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Jacobi Stability and Restoration of Parameters of the Nonlinear Double Pendulum
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424604178
P. M. Shkapov, V. D. Sulimov, A. V. Sulimov
{"title":"Jacobi Stability and Restoration of Parameters of the Nonlinear Double Pendulum","authors":"P. M. Shkapov,&nbsp;V. D. Sulimov,&nbsp;A. V. Sulimov","doi":"10.1134/S0025654424604178","DOIUrl":"10.1134/S0025654424604178","url":null,"abstract":"<p>The Jacobi stability analysis of the nonlinear dynamical system on base of Kosambi–Cartan–Chern theory is considered. Geometric description of time evolution of the system is introduced, that makes it possible to determine five geometric invariants. Eigenvalues of the second invariant (the deviation curvature tensor) give an estimate of Jacobi stability of the system. This approach is relevant in applications where it is required to identify the areas of Lyapunov and Jacobi stability simultaneously. For the nonlinear system – the double pendulum – the dependence of the Jacobi stability on initial conditions is investigated. The components of the deviation curvature tensor corresponding to the initial conditions and the eigenvalues of the tensor are defined explicitly. The boundary of the deterministic system transition from regular motion to chaotic one determined by the initial conditions has been found. The formulation of the inverse eigenvalue problem for the deviation curvature tensor associated with the restoration of significant parameters of the system is proposed. The solution of the formulated inverse problem has been obtained with the use of optimization approach. Numerical examples of restoring the system parameters for cases of its regular and chaotic behavior are given.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3336 - 3346"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Scattering of SH Guided Waves by a Semicircular Depression and a Linear Crack in a Strip Piezoelectric Medium
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424605822
Enxiang Qu, Hui Qi, Jing Guo, Jingyi Xu, Shangqi Yuan
{"title":"Scattering of SH Guided Waves by a Semicircular Depression and a Linear Crack in a Strip Piezoelectric Medium","authors":"Enxiang Qu,&nbsp;Hui Qi,&nbsp;Jing Guo,&nbsp;Jingyi Xu,&nbsp;Shangqi Yuan","doi":"10.1134/S0025654424605822","DOIUrl":"10.1134/S0025654424605822","url":null,"abstract":"<p>The scattering problem of the steady-state 0-order SH guided wave with a semicircular dip at the boundary of a zoning piezoelectric field and a linear crack in the inner plate is investigated using the complex variable function method, multiple coordinate method, and Green’s function. The guided wave expansion method is utilized in the construction of the SH guided wave, and the multiple mirror method is utilized to fulfill the requirements of stress freedom and electrical insulation. Under the time harmonic load with a semicircular depression in the zonal piezoelectric field, Green’s function represents the fundamental solution. By using the crack cutting method, it is possible to calculate the dynamic stress concentration factor and dynamic stress intensity factor values of the crack tip when both the crack and semicircle sag engage in joint action. The DSCF of a semicircular concave edge and the DSIF of a linear crack are studied in terms of the influence of various piezoelectric parameters, including wave number, crack length, and band domain thickness. The results indicate that it is important to study low frequency, make reasonable selections for piezoelectric parameters, and consider the length of a linear crack when dealing with the interaction between zonal piezoelectric materials with a semicircular sag and a linear crack.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3639 - 3655"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Numerical-Experimental Method of Determination of the Elastic Modulus of a Soil Massif
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424605378
G. N. Gusev, R. V. Tsvetkov, V. V. Epin
{"title":"Numerical-Experimental Method of Determination of the Elastic Modulus of a Soil Massif","authors":"G. N. Gusev,&nbsp;R. V. Tsvetkov,&nbsp;V. V. Epin","doi":"10.1134/S0025654424605378","DOIUrl":"10.1134/S0025654424605378","url":null,"abstract":"<p>The paper presents a numerical and analytical method for determining the modulus of elasticity of the soil, based on experimental results on the natural frequencies of vibration of a pile embedded in a soil mass and their theoretical dependence on the modulus of elasticity of the soil. Experimental results on the dynamic behavior of a pile embedded in a soil mass and numerical results based on the finite element method, which provide the construction of the dependence of the natural frequencies of vibration of the pile on the modulus of elasticity of the soil, are given. As a demonstration of the reliability and efficiency of the method under consideration, a comparison of numerical results on the natural frequencies of vibrations of the pile with different weights at its free end at the found dependence of the modulus of elasticity of the soil and the corresponding experimental results is given.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3390 - 3396"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Stress Intensity Factors at the Top of the Central Semi-Infinite Crack in an Arbitraly Loaded Isotropic Strip
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424603999
K. B. Ustinov
{"title":"Stress Intensity Factors at the Top of the Central Semi-Infinite Crack in an Arbitraly Loaded Isotropic Strip","authors":"K. B. Ustinov","doi":"10.1134/S0025654424603999","DOIUrl":"10.1134/S0025654424603999","url":null,"abstract":"<p>A two-dimensional problem of elasticity theory on an isotropic strip with a central semi-infinite crack is considered. The load in the form of a concentrated force is assumed to be applied at an arbitrary point of the strip. Using invariant mutual integrals and solutions for a strip loaded with bending moments and longitudinal forces applied at infinity, expressions for stress intensity factors (SIF) for the problem under consideration are obtained. The cases of forces applied at the crack faces, at the strip boundaries and at the internal points of the strip are considered. Asymptotic expressions are obtained for the cases of application of forces far from the crack tip and forces applied at the crack faces near its tip. The obtained solutions are shown to coincide with known solutions for special cases: loads in the form of a pair of normal forces applied to the crack faces and forces applied far from the crack tip.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3295 - 3314"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dynamic Analysis of the Perturbed Motion of the Earth’s Pole
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424603707
V. V. Perepelkin
{"title":"Dynamic Analysis of the Perturbed Motion of the Earth’s Pole","authors":"V. V. Perepelkin","doi":"10.1134/S0025654424603707","DOIUrl":"10.1134/S0025654424603707","url":null,"abstract":"<p>Within the framework of the spatial variant of the “deformable Earth-Moon” problem in the solar gravitational field for the viscoelastic Earth model, tidal deformations caused by long-period lunar disturbances are determined. The dynamics of the Earth’s pole motion with Chandler and annual frequencies is analyzed taking into account the obtained expressions for the centrifugal moments of inertia of the Earth. Using numerical integration of the equations of pole motion, it is shown that the found structure of variations in the centrifugal moments of inertia leads to oscillations in the amplitudes of the Chandler and annual harmonics with an 18-year period of precession of the Moon’s orbit.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3327 - 3335"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Type-II Thermoelasticity of Linear Anisotropic Micropolar Media
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424700304
Y. N. Radaev
{"title":"Type-II Thermoelasticity of Linear Anisotropic Micropolar Media","authors":"Y. N. Radaev","doi":"10.1134/S0025654424700304","DOIUrl":"10.1134/S0025654424700304","url":null,"abstract":"<p>In this paper, the mechanics of micropolar elastic solids is extended to a more general thermoelastic media in order to take account of the effect of temperature on their states and mechanical behavior. Since a thermoelastic micropolar medium conducts heat, it is required to include one or another mechanism of thermal propagation in the basic equations of micropolar thermoelasticity. A model of thermoelastic micropolar medium CGNII is developed on ground of the wave principle of heat transfer (i.e., thermal conductivity of the second type known from previous discussions by Green and Naghdi), characterized by zero internal entropy production. All the basic equations of the theory presented in this study are derived from the conventional balance equations of continuum mechanics and the fundamental thermodynamic inequality. Constitutive equations for a linear anisotropic thermoelastic micropolar medium (CGNII) are obtained by using a quadratic energy form for the Helmholtz free energy. Special attention is paid to hemitropic micropolar medium, when the components of one of the fourth rank constitutive pseudotensors demonstrate sensitivity to mirror reflections of three-dimensional space. A closed system of coupled differential equations is given in terms of translational displacement vector, spinor displacement vector and thermal displacement. It is important since can be used in formulations of applied problems of thermomechanics related to the wave heat transfer mechanism in micropolar elastic media.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3408 - 3416"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-Iterative Modeling and Vibration Characteristics Analysis of Multi-Layered Composite Thin-Walled Cylindrical Shell with Intermediate Layer Offset
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424605329
W. J. Pan, K. S. Kong, H. Y. Xu, J. Y. Wang, J. W. Bao, X. J. Zeng, P. Nie
{"title":"Non-Iterative Modeling and Vibration Characteristics Analysis of Multi-Layered Composite Thin-Walled Cylindrical Shell with Intermediate Layer Offset","authors":"W. J. Pan,&nbsp;K. S. Kong,&nbsp;H. Y. Xu,&nbsp;J. Y. Wang,&nbsp;J. W. Bao,&nbsp;X. J. Zeng,&nbsp;P. Nie","doi":"10.1134/S0025654424605329","DOIUrl":"10.1134/S0025654424605329","url":null,"abstract":"<p>The laminated thin-walled cylindrical shell structure can adapt to various complex working environments by using laminated shells made of different materials to generate different dynamic characteristics. Due to deviations in manufacturing accuracy and design requirements during the design and manufacturing process, there may be a certain degree of offset in the intermediate layer. Therefore, studying the free vibration characteristics of multi-layer thin-walled cylindrical shells with intermediate layer offset is of great significance. This article is based on the Love shell theory and Lagrangian equation, and establishes the energy function for the vibration of multi-layer thin-walled cylindrical shells with intermediate layer offset. The natural frequency characteristics are then calculated using the Rayleigh Ritz method. By comparing the natural frequencies and frequency parameters obtained in this article with known literature, the correctness of the model in this article was verified. This article also analyzes the influence of intermediate layer offset on the natural frequency of the entire thin-walled cylindrical shell under different circumferential wave numbers, axial half wave numbers, geometric parameters, and material parameters based on fixed boundary conditions at both ends.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3514 - 3538"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Characterizing Reflection and Refraction Phenomenon at the Interface Between Nonlocal Micropolar Elastic Solid and Viscous Liquid 表征非局部微波弹性固体与粘性液体界面的反射和折射现象
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424605548
Ravinder Kumar,  Priyadarshan, Pawan Kumar, Dinesh Kumar Madan, Neetu Malik
{"title":"Characterizing Reflection and Refraction Phenomenon at the Interface Between Nonlocal Micropolar Elastic Solid and Viscous Liquid","authors":"Ravinder Kumar,&nbsp; Priyadarshan,&nbsp;Pawan Kumar,&nbsp;Dinesh Kumar Madan,&nbsp;Neetu Malik","doi":"10.1134/S0025654424605548","DOIUrl":"10.1134/S0025654424605548","url":null,"abstract":"<p>This study examines the reflection and refraction of longitudinal waves obliquely incident at the interface between a nonlocal micropolar elastic solid half-space and a viscous liquid half-space. By applying appropriate boundary conditions, closed-form expressions for the reflection and refraction coefficients have driven and highlighting their significant dependence on the nonlocality parameter, Lamé’s constants, and the micropolar characteristics of the medium. A specific numerical model graphically illustrates the influence of the incident wave angle on these coefficients. The findings not only confirm certain previously established results, validating the current formulation, but also enhance understanding of wave behavior in complex media.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3571 - 3583"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Rotation and Hall Current on Rayleigh Waves in Transversely Isotropic Visco-Thermoelastic Half-Space with and without Energy Dissipation
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424605020
S. M. Abo-Dahab, Rajneesh Kumar, Saad Althobaiti, M. Saif AlDien, Mnahil M. Bashier, Saurav Sharma
{"title":"Rotation and Hall Current on Rayleigh Waves in Transversely Isotropic Visco-Thermoelastic Half-Space with and without Energy Dissipation","authors":"S. M. Abo-Dahab,&nbsp;Rajneesh Kumar,&nbsp;Saad Althobaiti,&nbsp;M. Saif AlDien,&nbsp;Mnahil M. Bashier,&nbsp;Saurav Sharma","doi":"10.1134/S0025654424605020","DOIUrl":"10.1134/S0025654424605020","url":null,"abstract":"<p>In the current work, Rayleigh waves in a homogeneous transversely isotropic viscoelastic rotating medium with two temperatures are investigated in the presence of the combined effects of magnetic field and Hall currents. The Green-Naghdi Theories of thermoelastic type-II and type-III are the theories of thermoelasticity to which the formulation is applied [1]. Mathematically, secular equations are obtained at the insulated and stress-free limits. Determinant of Rayleigh wave secular equation, Rayleigh wave velocity and attenuation coefficient are computed numerically and depicted graphically for a specific model. Some special cases are also deduced from the present investigation. The results obtained indicate to the strong effect for the rotation and viscosity on the Rayleigh waves propagation phenomenon that agree with the results obtained if the new parameters neglected. A comparison has been made between the current estimation and the previous works obtained by others that indicate to the strong impact for the external parameters on the phenomenon of Rayleigh waves in transversely isotropic visco-thermoelastic either with or without energy dissipation considering rotation and hall current.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3495 - 3513"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Description of Polymer Gel Properties in Framework of Generalized Mooney-Rivlin Model
IF 0.6 4区 工程技术
Mechanics of Solids Pub Date : 2025-03-09 DOI: 10.1134/S0025654424603677
E. Ya. Denisyuk
{"title":"Description of Polymer Gel Properties in Framework of Generalized Mooney-Rivlin Model","authors":"E. Ya. Denisyuk","doi":"10.1134/S0025654424603677","DOIUrl":"10.1134/S0025654424603677","url":null,"abstract":"<p>A polymer gel is considered as a mixture consisting of a highly elastic elastic material and a liquid (solvent) dissolved in it. Based on the generalized Mooney-Rivlin model, an expression for free energy is proposed that describes the deformation behavior and thermodynamic properties of polymer gels. In this model, it is assumed that the Mooney-Rivlin “constants” depend on the concentration of the liquid dissolved in the polymer. From this expression, the constitutive relations for the stress tensor, the chemical potential of the solvent, and the osmotic stress tensor are obtained. Based on these relations, an experimental study of the deformation properties of cross-linked elastomers of various chemical natures swollen in a solvent is performed. In particular, the dependence of the elastic properties of elastomers on the concentration of the solvent is studied and the parameters describing this dependence are determined.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 6","pages":"3282 - 3294"},"PeriodicalIF":0.6,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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