two-temperature variables of the applied force, affect the distributions of carrier density, force stress, temperature, and displacement components.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 10","pages":"2841 - 2857"},"PeriodicalIF":2.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570229","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}
引用次数: 0
Static, free vibration, and buckling analysis of functionally graded plates using the strain-based finite element formulation 使用基于应变的有限元公式对功能分级板进行静态、自由振动和屈曲分析
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-06 DOI: 10.1007/s00419-024-02635-0
Taqiyeddine Assas, Messaoud Bourezane, Madjda Chenafi
{"title":"Static, free vibration, and buckling analysis of functionally graded plates using the strain-based finite element formulation","authors":"Taqiyeddine Assas,&nbsp;Messaoud Bourezane,&nbsp;Madjda Chenafi","doi":"10.1007/s00419-024-02635-0","DOIUrl":"10.1007/s00419-024-02635-0","url":null,"abstract":"<div><p>In the current investigation, the novelty lies in the formulation of a novel four-node rectangular finite element with six degrees of freedom per node using the strain approach and first-order shear deformation theory, therefore, this is the first article to use this approach to analyze the static, free vibration, and buckling behaviors of functionally graded. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by a simple power law function. The notion of a neutral surface is presented to prevent membrane bending coupling. The displacement functions of the suggested element which possess higher-order expressions, is based on assumed functions of strain that satisfy both rigid body modes and compatibility equations. The performance of the developed element is verified and compared with the published results in the literature and excellent agreement is observed. The influence of the geometrical, material properties, and loading types with different boundary conditions on the bending, free vibration, and buckling analysis of FGM plate are also studied and discussed for the first time using the strain-based finite element formulation.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 8","pages":"2243 - 2267"},"PeriodicalIF":2.2,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570230","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}
引用次数: 0
Bending characteristics of a one-dimensional piezoelectric semiconductor curved beam 一维压电半导体弯曲梁的弯曲特性
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-07-04 DOI: 10.1007/s00419-024-02641-2
Qiaoyun Zhang, Jiahao Xu, Bingbing Wang, Minghao Zhao, Chunsheng Lu
{"title":"Bending characteristics of a one-dimensional piezoelectric semiconductor curved beam","authors":"Qiaoyun Zhang,&nbsp;Jiahao Xu,&nbsp;Bingbing Wang,&nbsp;Minghao Zhao,&nbsp;Chunsheng Lu","doi":"10.1007/s00419-024-02641-2","DOIUrl":"10.1007/s00419-024-02641-2","url":null,"abstract":"<div><p>A one-dimensional beam model with a curved longitudinal axis is established for piezoelectric semiconductors (PSCs) based on the first-order shear deformation theory and a small perturbation assumption of electron concentration. The PSC curved beam model is studied with one fixed end and a transverse force under the other end, and the analytical solutions of shear displacement, flexure displacement, electric potential, and electron concentration perturbation are derived using the differential operator method. The solutions of electromechanical fields are verified by degrading a curved beam into a straight one. According to numerical results, the distributions of electromechanical fields and effects of transverse force, initial electron concentration, and curvature radius are discussed on electromechanical fields. It is shown that the transverse force and curvature radius have an obvious influence on both the electrical and mechanical fields of the curved PSC beam, whereas the initial electron concentration mainly affects electrical quantities.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 10","pages":"2807 - 2818"},"PeriodicalIF":2.2,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546633","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}
引用次数: 0
Reflection of qP waves from an orthotropic layer overlying an orthotropic half-space: Explicit formulas for the reflection coefficients 从覆盖在正交半空间上的正交层反射 qP 波:反射系数的显式公式
IF 2.2 3区 工程技术
Archive of Applied Mechanics Pub Date : 2024-06-28 DOI: 10.1007/s00419-024-02625-2
Vu Thi Ngoc Anh, Pham Chi Vinh
{"title":"Reflection of qP waves from an orthotropic layer overlying an orthotropic half-space: Explicit formulas for the reflection coefficients","authors":"Vu Thi Ngoc Anh,&nbsp;Pham Chi Vinh","doi":"10.1007/s00419-024-02625-2","DOIUrl":"10.1007/s00419-024-02625-2","url":null,"abstract":"<div><p>There has been a considerable number of studies on the reflection and transmission of plane waves in anisotropic elastic half-spaces. However, the obtained formulas of the reflection and transmission coefficients are implicit, and the numbers of reflected and transmitted waves are undetermined. In this paper, the reflection of qP waves from an orthotropic elastic layer overlying an orthotropic elastic half-space is considered. It has been proved that an incident qP wave <i>always</i> creates two reflected waves, one qP wave and one qSV wave, and the reflection angle of the reflected qP wave is equal to the incident angle. Based on this fact, formulas for the reflection coefficients have been derived by using the transfer matrix method along with the effective boundary condition technique. It should be noted that, different from the previously obtained <i>implicit</i> formulas, these formulas are totally explicit functions of the incident angle, the (dimensionless) layer thickness and the material parameters of the half-space and the layer. Since the obtained formulas are totally explicit, they will be useful in various practical applications, especially in nondestructively evaluating the mechanical properties of deposited layers.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"94 8","pages":"2085 - 2099"},"PeriodicalIF":2.2,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506869","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}
引用次数: 0
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