Archive of Applied Mechanics最新文献

Abstract

This work investigates the dynamics of the modified circular restricted three-body problem. The triaxial shape of the massive body, a modified gravitational parameter, quantum correction effect, radiation pressure and small perturbations in the Coriolis and centrifugal forces are all taken into account. The impact of the considered parameters in the equilibrium points and their linear stability is studied. Some new significant results in the critical mass parameter, (mu _c) , are observed in the presence of perturbing parameters. It is found that the critical mass parameter, (mu _c) , increases in the presence of modified gravitational potential, and it slightly decreases due to the quantum correction effect. Analytical construction of periodic orbits around the collinear equilibrium points is performed. Additionally, analysis of the impact of perturbations on the shape of these periodic orbits is conducted.

Abstract

This study utilises the transfer matrix method (TMM) to address the acoustic characteristics of multilayered cylindrical shells lined with porous materials. The TMM theoretical model for the sound transmission loss of composite cylindrical shells with internal porous materials is derived by establishing transfer matrices for the air/composite material interface, composite material/foam interface, foam/air interface and boundary interfaces. The accuracy of the TMM model is validated through a comparison and analysis with experimental results. Building upon this, the impact of porous foam material parameters and types on the structural sound transmission loss is discussed. The results indicate that the use of TMM accurately reflects the acoustic performance of composite structures. Additionally, this model allows for the determination of the influence patterns of porous foam material parameters and types on the acoustic performance of composite structures. In the frequency range of 100–10,000 Hz, the sound transmission loss of the melamine foam-lined composite structure increases with the increase in flow resistance and porosity and the decrease of the tortuosity factor. The use of the porous lining material significantly enhances the structural sound insulation performance.

Drawing on the principles of fractal properties and nonlinear vibration analysis, this paper delves into the investigation of a moving bead on a vertically rotated parabola. The dynamical nonlinear equation of motion, incorporating fractal derivatives, transforms traditional derivatives within continuous space. Consequently, the equation of motion takes the form of the Duffing-Van der Pol oscillator. Utilizing a non-perturbative approach, the nonlinear oscillator is systematically transformed into a linear one, boasting an exact solution. The analytical solution yields two valid formulas governing the frequency-amplitude relationships. Numerical solutions affirm that these proposed formulas offer highly satisfactory approximations to the analytical solution. Leveraging fractal properties through Galerkin’s method, the paper successfully determines the fractalness parameter of the medium, shedding light on the intricate dynamics of the system.

An interface crack between dissimilar one-dimensional hexagonal quasicrystals with piezoelectric effect under anti-plane shear and in-plane electric loadings is considered. Mixed boundary conditions at the crack faces are studied. Using special representations of field variables via sectionally analytic vector-functions, a homogeneous combined Dirichlet–Riemann boundary value problem and a Hilbert problem are formulated. Exact analytical solutions of both these problems are obtained, and analytical expressions for the phonon and phason stresses and the electric field as well as for the derivative jumps of the phonon and phason displacements and also the electrical displacement jump along the bimaterial interface are derived. The field intensity factors are determined as well. The dependencies of the mentioned values on the magnitude and direction of the external electric loading and different ratios of electrically conductive and electrically permeable crack face zone lengths are demonstrated in graph and table forms.

This paper presents the formulation of a novel axisymmetric plate element capable of capturing size effects observed in micro-scaled structures. To establish the element formulation, a size-dependent beam element is considered, and by axisymmetric expansion of the model, the stiffness and mass matrices and force vector for an axisymmetric plate element are derived. Comparing the results of this model with those from literature and the outcomes of COMSOL confirms that the present FE formulation can accurately predict the static and dynamic behavior of microplates as well as macro-scale plates. Furthermore, a convergence analysis is performed which indicates that this model can accurately predict the static deflection and natural frequency of circular plates utilizing very low number of elements and consequently with low values of computation cost. As an example of real-world application, the model is applied to analysis of microelectromechanical devices and its accuracy is confirmed.

Venus, Earth’s closest neighbor in the Solar System, shares similar characteristics such as size, density, and location within the Sun’s hospitable zone. As a result, it has been proposed as an ideal destination for a range of missions, including Venus and Mercury planetary science, heliophysics observation, space weather monitoring, and Earth planetary defense. The current study examines exterior and interior resonance of discovered periodic orbits, as well as the creation families of Sun–Venus planar periodic orbits in the Sun–Venus system. The circular restricted three-body problem (CR3BP) is used to generate these orbit families via the method of pseudo-arclength continuation. This study identifies 16 exterior and 22 interior resonant periodic orbits from an initial collection of near-Venus and touring periodic orbits generated via a described grid search method. Next, the study produces a selection of 20 families of Sun–Venus periodic orbits with favorable stability properties that will serve to reduce orbit maintenance and station-keeping costs in terms of propellant expenditure, a primary constraint on spacecraft operational lifetime. This study aims to advance multi-body trajectory research and fill a catalog and wider literature hole by providing a preliminary investigation of Sun–Venus CR3BP periodic orbit resonance and orbit families.

The fracture grouting method can play a very good anti-seepage and reinforcement effect for some rock layer that are not compacted or have hidden dangers such as leakage channels, soft layers, cracks, and so on. However, the mechanism of action requires further in-depth study. In this study, to investigate the penetration of time-dependent viscosity of the slurry in the surrounding rock, cement-based slurry was used as the object of research to carry out the time-dependent viscosity tests, analyze its rheological characteristics, and determine its time-dependent viscosity. Based on the Bingham model of slurry, a grout diffusion model was established, considering into consideration slurry time-dependent viscosity and the rock type I fracture toughness. In addition, this study considered the impact of rock aperture deformation on the grout process, established a grout penetration equation, and explored the influencing factors of the slurry penetration range. The process of grouting’s strengthening of the fractured rock mass is addressed from both macroscopic and microscopic perspectives, and the correctness of the grouting penetration formula is confirmed by comparing in-situ grouting borehole endoscopic pictures in the coal mine tunnel. This study demonstrates that the grouting penetration radius increases very slowly after the grouting pressure reaches a certain level, but it is easier for the slurry to combine with the coal rock body to form a tightly consolidated body under high pressure. Therefore, the grouting pressure should be designed based on the rock media type and engineering disturbance. The results of this study could give a theoretical foundation for the selection and design of parameters required for grouting engineering practice.

This paper proposes a study of the kinetics and dynamics of slalom waterskiing. The discipline of slalom waterskiing is first described. Then the forces applied on a “static” skier, i.e. just pulled behind a boat, are expressed as a function of water drag coefficients, speed and pitch angle. A slalom point model is finally proposed, made of three major contributions: water friction, water lift and an additional water drag contribution on the slalom skier, creating the traverse motions. Assumptions are made in order to quantify the three angles characterizing the ski position during the slalom traverses. The model is simulated on an EXCEL worksheet, for a large range of conditions (boat speed between 52 and 58 km/h, rope length between 18.25 and 13 m, and three skier masses of 60, 80 and 100 kg). The water friction coefficient was fitted to a value allowing to simulate successful slalom courses. The simulations provide a significant set of kinematics and dynamics parameters (skier velocity, acceleration, tangential force and rope tension). The model duly renders the variations of the skier velocity, and it reflects the increasing difficulty for the skier to complete the slalom at higher boat speed and shorter rope length.

In the current study, we explore stability of satellite motion around the natural moons of planets in solar system using the novel concept of ER3BP with variable eccentricity. This concept was introduced earlier when novel type of ER3BP (Sun–planet–satellite) was investigated with variable spin state of secondary planet correlated implicitly to the satellite motion (in the synodic co-rotating Cartesian coordinate system) for its trapped orbit near the secondary planet (which is involved in Kepler’s duet “Sun–planet”). However, it is of real interest to explore another kind of aforedescribed problem, ER3BP (planet–moon–satellite) with respect to investigation of satellite motion m around the natural moon m_moon of planet with variable eccentricity of the moon in its motion around the planet. Therefore, we consider here two primaries, M_planet and m_moon, the latter orbiting around their common barycenter on quasi-elliptic orbit with slow-changing, not constant eccentricity (on a large-time scale) due to tidal phenomena. Our aim is to investigate the motion of a small dot satellite around the natural moon of planet on quasi-stable elliptic orbit. Both novel theoretical and numerical findings (for various cases of trio “planet–moon–satellite”) are presented in the current research.

The present research focuses on proposing a novel theoretical micromechanical model (TMM) designed to derive the frequency-dependent storage and loss moduli of woven fabric (WF)-matrix composites, as well as WF-particulate matrix (Hybrid) composites, based on their constituent properties. The TMM serves as a higher-order modulus operator, accounting for the composite woven fabric unit cell geometry and the effective modulus of both the fabric and matrix using equivalent modulus theory. This model also incorporates viscoelastic parameters obtained from literature and experiments for each constituent, namely woven glass fabric and SiC particles embedded in an epoxy matrix. The proposed TMM is validated by comparing its predictions of the frequency-dependent storage modulus and loss factor with experimental data acquired through dynamic mechanical analyzer tests on samples with varying fiber and particulate volume fractions. To address the inherent complexities of the higher-order modulus operator, the model is streamlined into a lower-order form expressed as a function of two separate variables: volume fraction and a differential time operator. This advancement enhances the applicability and usability of the model for predicting the mechanical behaviour of these complex composite materials. This novel mathematical model eliminates the cost and time for conducting the explicit experiments as well as can be applied to different range of similar hybrid composites considering the fact that the constituent properties are known.