Search Results (13)

The size-dependent out-of-plane vibrational behavior of graphene-based nanoelectromechanical (NEMS) resonators is investigated using a molecular mechanics (MM) finite element approach. Each carbon–carbon (C–C) bond is modeled as an Euler–Bernoulli beam element, with the bending stiffness derived from the bond-angle potential, yielding an equivalent plate flexural rigidity D = (√3/6) kθ. The natural frequencies of the first four vibration modes are computed for square graphene sheets of increasing size with both zigzag (ZZ) and armchair (AC) chirality configurations under simply supported boundary conditions on all four edges. A chirality-induced frequency deviation δ(L) is defined to quantify the difference between ZZ and AC results, and a threshold size L* is identified as the sheet size at which δ falls below 1%. For mode 1, the threshold is L* = 18.5 nm; the values increase monotonically to 24.5 nm, 28.0 nm, and 31.5 nm for modes 2 through 4, indicating that higher modes require larger sheet dimensions before continuum plate theory becomes reliable. A dimensionless frequency parameter Ω = f_MM/f_CT is introduced to directly compare MM predictions with the Kirchhoff plate theory analytical solution, and the AC frequency ratio Ω = f_MM/f_CT is shown to converge toward unity with increasing sheet size. The present results provide quantitative design guidelines for graphene NEMS resonators and establish the minimum device dimensions for which isotropic continuum models yield accurate dynamic predictions. Full article

In karst tunnel engineering, water-filled cavities located above the tunnel crown, under the combined effects of excavation disturbance and hydraulic pressure, are prone to triggering water and mud inrush disasters. The thickness of the water-resisting rock layer is therefore a key factor controlling the stability of the surrounding rock. To address the difficulty in accurately characterizing the mechanical behavior of the crown of horseshoe-shaped tunnels using conventional circular plate or beam models, this study innovatively develops an explicit analytical model for the minimum safe thickness of the water-resisting rock layer based on clamped elliptical thin plate theory and Kirchhoff plate theory, incorporating the influence of cross-sectional geometry. Parametric sensitivity analysis indicates that both karst water pressure and tunnel crown height significantly amplify the required minimum safe thickness, whereas an increase in the tensile strength of the surrounding rock effectively reduces the thickness demand. Specifically, when the karst water pressure increases from 2.5 MPa to 4.5 MPa, the minimum safe thickness rises from 7.5 m to 10.0 m, showing an approximately linear growth trend. The analytical model is further validated through numerical simulations under different “water pressure–thickness” conditions. The results demonstrate that at the calculated recommended thickness, the surrounding rock achieves stable convergence after excavation. High tensile stress and elevated pore pressure zones are mainly concentrated near the tunnel crown, without the formation of through-going tensile failure. Engineering application indicates that the proposed model can provide a quantitative basis for the design of water-resisting rock layer thickness and the assessment of water inrush risk in karst tunnels. Full article

Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of geometric algebra, offering a unified and coordinate-free approach. This work systematically derives the Frenet, Darboux, and Bishop frames within the three-dimensional geometric algebra and employs them to integrate the elastica equation. A concise Lagrangian formulation of the problem is introduced, enabling the identification of Noetherian, conserved, multi-vector moments associated with the elastic system. A particularly compact form of the elastica equation emerges when expressed in the Bishop frame, revealing structural simplifications and making the equations more amenable to analysis. Ultimately, the geometric algebra perspective uncovers a natural correspondence between the theory of free elastic curves and classical beam models, showing how constrained theories, such as Euler–Bernoulli and Kirchhoff beam formulations, arise as special cases. These results not only clarify foundational aspects of elasticity theory but also provide a framework for future applications in continuum mechanics and geometric modeling. Full article

Prestress force dominates the carrying capacity of concrete girders, and is vital for bridge health monitoring. Many vibrational-based methods have been proposed to determine prestress using bridge responses induced by known excitations, which means that they can barely use the normal traffic of in-service bridges as excitation to achieve long-term monitoring. Moreover, most studies are based on beam theory, which may not be precise for plate-like bridges. Hence, this paper establishes a motion equation for a prestressed slab via Kirchhoff’s plate theory and proposes a two-step procedure to assess the prestress and general excitation simultaneously through only bridge responses. The excitation is determined in the first step via the Load Shape function method and used as input for the prestress identification via state-space formulation in the second step. A numerical study on a prestressed plate subjected to a moving load is conducted. Considering different levels of measurement noise and load speed, the proposed method can determine the prestress and moving load with 7.33% and 10.18% error, respectively. A laboratory test on a prestressed box girder subjected to a fixed cyclic load is performed, the prestress and cyclic load are both determined to have good stability, and the errors are under 11.32%. Full article

The limitations associated with traditional screw-based and cable-based deployment mechanisms for space deployable structures, such as deployment stiffness, accuracy, and distance, are effectively overcome by introducing the concept of a variable diameter internal drive device. To enhance stability during the discontinuous surface transition phase inside the tubular structure, a thin-walled flexible beam structure is adopted for the driving deployment unit. The analysis employs the spatial absolute nodal coordinate formulation, integrating the pose states of each node into the global coordinate system. The three-dimensional displacement field and rotational angle changes at different time intervals are obtained using the unit shape function matrix and Kirchhoff theory. Subsequently, a dynamic model of the corresponding spatial nodes is established using the virtual work principle. This significant improvement enhances the dynamic characteristics of the coupled rigid-flexible deformation of the driving deployment unit under radial and axial external forces, surpassing the previously used flexible beam structure. The dynamic simulation analysis is performed using the finite element method and validated through experimental tests. The experimental results confirm the driving deployment unit’s stability and successful achievement of the desired functionalities, as demonstrated by the endpoint displacement, three-dimensional centroid displacement, and trajectory rotation angle. Full article

This study analyzes the composite laminated T-beams using the composite beam and laminated composite plate theories. The theoretical formula was derived assuming that the composite T-beam has one- and two-dimensional (1D and 2D) structures. The 1D analysis was performed according to the Kirchhoff-Love hypothesis, thereby considering only the axial strain to derive a relationship between the strain and displacement. The 2D analysis was performed considering the T-beam as a combination of two composite sheets. The effective stiffness of the beam was derived from the stress-strain and moment-curvature relationships. Furthermore, the deflection of the beam and the stress of each laminate were calculated. A simple support beam, made of AS4/3501-6 carbon/epoxy, was used as a composite laminated T-beam. MSC/NASTRAN finite element software was used for analysis. The accuracy of the theoretical formula and limitations of its use was verified using the finite element analysis. Higher accuracy of the theoretical formula was obtained at a composite beam aspect ratio greater than 15. The formula derived in this study is suitable for thin and long beams. Full article

In our experiments, we develop and test portable multi-element receiver antenna arrays, electrically scanned in order to immediately obtain a recognizable image of subsurface objects. Two quadrature components of the radar return signal are processed with a Kirchhoff backward migration algorithm. Physical theory is used to assess the quality of the holographic image, and the synthetic aperture approach is developed and tested. The parabolic wave equation and Gaussian beam technique are used in order to take into account refraction effects and to suppress specular reflection from the air-ground interface. Laboratory and field tests confirmed the predicted device parameters. Full article

This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis. Full article

This paper presents, for the first time, the mechanical model and theoretical analysis of free vibration of a spinning functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) porous double-bladed disk system. The nanocomposite rotor is made of porous metal matrix and graphene nanoplatelet (GPL) reinforcement material with different porosity and nanofillers distributions. The effective material properties of the system are graded in a layer-wise manner along the thickness directions of the blade and disk. Considering the gyroscopic effect, the coupled model of the double-bladed disk system is established based on Euler–Bernoulli beam theory for the blade and Kirchhoff’s plate theory for the disk. The governing equations of motion are derived by employing the Lagrange’s equation and then solved by employing the substructure mode synthesis method and the assumed modes method. A comprehensive parametric analysis is conducted to examine the effects of the distribution pattern, weight fraction, length-to-thickness ratio, and length-to-width ratio of graphene nanoplatelets, porosity distribution pattern, porosity coefficient, spinning speed, blade length, and disk inner radius on the free vibration characteristics of the FG-GPLRC double-bladed disk system. Full article

Aeronautical stiffened panels composed of thin shells and beams are prone to deformation or buckling due to the combined loading, functional boundary conditions and interface forces between joined parts in the assembly processes. In this paper, a mechanical prediction model of the multi-component panel is presented to investigate the deformation propagation, which has a significant effect on the fatigue life of built-up structures. Governing equations of Kirchhoff–Love shell are established, of which displacement expressions are transformed into Fourier series expansions of several introduced potential functions by applying the Galerkin approach. This paper presents an intermediate quantity, concentrated force at the joining interface, to describe mechanical interactions between the coupled components. Based on the Euler–Bernoulli beam theory, unknown intermediate quantity is calculated by solving a 3D stringer deformation equation with static boundary conditions specified on joining points. Compared with the finite element simulation and integrated model, the proposed method can substantially reduce grid number without jeopardizing the prediction accuracy. Practical experiment of the aircraft panel assembly is also performed to obtain the measured data. Maximum deviation between the experimental and predicted clearance values is 0.193 mm, which is enough to meet the requirement for predicting dimensional variations of the aircraft panel assembly. Full article

The literature on piezoelectric energy harvesting (PEH) is strongly focused on structures, like cantilever beams with piezoceramic layers, due to the fact that they are easily modelled and implemented. As compared to the number of studies dealing with the aforementioned case, research on 2D structures with an attached piezoceramic patch harvester is very limited. Thus, an analytical modeling and experimental validations of a piezo harvester structurally integrated on a thin plate with SFSF (Simply supported-Free-Simply supported-Free) boundary conditions is presented in this paper. The distributed parameter electroelastic model of a harvester bonded to an aluminum plate with both piezo-patch actuators is developed on the basis of the Kirchhoff plate theory and the modal analysis for physical and modal coordinates. This allows to estimate the steady-state value output voltage for each odd mode in the frequency range of 10–300 Hz. Finally, the obtained results for the electroelastic analytical model is experimentally verified on a laboratory stand. Full article

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage. Full article

By simulating the sound field of a round piston transducer with the Kirchhoff integral theorem and analyzing the shape of ultrasound beams and propagation characteristics in a metal container wall, this study presents a model for calculating the echo sound pressure by using the Kirchhoff paraxial approximation theory, based on which and according to different ultrasonic impedance between gas and liquid media, a method for detecting the liquid level from outside of sealed containers is proposed. Then, the proposed method is evaluated through two groups of experiments. In the first group, three kinds of liquid media with different ultrasonic impedance are used as detected objects; the echo sound pressure is calculated by using the proposed model under conditions of four sets of different wall thicknesses. The changing characteristics of the echo sound pressure in the entire detection process are analyzed, and the effects of different ultrasonic impedance of liquids on the echo sound pressure are compared. In the second group, taking water as an example, two transducers with different radii are selected to measure the liquid level under four sets of wall thickness. Combining with sound field characteristics, the influence of different size transducers on the pressure calculation and detection resolution are discussed and analyzed. Finally, the experimental results indicate that measurement uncertainly is better than ±5 mm, which meets the industrial inspection requirements. Full article