Archive of Applied Mechanics最新文献

In this research, the thermally induced vibration of the plates on the elastic foundation has been investigated. The plate is made of functionally graded materials (FGMs) that is graded along the thickness. All mechanical and thermal properties dependent on temperature are taken into account. To apply the temperature dependence of thermomechanical properties, the well-known Touloukian equation is used. The two-parameter elastic foundation, Winkler–Pasternak, is considered to be linear, isotropic, and homogeneous. The general formulation and equations governing the phenomenon of thermally induced vibration have been written under the assumptions of linear uncouple thermoelasticity. The one-dimensional transient heat conduction equation has been discretized with the help of the finite element method in the direction of thickness, and it has been solved over time by applying the Crank–Nicolson method. Also, the thermally induced force and moment resultants in each time step have been calculated based on the temperature profile. To obtain the equations of motion, Hamilton’s principle based on the first-order shear deformation theory has been used, and the obtained equations and boundary conditions have been discretized by applying the generalized differential quadrature (GDQ) method and solved by using Newmark time marching scheme.

The applications of piezoelectric materials in the field of smart structures have received significant attention from both the communities of science and engineering. Numerous experimental studies have been carried out to endow smart structures with good flexibility. The flexible/stretchable piezoelectric materials are developed to fit this emerging trend. Generally, these materials undergo significant deformation before reaching fracture failure, and they often exhibit a stress-softening phenomenon during the deformation process. However, the traditional linear constitutive model, typically used for rigid piezoelectric ceramics, continues to dominate theoretical and modeling processes in many scenarios. Existing nonlinear constitutive models usually introduce additional coefficients besides elastic, piezoelectric, and dielectric coefficients. Determining these coefficients requires a substantial number of experiments. In this work, based on a Neo-Hookean material model and electromechanical theory, a novel model for flexible piezoelectric material considering large deformation has been established. In contrast with existing models, the present model describes the nonlinear behavior of flexible piezoelectric material without the need for introducing additional parameters. Furthermore, this model exhibits a quadratic dependence of stress on the electric field. To facilitate practical applications, the constitutive model has been implemented using the commercial simulation software ABAQUS through a user subroutine. The accuracy of the subroutine is validated by comparing simulations with analytical solutions for uniaxial stretching of a flexible piezoelectric ribbon. Several numerical examples are followed to demonstrate the robustness of the elements. The proposed model offers a valuable tool for the analysis and design of flexible piezoelectric material.

Dynamic damage constitutes a significant factor influencing engineering safety. Constitutive models predicated on statistical distribution demonstrate a capability in accurately representing the dynamic failure process of rocks. This study employs the high-strain-rate Hoek–Brown criterion to delineate the strength characteristics of rock microelements, subsequently establishing a novel dynamic statistical damage constitutive model based on statistical damage theory. Firstly, the model’s validity was corroborated using test data from different rocks (sandstone, granite, and marble) under varying confining pressure conditions. Subsequently, the influence of parameters F₀ and m on the stress–strain curve was discussed. Finally, the relationships between the Hoek–Brown criterion parameters ((sigma_{{cdot{varepsilon }}}), (m_{{dot{varepsilon }}})) and the strain rate for different rocks were analyzed. The findings suggest that the model effectively characterizes the stress–strain relationship during the dynamic failure process.

In this paper, new analytic solutions for the free vibration analysis of passive constrained layer damping (PCLD) beams, which are widely used in engineering to suppress vibrations and noise, are shown based on the symplectic method. The Hamiltonian-based governing equations and the new boundary condition expressions of PCLD beams are established by the original vector and its dual vector obtained by variation of the quasi Lagrangian function. The explicit solutions are obtained in the symplectic space in a direct, rigorous way without any trail functions under various boundary conditions. To verify the accuracy of the present method, the frequency parameters and loss factors of PCLD beams are compared with the results available in the literature. Comprehensive results under various boundary conditions are also tabulated for further benchmark use.

The primary objective of this paper is to identify periodic orbits for solar sails within the oblate Earth-Moon Circular Restricted Three-Body Problem (CR3BP). Incorporating solar acceleration into the Earth-Moon system modifies the governing orbital equations, transforming the traditional CR3BP from an autonomous to a non-autonomous system. As a result, the procedure for identifying periodic orbits diverges from the conventional autonomous CR3BP method. Thus, this paper introduces a novel methodology to identify new periodic Halo and Lyapunov orbits within the non-autonomous CR3BP. Our proposed approach comprises four hierarchical steps: first, a surface of section simulation (Poincaré map) is conducted to obtain an initial approximation of the orbital state vector within the autonomous CR3BP. Second, a periodic orbit correction algorithm is developed using the autonomous CR3BP equations to acquire precise initial conditions. In the third step, initial conditions for solar sail periodic orbits are derived by applying the initial conditions of autonomous CR3BP periodic orbits as inputs to the periodic orbit correction algorithm, which is now executed using non-autonomous CR3BP equations. In the final step, a family of orbits is generated by gradually increasing the sail's characteristic acceleration. Our work addresses limitations in previous studies that relied on initial guesses derived solely from the unperturbed autonomous CR3BP reported in earlier research, which often resulted in the missing of numerous solar sail periodic orbits in the non-autonomous system. This approach enables the discovery of new periodic orbits within the Earth-Moon system, accounting for perturbations from the oblate primaries, including zonal harmonic terms from ({j}_{2}) to ({j}_{6}). The methodology is validated through simulations of solar sail Lyapunov and Halo orbits, offering a comprehensive understanding of the Earth-Moon CR3BP under non-autonomous conditions.

Bistable laminates (BSLs) are prone to vibration and dynamical snap-through behavior (STB) under the action of external environment. To control them, active vibration control using smart material is a terrific choice because it can minimize the impact on the stable configuration and properties of bistable laminate. This paper focuses on the active vibration control of rectangular asymmetric and anti-symmetric cross-ply bistable laminates under impact loadings using piezoelectric macro-fiber composite (MFC) whose size and position of paste are optimized instead of pasting randomly or middle of the laminate. The bistable laminated structures are simply supported at four selected points, while all the edges of them are free. With the aid of energy principle, governing equations of vibration of the bistable laminated structure are acquired with regard to two principal curvatures. The accuracy and validation of present formulation are verified by comparison studies of stable configurations and snap-through voltage of MFC. Then, the positions and geometric dimensions of piezoelectric macro-fibers are optimized by using genetic algorithm. The active vibration control of the bistable laminated structures subjected to step loading, decreasing loading, increasing loading and sinusoidal loading is studied for various control gains, geometries and different simply supported points.

In this study, a general method is developed for the torsional vibration of non-circular-shaped nanorods with varying boundary conditions using second-order strain gradient theory. In most of the studies in the literature, the cross section of the rods is considered to be circular. The reason for this is that the use of warping function is inevitable when the cross section geometry is not circular. For circular cross sections after torsion, the warping is very small and is considered to be non-existent. For non-circular sections, cross section warping should be taken into account in mathematical calculations. The cross section geometry is different from circular in this study, and the boundary conditions are not rigid, contrary to most studies in the literature. In this paper, the second-order strain gradient theory and the most general solution method are discussed. In some specific cases, it is possible to transform the problem into many studies found in the literature. The correctness of the algorithm is tested by comparing the resulting solutions with closed solutions found in the literature. The influence of some variables on the torsional frequencies is illustrated by a series of graphical figures, and the superiority of the applied method is summarized.

This study presents a comprehensive bending analysis of carbon nanotube-reinforced (CNTR) sandwich plates with varying stacking sequences, utilizing a non-polynomial zigzag theory based on the secant function. The secant function implicitly accommodates higher-order bending deformation with lesser computational costs and encompassing the cross-sectional warping. Principle of virtual work in conjunction with Navier’s solution methodology is used to develop the governing differential equation for the plate and to propose the solution of the system of equation, respectively. The analysis considers transverse deflection, normal stresses, in-plane shear stress, and transverse shear stresses to capture the complex behavior of CNTR sandwich composite plate structures. Different parametric studies are performed, exploring the effects of various reinforcement distributions of carbon nanotubes (CNTs) within the CNTR sandwich plate face sheet layers mainly, UD and FG. The superimposition of non-polynomial shear deformation theory based on secant function with zigzag functions provides accurate and efficient solutions, addressing the intricate stress distribution and deformation characteristics of CNTR sandwich plate. The findings offer valuable insights for the optimal design and application of CNTR sandwich plates in engineering fields, ensuring enhanced performance and structural integrity.

In the present study, maximum principal stress (MPS) criterion is incorporated into the reinforced isotropic solid (RIS) model to investigate the fracture behavior of orthotropic materials. Cracks are assumed along and across to the fibers in the linear elastic fracture mechanics context. Our experimental observations have shown that in macro point of view cracks in orthotropic materials always occur and grow between the fibers in the isotropic matrix media of orthotropic materials. When the composites are subjected to the pure mode I of loading which is across the fibers, the fibers do not react to the applied load. It means that they do not have effects on load bearing. On the other hand, when the mixed mode I/II of loading is applied to the same material, the fibers play a significant role in load bearing. In the present research, these effects are proposed in the form of reinforcement isotropic solid (RIS) coefficients. Taking an analytical approach, RIS coefficients are embedded into the MPS formulation to obtain the new extended maximum principal stress criterion (EMPS) with high accuracy. For the case of cracks across to the fibers, the crack kinking phenomenon has also been used and proved that when the cracks collide with the fibers, they kink and propagate along the fibers. To validate the proposed criterion, center notch disk tension (CNDT) specimens as appropriate ones for mixed mode I/II fracture test of orthotropic materials are fabricated which can cover the different range of mixed mode I/II loadings. Critical forces range from 452 to 1554 N for cracks along the fibers and 730–2399 N for cracks across the fibers. The fracture limit curves in comparison with the obtained experimental data indicate the compatibility of this criterion with the nature of fracture of the orthotropic materials.