Search Results (36)

In this study, a high-order Galerkin–Numerov approach is presented to solve the transient vibration problem of anisotropic Kirchhoff plates supported by a uniform Vlasov foundation. A discretization of the governing fourth-order plate equation is derived based on a mixed boundary value problem and a hybrid Hermite–sine Galerkin formulation, which maintains the C1-continuity properties of classical plate theory. The resulting reduced-order modal system is integrated in time with the Numerov scheme, which is fourth-order accurate, and has a small numerical dispersion and good phase-preserving properties for oscillatory dynamics. The proposed methodology is evaluated using stability and convergence tests and parametric investigations. The fourth-order temporal convergence and rapid spectral-like spatial convergence of the numerical results are validated, and the long-time accuracy and robustness of the formulation is confirmed by the negligible phase error and bounded energy drift. The results from the parametric study indicate that the thickness of the plates and the stiffness of the Winkler foundation are the two most important mechanisms for vibration suppression, while the orthotropic coupling and the Vlasov shear interaction have substantial effects on the modal redistribution and transient deformation properties. The proposed method is compared with the conventional lower-order integration schemes, and it is observed that the method gives better phase fidelity and computational efficiency, and it is possible to predict the vibration amplitude and vibration timing accurately. In addition to the numerical benefits, the framework also provided physical insights on the coupled effect of anisotropy, foundation interaction and boundary restraint. The suggested model is directly applicable for composite floor systems, aerospace panels, foundation supported slabs, biomechanical plate analogs, etc., and smart vibration control platforms. This work thus lays the groundwork for future studies of nonlinear behavior, adaptive foundations and digital twin simulation of structural systems and presents a strong and scalable computational tool for the study of plate–foundation dynamics. Full article

Studies of third-order shear-deformation theory (TSDT) and an advanced shear coefficient for thick-walled functionally graded material (FGM) spherical shells subjected to thermal vibrations triggered by sinusoidal temperature are presented. The nonlinear TSDT and linear and nonlinear shear coefficient can be converted into fully homogeneous equation algorithms under the sinusoidal form of free vibrations to obtain the fundamental natural frequency by using Newton’s numerical method. Then, the generalized differential quadrature (GDQ) method can be used to prepare dynamic discrete equations of motion triggered by sinusoidal temperature field in thick FGM spherical shells for materials SUS304 and Si₃N₄. The Young’s modulus expressed as a power-law function of thick FGM spherical shells is considered and subjected to applied thermal load. The response results of thermal stress and center displacement are compared for the cases of linear and nonlinear advanced shear coefficient, and simply and fully homogeneous equation algorithms, respectively. The practical insights for temperature effect considered in the calculation of stress and displacement are very clear and practical for FGM structures with geometries of spherical shells. The power-law function property of FGMs can be used under high temperature for four-sided simply supported constraints. Full article

This paper analyzes the vibrational characteristics of a novel sandwich plate configuration composed of an auxetic honeycomb (AH) core and laminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets, hereafter referred to as the SD-AuCNT plate. Based on Reddy’s third-order shear deformation theory (SDT), which accurately accounts for transverse shear effects without requiring shear correction factors, the equations of motion are derived using Hamilton’s principle and subsequently solved using a pb-2 Ritz formulation combined with the Newmark time integration scheme for dynamic response analysis. By combining an auxetic core with negative Poisson’s ratio characteristics and laminated FG-CNTRC face sheets featuring tailored CNT distribution patterns and orientations, the hybrid SD-AuCNT plate can improve structural stiffness, energy absorption, and dynamic performance; however, it has not been thoroughly investigated in the existing literature. After verifying the accuracy of the proposed computational procedure, the effects of auxetic core geometry, CNT distribution patterns, thickness ratios, and boundary conditions on the natural frequencies and transient responses of the plate are comprehensively investigated. The results provide new insights into the dynamic behavior of advanced sandwich plates and offer practical guidance for the design of high-performance lightweight structures in aerospace, marine, defense, and other engineering applications. Full article

This paper presents an analytical investigation of the free vibration behavior of fiber metal laminate (FML) beams with three types of boundary conditions, considering the temperature-dependent properties and the interfacial slip. In the proposed model, the non-uniform temperature field is derived based on one-dimensional heat conduction theory using a transfer formulation. Subsequently, based on the two-dimensional elasticity theory, the governing equations are established. Compared with shear deformation theories, the present solution does not rely on a shear deformation assumption, enabling more accurate capture of interlaminar shear effects and higher-order vibration modes. The relationship of stresses and displacements is determined by the differential quadrature method, the state-space method and the transfer matrix method. Since the corresponding matrix is singular due to the absence of external loads, the natural frequencies are determined using the bisection method. The comparison study indicates that the present solutions are consistent with experimental results, and the errors of finite element simulation and the solution based on the first-order shear deformation theory reach 3.81% and 3.96%, respectively. At last, the effects of temperature, the effects of temperature degree, interface bonding and boundary conditions on the vibration performance of the FML beams are investigated in detail. The research results provide support for the design and analysis of FML beams under high-temperature and vibration environments in practical engineering. Full article

This study investigates the free vibration behaviors of functionally graded (FGM) plates with a porous structure, resting on a Kerr-type elastic foundation, while accounting for thermal effects and complex material property distributions. Within the framework of higher-order shear deformation theory (HSDT), two novel shape functions are introduced to accurately model transverse shear deformation across the plate thickness without employing shear correction factors. These functions are constructed to satisfy shear stress boundary conditions and capture nonlinear effects induced by material gradation and porosity. A variational formulation is developed to describe the dynamic response of FGM plates in a thermo-mechanical environment, incorporating temperature-dependent material properties and three porosity distributions: uniform, linear, and trigonometric. Numerical solutions are obtained using in-house MATLAB codes, allowing complete control over the formulation and interpretation of the results. The model is validated through detailed comparisons with existing literature, demonstrating high accuracy. The findings reveal that the porosity distribution pattern and gradient intensity significantly influence natural frequencies and mode shapes. The trigonometric porosity distribution exhibits favorable dynamic performance due to preserved stiffness in the surface regions. Additionally, the Kerr-type elastic foundation enables fine tuning of the dynamic response, depending on its specific parameters. The proposed approach provides a reliable and efficient tool for analyzing FGM structures under complex loading conditions and lays the groundwork for future extensions involving nonlinear, time-dependent, and multiphysics analyses. Full article

Elastic solutions of a differential system of vibrational responses of a bidirectional porous functionally graded plate (BPFG) are described by employing high-order normal and shear deformation theory, in the present study. Natural frequency values are computed for the plates with simply supported boundary conditions and taking into consideration the thickness stretching effect. Grading of the effective material property for the BPFG plate is defined according to a power-law distribution. Navier’s approach is applied to determine the governing differential equations solution of the studied model derived by Hamilton’s principle. To confirm the reliability of the solution and the model accuracy, a comparison study with various studies that are presented in the literature is carried out. Numerical illustrations are presented to discuss the influences of the plate geometry, the porosity, the volume fraction distribution, and the nonlocality on the vibration behaviors of the model. The dynamic responses of unidirectional and bidirectional porous functionally graded nanoplates are analyzed in detail, employing two parametric numerical examples. Numerical results show the sensitivity of frequencies to the studied parametric factors and their dependence on porosity and nonlocality coefficients. Frequencies of BPFG with uneven/even distribution porosity decrease when increasing the transverse and axial power-law indexes ($P\ne 0$), and the same effect appears when increasing the nonlocal parameter. Full article

This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams demonstrates that HSDT yields more accurate predictions than the Classical Beam Theory (CBT), especially for thick beams; for instance, at a span-to-thickness ratio of h/L = 12.5, HSDT predicts increases of approximately 6%, 7%, and 12% in displacement, voltage, and harvested power, respectively, compared to CBT. Parametric studies further reveal that increasing the load velocity significantly enhances the strain rate in the piezoelectric layer, resulting in higher voltage and power output, with the latter exhibiting quadratic growth. Moreover, increasing the material gradation index n reduces the beam’s effective stiffness, which amplifies vibration amplitudes and improves energy conversion efficiency. These findings underscore the importance of incorporating shear deformation and material gradation effects in the design and optimization of piezoelectric energy harvesting systems using FGM beams subjected to dynamic loading. Full article

Laminate plate and shell structures with symmetric cross-ply configurations are widely used due to their high stiffness-to-weight ratio. However, conventional lamination theories rely on simplifying assumptions that may introduce inaccuracies. This study evaluates the predictive capability of such theories by integrating multiple micromechanics models with First-Order Shear Deformation Theory (FSDT), and comparing the results against voxel-based finite element modeling (VB-FEM), which serves as a high-fidelity numerical reference. A range of models—including Voigt–Reuss, Chamis, Halpin–Tsai, Bridging, and two iterative isotropized formulations—are assessed for unidirectional laminae with fiber volume fractions from 40% to 73%. Quantitative comparison reveals that while all models predict the longitudinal modulus accurately, significant deviations arise in predicting transverse and shear properties. The Bridging Model consistently yields the closest agreement with VB-FEM across all five elastic constants, maintaining accuracy even at high volume fractions where the modified Halpin–Tsai model begins to fail. Discrepancies in micromechanics-based lamina properties propagate to laminate-level stiffness predictions, highlighting the critical role of model selection. These findings establish VB-FEM as a valuable tool for validating analytical models and guide improved modeling strategies for laminated composite design. Full article

This research examines the free vibration characteristics of composite ring-like structures enhanced with carbon nanotubes (CNTs), taking into account the effects of CNT agglomeration. The structural framework comprises two concentric composite rings linked by elastic springs, creating a coupled beam ring (CBR) system. The first-order shear deformation theory (FSDT) is applied to account for transverse shear deformation, while Hamilton’s principle is employed to formulate the governing equations of motion. The effective mechanical properties of the composite material are assessed with regard to CNT agglomeration, which has a significant impact on the elastic modulus and the overall dynamic behavior of the structure. The numerical analysis explores the influence of porosity distribution, boundary conditions (BCs), and the stiffness of the springs on the natural vibration frequencies (NVFs). The results demonstrate that an increase in CNT agglomeration leads to a reduction in the stiffness of the composite, consequently decreasing the NVFs. Furthermore, asymmetric porosity distributions result in nonlinear fluctuations in NVFs due to irregularities in mass and stiffness, whereas uniform porosity distributions display a nearly linear relationship. This study also emphasizes the importance of boundary conditions and elastic coupling in influencing the vibrational response of CBR systems. These findings offer significant insights for the design and optimization of advanced composite ring structures applicable in aerospace, nanotechnology, and high-performance engineering systems. Full article

The incorporation of waste fluid catalytic cracking (FCC) catalysts (WFCs) into asphalt pavements represents an effective strategy for resource utilization. However, the influences of the composition of the waste catalyst and its surface characteristics on the performance of asphalt mortars are still unclear. Herein, five WFCs were selected as powder filler to replace partial mineral powder (MP) to prepare five asphalt mortars. The diffusion behaviors of asphalt binder on the components of WFCs were investigated based upon molecular dynamic simulation, as was the interfacial energy between them. The adhesion work values between asphalt and WFCs were evaluated based upon the surface free energy theory. A dynamic shear rheology test and multiple stress creep recovery test on the WFC asphalt mortar were also conducted. Furthermore, the gray correlation analysis (GCA) method was employed to analyze the correlation between the diffusion coefficient and interfacial energy with the performance of WFC asphalt mortar. The results showed that the asphalt exhibited a low diffusion coefficient and high interfacial energy with the alkaline components of WFCs. The adhesion work values between asphalt and WFCs are higher than those with MP. The addition of WFCs can enhance the anti-rutting property of asphalt mortar significantly. Among the five WFCs, 2# exhibited the best improvement effect on the anti-permanent deformation ability of asphalt mortar, which may be due to its large specific surface area and moderate pore width. The GCA results suggest that the diffusion coefficient and interfacial energy strongly correlated with the performance of asphalt mortar, with an order of adhesion > permanent deformation resistance > rutting resistance. This study provides both theoretical and experimental support for the application of WFCs in asphalt materials. Full article

CrCoNi medium-entropy alloys (MEAs), characterised by their high configurational entropies, have become a research hotspot in materials science. Recent studies have indicated that MEAs exhibit short-range order (SRO), which affects their deformation mechanisms. In this study, the micro-mechanisms of SRO within the framework of mesoscale continuum mechanics are mathematically evaluated using an advanced, non-local crystal plasticity constitutive framework. Furthermore, a crystal plasticity model considering the impact of SRO on slip is established. By combining nanoindentation simulations and multi-level grain model tensile simulations, the load–displacement and stress–strain curves demonstrated that the presence of SRO increases the hardness of MEAs. More specifically, considering the distribution of shear strain and geometrically necessary dislocations, the heterogeneity of MEAs increases with an increase in the degree of SRO. This study not only enriches the crystal plasticity theory but also provides references for the microstructure and performance regulation of high-performance multi-level grain structure materials. Full article

The objective of the present paper is to demonstrate the effects of shear deformation and large deflections on the piezoelectric materials and structures which often serve as substrate layers of multilayer composite sensors and actuators. Based on a displacement-unified high-order shear deformation theory and the von Kármán geometric nonlinearity, a general theory (governing equations and associated boundary conditions) for the analysis of piezoelectric beams is developed using Hamilton’s principle. Nonlinear effects due to the coupling between extensional and bending responses in beams with moderately large rotations but small strains are included. A bending problem for a piezoelectric beam is solved analytically, and the obtained results are compared to the results available in the literature. The numerical results show that both shear deformation effects and von Kármán geometric nonlinearity have a stiffening effect and therefore reduce the displacements. The influence of geometric nonlinearity is more prominent in the case of thin beams, while the effects of shear deformation dominate in the case of thick beams. The proposed unified methodology for the analysis of bending problems is independent of the thickness of the piezoelectric beam. Full article

This paper presents numerical investigations into the free vibration properties of a sandwich composite plate with two fiber-reinforced plastic (FRP) face sheets and a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) core made of functionally graded carbon nanotube-reinforced composite resting on Winkler/Pasternak elastic foundation. The material properties of the FG-CNTRC core are gradient change along the thickness direction with four distinct carbon nanotubes reinforcement distribution patterns. The Hamilton energy concept is used to develop the equations of motion, which are based on the high-order shear deformation theory (HSDT). The Navier method is then used to obtain the free vibration solutions. By contrasting the acquired results with those using finite elements and with the previous literature, the accuracy of the present approach is confirmed. Moreover, the effects of the modulus of elasticity, the carbon nanotube (CNT) volume fractions, the CNT distribution patterns, the gradient index p, the geometric parameters and the dimensionless natural frequencies’ elastic basis characteristics are examined. The results show that the FG-CNTRC sandwich composite plate has higher dimensionless frequencies than the functionally graded material (FGM) plate or sandwich plate. And the volume fraction of carbon nanotubes and other geometric factors significantly affect the dimensionless frequency of the sandwich composite plate. Full article

In order to investigate the effect of pre-tension on the anchoring and crack-arresting effect of rockbolts, a theoretical model of stress intensity factor at the crack tip in anchored surrounding rock was established using fracture mechanics theory. An expression for the difference in stress intensity factor due to axial force on the rockbolt was derived, exploring the influence of pre-tension on the stress intensity factor of cracks. A numerical model of anchored crack specimens was developed using UDEC (V6.0) software to simulate and analyze the mechanical performance and damage characteristics of specimens anchored with different pre-tension. The results indicate that the difference in stress intensity factor of cracks is positively correlated with pre-tension. High-pre-tensioned rockbolts can effectively reduce the stress intensity factor of cracks. Prestressed rockbolts can alter the failure mode of rock masses from shear failure along pre-existing cracks to tensile splitting failure. The application of high pre-tension significantly enhances the strength of the rock mass, reducing both the damage degree and the number of internal cracks. After anchoring with high-pre-tensioned rockbolts, the peak strength and elastic modulus of the crack specimens increased by 22.5% and 31.9%, respectively, while damage degree decreased by 17.4%, the number of shear cracks decreased by 22.6%, and the number of tensile cracks decreased by 42.9%. The pre-tensioned rockbolt method proposed in this study was applied to the support of roadway widening. Field monitoring data indicated that the axial force of the rockbolts in the test section generally exceeded 60 kN, effectively controlling the deformation of the roadway surrounding the rock. The convergence of the two sides decreased by 22%, and borehole inspections showed a significant reduction in internal cracks. The research results provide a theoretical basis for controlling the discontinuous deformation of deep broken surrounding rock roadways. Full article

The density functional theory (DFT) framework in the generalized gradient approximation (GGA) was employed to study the mechanical, dynamical, and thermodynamic properties of the ordered bimetallic Fe-Pt alloys with stoichiometric structures Fe₃Pt, FePt, and FePt₃. These alloys exhibit remarkable magnetic properties, high coercivity, excellent chemical stability, high magnetization, and corrosion resistance, making them potential candidates for application in high-density magnetic storage devices, magnetic recording media, and spintronic devices. The calculations of elastic constants showed that all the considered Fe-Pt alloys satisfy the Born necessary conditions for mechanical stability. Calculations on macroscopic elastic moduli showed that Fe-Pt alloys are ductile and characterized by greater resistance to deformation and volume change under external shearing forces. Furthermore, Fe-Pt alloys exhibit significant anisotropy due to variations in elastic constants and deviation of the universal anisotropy index value from zero. The equiatomic FePt showed dynamical stability, while the others showed softening of soft modes along high symmetry lines in the Brillouin zone. Moreover, from the phonon densities of states, we observed that Fe atomic vibrations are dominant at higher frequencies in Fe-rich compositions, while Pt vibrations are prevalent in Pt-rich. Full article