{"title":"Mathematical Modeling of Timoshenko Beam Elements Vibrations with due Account for Nonlocal Damping","authors":"V. N Sidorov, M. V. Shitikova, E. S. Badina","doi":"10.1134/S0025654425604859","DOIUrl":"10.1134/S0025654425604859","url":null,"abstract":"<p><b>Abstract</b>—The paper is devoted to the finite-element modeling of dynamic deformation of Timoshenko-type beam elements considering the non-local in time material damping. The shear stiffness and shear damping matrices of the beam element are derived using the requirement of the stationary state of the total energy of the vibrating system. Damping in the model is considered to be non-local in time, i.e., it is assumed that dissipative forces in the system depend both on the current value of the strain rates and on the values of the strain rates during the previous history of the oscillatory process. The Timoshenko beam dynamic problem is solved in local and nonlocal time formulations. An implicit scheme is used to solve the equation of motion. It is shown how the control parameter of the nonlocal model affects the results of numerical simulation of the beam’s dynamic behavior.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035089","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}
Yipei Zeng, Langhong Tang, Zonglai Peng, Yi Fang, Xiujin Zhou, Xiaoyu Sun
{"title":"Flexural-Torsional Coupling Behavior of channel Steel Beam-Column Considering Plate Theory: Theory and Experiment","authors":"Yipei Zeng, Langhong Tang, Zonglai Peng, Yi Fang, Xiujin Zhou, Xiaoyu Sun","doi":"10.1134/S0025654426600959","DOIUrl":"10.1134/S0025654426600959","url":null,"abstract":"<p>Open thin-walled channel steel columns are widely used in modern steel structures; however, their flexural-torsional buckling behavior under combined compression and bending remains insufficiently understood. This paper presents a theoretical model for such columns that accounts for interactive buckling between the web and flanges, developed on the basis of plate theory and the stationary potential energy principle. The governing differential equations are derived using the separation of variables method, yielding a closed-form expression for the critical buckling load. Experimental validation is conducted on three typical channel steel sections with three effective lengths, showing good agreement between theoretical predictions and experimental results. In the parametric study, the critical buckling load exhibits differential sensitivity to web height and flange width: increasing web height is more effective for short columns, whereas flange width becomes increasingly important for slender members. The proposed formula provides a practical reference for the stability design and safety evaluation of open thin-walled channel steel columns.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035282","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}
{"title":"A Spatio-Temporal Nonlocal Hydro-Thermo-Poro-Viscoelastic Model to Laser-Impact Responses of Saturated Cylindrical Unlined Tunnel Based on Klein-Gordon Elasticity and Two-Parameter Mittag-Leffler Fractional Dual-Phase-Lag Heat-Conduction Law","authors":"Chenlin Li, Dechen Wang, Yueqiao Niu, Chang Chang","doi":"10.1134/S0025654426601990","DOIUrl":"10.1134/S0025654426601990","url":null,"abstract":"<p>Laser-assisted rock breaking technology has aroused great attention in tunneling and underground engineering since the high excavation efficiency in hard-rock formations, where the laser-affected zone is small to the micro/nano-meter scale and the heating duration time is short to the pico/femto-seconds. Nevertheless, in such condition, the current theoretical models and impact responses on the hydro-thermo-poro-viscoelastic models neglect the inherent spatio-temporal nonlocal effects of the deformation and thermal lagging behavior. To address the deficiency, this work establishes a novel spatio-temporal nonlocal hydro-thermo-poro-viscoelastic model based on Klein-Gordon nonlocal elasticity and two-parameter Mittag-Leffler fractional dual-phase-lag heat conduction law. The newly developed model is applied to investigate the laser-impact responses of saturated cylindrical unlined tunnel by performing Laplace transformation techniques. The dimensionless results indicate that the decrease of the fractional order parameter in the new heat conduction model enhance the dynamic responses of temperature, deformation and hydraulic stress. The increases of spatio-temporal nonlocal parameter of the Klein-Gordon elasticity model lower the local pore-pressure and delays pore-pressure dissipation.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035284","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}
{"title":"A Laminated Composite Viscoelastic Shaft Element in State Space with Non-Isotropic Damping","authors":"Hrishita Barman, Arghya Nandi, Chandan Datta","doi":"10.1134/S0025654426600844","DOIUrl":"10.1134/S0025654426600844","url":null,"abstract":"<p>This paper formulates a shaft finite element for layered composites with directional viscoelastic damping. The element formulation is performed in a frame spinning with the shaft and accounts for rotary inertia, gyroscopic effect and rotating damping. Along with orthotropic elastic material properties, directional damping properties are considered for longitudinal, transverse and in-plane shear deformations for each layer. This demands the use of an extended Maxwell–Wiechert viscoelastic material model. The parameters of the extended Maxwell–Wiechert model are extracted from frequency dependent loss and storage modulus data using non-linear optimization technique. The material model requires damping variables which are interpolated using standard interpolation functions from nodal damping degrees of freedom. The shaft element, as a consequence, thus has damping degrees of freedom in addition to the standard ones and finite element matrices are generated directly in state-space. Shaft-disk systems with composite shafts of various materials and lay up sequences and angles are analyzed for stability limits. Forward and backward whirl speeds are computed, plotted against spin speed and plotted in Campbell diagrams. Finally, time response analyses to unbalance and step excitations are computed in stable and unstable regions.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035093","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}
{"title":"Love Waves Propagation in an Anisotropic Porous Layer above a Dry Sandy Half-Space with a Parabolic Interface Irregularity","authors":"Kanika Chadha, Dinesh Kumar Madan, Kuldip Singh, Naveen Kumar","doi":"10.1134/S0025654426600418","DOIUrl":"10.1134/S0025654426600418","url":null,"abstract":"<p>The current article examines the transmission of Love waves in a stratified geological microstructure of an anisotropic permeable elastic substrate which is above dry sandy anisotropic elastic semi-infinite medium. It assumes that interface that separates the permeable layer to underlying semi-infinite medium is irregular and models such as irregularities by a parabolic geometry. Theoretical formulation of porous layer is carried out under the theory of Biot’s poroelasticity and the mechanical response of the dry sandy half-space is formulated with modified constitutive relations that have the influence of sandiness. Appropriate boundary conditions of free surface, continuity of displacements and continuity of shear stresses are applied to the traction-free interface for the pair and to the parabolically irregular surface. By using these boundary conditions, a dispersion relation describing the transmission of Love waves at the surface is determined. The dispersion characteristics are numerically calculated and the influence of the porosity, parameter of sandiness and interface irregularity on the phase velocity of waves of Love is investigated. The findings show that the higher porosity the lower the phase velocity is because the effective stiffness of the porous layer is lowered. In a similar manner, the increased sandiness of the half-space results in the even more decreased speed of waves. The existence of the parabolic irregularity adds to the dispersion effects, which change the propagation features highly. The results of this experiment can be applicable in the description of porous and sandy geological structures. It can be considered that the findings of the present work will find application in site-response studies, seismic hazard assessment and geophysical exploration where it is of vital importance to model realistic near-surface media and irregular interfaces.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035216","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}
Guoping Yan, Kewei Jia, Maoshuo Feng, Lan Xiao, Xingan Zhang
{"title":"Dynamic Response Analysis of Non-contacting Mechanical Seals with Random Micro-pores under Rough Surface Morphology","authors":"Guoping Yan, Kewei Jia, Maoshuo Feng, Lan Xiao, Xingan Zhang","doi":"10.1134/S0025654426602041","DOIUrl":"10.1134/S0025654426602041","url":null,"abstract":"<p>To address the dynamic characteristics and leakage issues of non-contact mechanical seals in marine stern shafts under complex operating conditions, this paper proposes a computational method based on Gaussian rough surfaces with random microporous end faces. Numerical simulations of the liquid film distribution on the stationary ring end face were conducted via the MATLAB platform, and a multi-degree-of-freedom dynamic model, accounting for axial vibration and angular misalignment, was established. The fourth-order Runge-Kutta algorithm was employed to analyze the influence of key parameters—such as random micropores, Gaussian surface roughness, and initial clearance—on the dynamic behavior of the seal, alongside the variation laws of liquid film force, contact force, and pressure distribution. The results indicate that the integration of random micropores and Gaussian rough surfaces significantly enhances the hydrodynamic effect, thereby improving lubrication and sealing performance simultaneously. It was found that both spindle speed and initial clearance exhibit a positive correlation with the leakage rate, while the liquid film pressure follows a parabolic distribution in the radial direction and displays topological features corresponding to the micropore structures. Furthermore, the stationary ring’s axial vibration manifests as underdamped oscillatory convergence, whereas the angular vibration shows overdamped monotonic decay, demonstrating robust dynamic stability under external disturbances. This research validates the efficacy of random micropore textures in optimizing end-face lubrication and suppressing leakage, providing a comprehensive theoretical foundation for the structural optimization of non-contact mechanical seals.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035223","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}
{"title":"Geometric Imperfections in CFS Structures: A Comprehensive Review from Initial Measurement to Digital Design","authors":"Yuxiang Shen, Laifu Zhang, Yong Cai","doi":"10.1134/S0025654426602235","DOIUrl":"10.1134/S0025654426602235","url":null,"abstract":"<p>The nonlinear stability of cold-formed steel (CFS) members exhibits high sensitivity to initial geometric imperfections, which introduces uncertainties in the prediction of their ultimate load-bearing capacity. Although measurement technologies have evolved from point-based methods to full-field 3D scanning, current design codes still rely on simplified deterministic assumptions with low-fidelity data. This situation impedes the implementation of advanced analysis in design due to the lack of consensus on input parameters. This paper examines the disparity between the “high-precision measurement capabilities” and the “assimilation capacity of design methods” in the research on CFS geometric imperfections, and posits that bridging this gap necessitates a standardized probabilistic equivalent imperfection framework. Firstly, it assesses laser scanning and photogrammetry for capturing full-field geometric characteristics. Secondly, it tracks the evolution of modeling strategies from single eigenmode approaches to stochastic field models based on the spectral representation method (SRM) and Karhunen–Loève (K-L) expansion, highlighting data-driven methods for generating virtual specimens. Finally, it explores how high-fidelity models facilitate the transition from the implicit direct strength method (DSM) to explicit analysis-based design. In conclusion, the development of standardized probabilistic imperfection databases and their integration into digital twin frameworks are crucial for the next-generation precision prediction of CFS structures.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035442","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}
{"title":"Enhanced Mechanical Performance of Hierarchically Nested Honeycombs","authors":"Dunli Zhang, Guodong Zhou","doi":"10.1134/S0025654426602302","DOIUrl":"10.1134/S0025654426602302","url":null,"abstract":"<p>By mimicking the hierarchical structure of tortoise shells, we propose a nested honeycomb system incorporating gradient arrangements and varied connection topologies. We employed a combination of physical compression tests and finite element analysis to investigate these structures, ensuring model validity through consistent failure mode replication. Results demonstrate that the bio-inspired double-layer design offers superior mechanical properties, increasing energy absorption and specific energy absorption by nearly three times and over 50%, respectively. The H-T-1 model achieved a specific strength more than double that of the baseline. This nested approach provides significant insights for designing lightweight protective structures.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035140","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}
{"title":"Reflection and Transmission of Plane Waves at an Interface between two Non-Local Rotating Micropolar Piezoelectric Solid","authors":"P. Gupta, N. Malik, J. S. Sikka","doi":"10.1134/S0025654426600637","DOIUrl":"10.1134/S0025654426600637","url":null,"abstract":"<p>The focus of the present study is to analyze the impact of rotation and nonlocal parameters on the propagation of the plane waves for various rotation and nonlocal parameter values. For this purpose, we investigated a problem with the reflection and transmission of plane waves at the interface between two different transversely isotropic nonlocal rotating micropolar piezoelectric half-spaces. The nonlocal theory of elasticity is used in a rotating frame to create the governing equations of a nonlocal micropolar piezoelectric material. For the incident CLD wave, there exist three reflected coupled plane waves and three transmitted waves that propagate at different speeds. The expressions for the amplitude ratios and the energy ratios are obtained for reflected and transmitted waves. The graphs of plane wave speeds, amplitude ratios, and energy ratios are plotted against the angle of incidence to show the impact of rotation parameters and non-local parameters. The results show that wave speeds strongly depend on the propagation angle, confirming the anisotropic nature of the medium. Increasing the rotation parameter significantly modifies wave speeds due to inertial effects, while the nonlocal parameter generally decreases them because of scale-dependent softening. Moreover, amplitude and energy ratios vary notably with propagation angle, indicating strong mode conversion and energy transfer at the interface. These findings are useful for designing advanced piezoelectric devices, MEMS, surface acoustic wave devices, and non-destructive testing systems.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035141","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}
{"title":"Propagation and Reflection of Thermoelastic Waves in Nonlocal Solids: A Three-Phase-Lag Framework","authors":"Ammara Saeed, Hashmat Ali","doi":"10.1134/S0025654426600935","DOIUrl":"10.1134/S0025654426600935","url":null,"abstract":"<p>The present study investigates the reflection and propagation of thermoelastic waves in a nonlocal elastic medium within the framework of three-phase-lag (TPL) thermoelasticity. The influence of nonlocal elasticity and thermal phase-lag parameters on coupled primary (CP), coupled thermal (CT), and shear vertical (SV) waves is analyzed in terms of phase speeds, attenuation coefficients, and amplitude ratios at a thermally insulated rigid boundary. The results show that nonlocality introduces strong frequency dependent dispersion, particularly at higher frequencies, and introduces finite cutoff frequencies beyond which wave propagation ceases. The CP and CT waves are significantly affected by both nonlocal and thermal phase lag effects, while the SV wave remains largely insensitive to thermal parameters. Among all modes, the CT wave exhibits the highest sensitivity, with noticeable variations in both phase speed and amplitude ratio due to thermal relaxation. Comparison with the Green Naghdi type II (GN-II) model shows similar behavior for CP and SV waves, whereas the CT wave displays marked differences. The TPL model predicts reduced amplitudes and nonzero attenuation due to thermal phase-lag effects, unlike the non-dissipative GN-II theory. Further comparisons with GN-I, Lord–Shulman (LS), and dual-phase-lag (DPL) models reveal systematic variation of wave characteristics with the degree of thermal relaxation and inclusion of nonlocal effects. The energy conservation condition is satisfied across all incidence angles, confirming the physical consistency of the formulation. The results are relevant to ultrasonic nondestructive testing, thermal shock analysis, and wave propagation in micro- and nano-scale devices.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035281","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}