Search Results (51)

A theoretical model of the interaction between a following current and a semi-infinite floating ice sheet under compressive stress near a vertical impermeable wall is developed, within the scope of linear water wave theory, to study the hydroelastic behavior. The conceptual framework defining the buoyant ice structure incorporates the tenets of elastic beam theory. The associated fluid dynamics are governed by strict adherence to the potential flow paradigm. To resolve the undetermined parameters appearing in the Fourier series decomposition of the potential functions, investigators systematically apply higher-order criteria detailing the coupling relationships between modes. The current results are compared with a specific case of results available in the literature, and the convergence analysis of the analytical solution is made for computational accuracy. Further, the free edge conditions are applied at the edge of the floating ice sheet, and the effects of current speed, compressive stress, the thickness of the ice sheet, flexural rigidity, water depth on the strain, displacements, reflection wave amplitude, and the horizontal force on the rigid vertical wall are analyzed in detail. It is found that the higher values of the following current heighten the strain, displacements, reflection amplitude, and force on the wall. The study’s outcomes are considered to benefit not just cold region design applications but also the engineering of resilient floating structures for oceanic and offshore environments, and to the design of marine structures. 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 work analyzes the aero-elastic oscillations of cantilever beams reinforced by carbon nanotubes (CNTs). Four different distributions of single-walled CNTs are assumed as the reinforcing phase, in the thickness direction of the polymeric matrix. A modified third-order piston theory is used as an accurate tool to model the supersonic air flow, rather than a first-order piston theory. The nonlinear dynamic equation governing the problem accounts for Von Kármán-type nonlinearities, and it is derived from Hamilton’s principle. Then, the Galerkin decomposition technique is adopted to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation. This is solved analytically according to a multiple time scale method. A comprehensive parametric analysis was conducted to assess the influence of CNT volume fraction, beam slenderness, Mach number, and thickness ratio on the fundamental frequency and lateral dynamic deflection. Results indicate that FG-X reinforcement yields the highest frequency response and lateral deflection, followed by UD and FG-A patterns, whereas FG-O consistently exhibits the lowest performance metrics. An increase in CNT volume fraction and a reduction in slenderness ratio enhance the system’s stiffness and frequency response up to a critical threshold, beyond which a damped beating phenomenon emerges. Moreover, higher Mach numbers and greater thickness ratios significantly amplify both frequency response and lateral deflections, although damping rates tend to decrease. These findings provide valuable insights into the optimization of CNTR composite structures for advanced aeroelastic applications under supersonic conditions, as useful for many engineering applications. 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

This study presents a closed-form solution for the dynamic response of a sandwich beam subjected to arbitrary impact loading, with a particular focus on energy harvesting from an attached piezoelectric layer. A thin piezoelectric patch is bonded to the bottom surface of the beam to convert mechanical vibrations into electrical energy. The governing equations of motion are derived using Hamilton’s principle, considering a non-symmetric sandwich cross-section and incorporating higher-order shear deformation effects. The state–space method is employed to obtain the exact dynamic response of the beam under impact excitation. The differential equations governing the output voltage and harvested power are solved analytically based on the derived response. The natural frequencies and dynamic responses are validated against classical beam theory, highlighting the significance of shear deformation. Numerical examples are provided to evaluate the generated voltage and energy harvesting efficiency. The results demonstrate the strong potential for energy harvesting from sandwich beam vibrations and elucidate the influence of impact loading conditions, distributed load amplitude, and the geometric dimensions of the beam on the harvested output. Full article

The present research analyzed the nonlinear vibration of a CNTRC embedded in a nonlinear Winkler–Pasternak foundation in the presence of an electromagnetic actuator and mechanical impact. A higher-order shear deformation beam theory was applied to various models, as well as Euler–Bernoulli, Timoshenko, Reddy, and other beams, using a unified NSGT. The governing equations were obtained based on the extended shear and normal strain component of the von Karman theory and a Hamilton principle. The system was discretized by means of the Galerkin–Bubnov procedure, and the OAFM was applied to solve a complex nonlinear problem. The buckling and bending problems were studied analytically by using the HPM, the Galerkin method in combination with the weighted residual method, and finally, by the optimization of results for a simply supported composite beam. These results were validated by comparing our results for the linear problem with those available in literature, and a good agreement was proved. The influence of some parameters was examined. The results obtained for the extended models of the Euler–Bernoulli and Timoshenko beams were almost the same for the linear cases, but the results of the nonlinear cases were substantially different in comparison with the results obtained for the linear cases. Full article

In the framework of lightweight aircraft preliminary design and optimisation, different computational approaches are formulated and assessed for the large-amplitude static aeroelastic response of very-flexible slender thin wings in subsonic incompressible flow at low speed. Starting from either a continuous or a discrete model, either numerical or semi-analytical solutions are derived and compared for several combinations of flow speed and angle of attack. Exploiting the Euler–Bernoulli beam idealisation for the wing structure and its local deformation, non-linear and quasi-linear models are presented where the elastic axis is inextensible and its global displacement is geometrically nonlinear; to this purpose, Hencky’s model is also adopted. Employing modified strip theory for the airload, reduced-order conceptual assessments and parametric evaluations are possible, and the results are shown for the Pazy wing which exhibit excellent agreement with nonlinear higher-fidelity simulations in the literature. Both closed-loop and open-loop solutions are then provided, with the latter being readily resumed from the former in the low-speed limit far away from static aeroelastic divergence. In conclusion, the novel approaches hereby explored demonstrate overall consistency while offering both theoretical insights and practical recommendations for their trust region, especially in terms of the impact and importance of the linear and nonlinear features as well as their effects. Full article

This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupling methods often neglect rotational effects, leading to significant inaccuracies at higher frequencies. Additionally, approaches that implicitly include full dynamics frequently result in redundancy of generalized coordinates, especially at connection points. To address these limitations, the generalized receptance coupling method using Frequency-Based Substructuring is extended to explicitly account for rotational dynamics resulting in a refined GRCFBS approach. This extension enhances both the understanding and prediction of system responses, which are represented through the receptance matrix or Frequency Response Function. Building on Jetmundsen’s foundational work, the proposed framework introduces a practical, generalized formulation that explicitly incorporates full translational and rotational dynamics at each substructure node. This explicit definition provides deeper insights into system behavior, particularly for complex interactions between substructures under weak and strong coupling scenarios at interface points. The Euler–Bernoulli beam theory is employed to model rotational behavior at critical points, yielding reduced-order and explicit receptance matrices for substructures in the coupling process. The methodology’s accuracy and applicability in capturing resonance and anti-resonance modes are validated through two case studies: the coupling of two flexible subsystems and the integration of flexible and rigid components. Results are benchmarked against numerical finite element analysis, and all limitations and potential improvements are discussed. By directly incorporating rotational dynamics directly, this approach enables more reliable dynamic response predictions under multi-directional loading conditions, particularly for vehicle and machinery system design. The GRCFBS method offers a versatile and reliable tool for dynamic system analysis, with significant potential for vibration analysis over a broad frequency range. 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

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials. Full article

In order to reduce the loss of laser point cloud appearance contours by point cloud lightweighting, this paper takes the laser point cloud data of the segment beam of the expressway viaduct as a sample. After comparing the downsampling algorithm from many aspects and angles, the voxel grid method is selected as the basic theory of the research. By combining the characteristics of the normal vector data of the laser point cloud, the top surface point cloud edge data are extracted and the voxel grid method is fused to establish an optimized point cloud lightweighting algorithm. The research in this paper shows that the voxel grid method performs better than the furthest point sampling method and the curvature downsampling method in retaining the top surface data, reducing the calculation time and optimizing the edge contour. Moreover, the average offset of the geometric contour is reduced from 2.235 mm to 0.664 mm by the edge-optimized voxel grid method, which has a higher retention. In summary, the edge-optimized voxel grid method has a better effect than the existing methods in point cloud lightweighting. Full article

In order to study the transmission characteristics of Airy beams in the plasma sheath, the flow field around a hypersonic vehicle was numerically simulated and analyzed based on the Navier–Stokes (N-S) equation and a turbulence model. Then, according to the characteristics of the thickness of the plasma flow field around the supersonic vehicle at the centimeter level, the double fast Fourier transform (D-FFT) algorithm and multi-random phase screens theory were used to predict the propagation characteristics of the Airy beams in the turbulent plasma sheath. The results show that the lower the height and the higher the speed, the smaller the thickness of the plasma sheath shock layer. The refractive index variation in the sheath shock layer has a significant influence on Airy beam transmission. At the same time, the transmission distance and the attenuation factor of the Airy beams also change the transmission quality of the Airy beams. The larger the attenuation factor, the smaller the drift, and the standard deviation decreases with an increase in the refractive index. Airy beams have smaller drifts compared to Gaussian beams and have advantages in suppressing turbulence. Full article

Presented herein is the free vibration analysis of functionally graded beams (FGMs) via higher-order shear deformation theory and an artificial neural network method (ANN). The transverse displacement (w) is expressed as bending (w_b) and shear (w_s) components to define the deformation of the beam. The higher-order variation of the transverse shear strains is accounted for through the thickness direction of the FGM beam, and satisfies boundary conditions. The governing equations are derived with the help of Hamilton’s principle. Non-dimensional frequencies are obtained using Navier’s solution. To validate and enrich the proposed research, an artificial neural network method (ANN) was developed in order to predict the dimensionless frequencies. Material properties and previous studies were used to generate the ANN dataset. The obtained frequency values from the analytical solution and ANN method were compared and discussed with respect to the mean error. In conclusion, the solutions were demonstrated for various deformation theories, and all of the results were thereupon tabularized and visualized using 2D and 3D plots. Full article

This study investigates the dynamic characteristics of natural rubber (NR)/polybutadiene rubber (PBR)-based hybrid magnetorheological elastomer (MRE) sandwich composite beams through numerical simulations and finite element analysis, employing Reddy’s third-order shear deformation theory. Four distinct hybrid MRE sandwich configurations were examined. The validity of finite element simulations was confirmed by comparing them with results from magnetorheological (MR)-fluid-based composites. Further, parametric analysis explored the influence of magnetic field intensity, boundary conditions, ply orientation, and core thickness on beam vibration responses. The results reveal a notable 10.4% enhancement in natural frequencies in SC4-based beams under a 600 mT magnetic field with clamped–free boundary conditions, attributed to the increased PBR content in MR elastomer cores. However, higher magnetic field intensities result in slight frequency decrements due to filler particle agglomeration. Additionally, augmenting magnetic field intensity and magnetorheological content under clamped–free conditions improves the loss factor by from 66% to 136%, presenting promising prospects for advanced applications. This research contributes to a comprehensive understanding of dynamic behavior and performance enhancement in hybrid MRE sandwich composites, with significant implications for engineering applications. Furthermore, this investigation provides valuable insights into the intricate interplay between magnetic field effects, composite architecture, and vibration response. Full article

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler–Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors. Full article