Mechanics of Solids最新文献

The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of motion of a gyrostat are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations is conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2 : 1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It is proved that the obtained solutions can be described by elementary functions of time.

The changes in stiffness and damping of the bolted joint surface may lead to variations in the dynamic properties of the overall bolted connection structure. Therefore, accurately determining the dynamic parameters of the joint surface holds significant practical importance in engineering. This paper focuses on a matrix distributed bolt connection structure and develops a bolt elastic interaction model to examine the changes in bolt pre-tension. The stiffness parameters of the bolt connection joint surface were identified by utilizing a genetic algorithm, taking into account the variation in bolt pre-tightening force. This identification process involved a combination of experiments and finite element analysis. The analysis focus on the disparity between the outcomes of recognition and the results derived from theoretical calculations. The research proposed an improved model that accounts for the non-uniform distribution of joint surface stiffness across varying levels of bolt pre-tightening force. Additionally, the paper examined the impact of various joint surface and bolt modeling techniques on the precision of identifying joint surface stiffness parameters. This study aimed to develop joint surface models for bolted connection structures through various equivalent modeling techniques. Subsequently, finite element modal simulations was performed, and the obtained results were compared alongside error analysis. The results suggested that taking into account the variations in bolt pre-tension resulting from the elastic interaction among bolts and the non-uniform distribution of stiffness on joint surfaces within the bolt pre-tension range can significantly improve the accuracy of equivalent modeling for bolted connection structures.

Using shape memory polymer as matrix material to prepare negative Poisson’s ratio structure, the shape memory performance, impact resistance, light weight and other characteristics are integrated, which has great application prospects in vehicle collision, aerospace, military, medicine and other fields. PLA, TPU, and PETG materials were selected for shape memory performance test, and the shape recovery rate, shape recovery time and shape fixation rate were analyzed to show that the shape memory performance of PLA materials was better. The quasi-static compression test and simulation analysis were carried out for four typical negative Poisson’s ratio structures with PLA as the base material: concave hexagon, concave triangle, star and rotating cell. Through the analysis of Poisson’s ratio effect, impact resistance and energy absorption ability, the mechanical properties of the concave hexagonal structure are better, and the negative Poisson’s ratio effect is obvious. When the compressive strain is less than 15%, the rebound rate of other structures is above 90% except star structure. The response surface optimization method is used to optimize the impact response of the concave hexagonal structure with the maximum residual displacement after impact deformation. After optimization, the maximum displacement under energy impact deformation is reduced by 21.76% and the energy absorption is increased by 3.29%, and the optimized structure has better shape recovery performance, which provides a reference for designing the buffer structure with self-recovery performance.

This study examines the dynamic responses of wet long bones, conceptualized as transversely isotropic, hollow cylinders (crystal class 6) when subjected to rotational forces and magnetic field. The wave propagation analysis is articulated through a potential function, meeting the criteria of an eighth-order partial differential equation, from which the wave equation’s explicit solution is deduced. Mechanical boundary conditions are defined for a stress-free lateral surface, complemented by fluidic boundary conditions for stress-free fluidic surfaces. Fulfilling these boundary conditions facilitates the derivation of a dispersion relation, subsequently resolved through numerical methods. Frequency calculations for the poroelastic bone consider various rotational speeds, magnetic field and porosity levels. This research offers insights that could enhance the theoretical framework for orthopedic studies related to the behavior of cylindrical poroelastic long bones. Furthermore, a comparative analysis is conducted between the theoretical outcomes and the empirical data obtained from an innovative non-contact measurement device, thereby validating the theoretical model. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field, rotation and initial stress. The numerical and graphical results underscore the significant influence of magnetic field, rotation, and initial stress on the various wave velocity and attenuation coefficient.

The tremendous attention of researchers has been attracted to the unusual properties of piezoelectric ceramic materials. A semi-analytical approach to estimate the electromechanical coupling characteristics of multilayered functionally graded piezoelectric ceramic beams with different boundary conditions is presented. The state space method is formulated to the electroelastic theory to derive the state equations for ceramic beams along the thickness direction. The mixed supported boundary conditions are represented by means of the displacement function and Fourier series expansions, respectively. A global propagator matrix is used to connect the field variables at the internal interface to those at the external interface for the whole structure. Governing equations of the models with geometrical nonlinearity are solved using the secant method. Numerical examples show the correctness of the proposed method by finite element model and the influence of the functional gradient index factors η, different boundary conditions, and loading voltage on the static behavior of piezoelectric ceramic beams. Our results show that the modified state space approach overcomes the disadvantage of the inability to address clamped supported and free boundary conditions. η possesses the ability to improve interfacial stress discontinuities.

The present paper deals with problems of propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The requisite constitutive and differential equations of semi-isotropic solids are revisited. Dispersion equation for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic algebraic equation) are obtained and analyzed. Dispersion equations for the transverse waves (equation of the 8th algebraic degree) are splitted into two algebraic quartic equations and then solved. For a longitudinal wave, the complex amplitudes of temperature increment, translational displacements and spin–vector are coupled, unlike a transverse wave. The roots of mentioned algebraic equations are calculated by using the Wolfram Mathematica 13 symbolic computing system. The normal wavenumbers with positive real part are discriminated.

The paper examines the process of thermoelastic instability occurrence during unsteady friction of anisotropic disk samples in the presence of a third body film on the friction surface. This process takes place during the operation of highly loaded braking systems (in aviation and railway transport), specialized clutches of motor vehicles and in other mechanisms. The presence of surface film leads to a decrease in surface wear simultaneously with the emergence of significant nonlinearity in the wear rate. The finite difference method was used to simulate the mutual influence of wear, frictional heating, elastic deformations and the evolution of the film on the friction surface. The process of friction and wear of discs was studied taking into account the history of a series of braking events. The annular shape of surface pressures and temperatures distribution is considered. The evolution of disc wear from braking to braking for the case of the film presence was compared with the case of film absence and experimentally measured wear.

Nowadays, various Delta-type robots are widely used in many technological fields. In this work, we propose a novel 5-DOF Delta-type parallel robot with four linear and one rotational actuators. The major part of the article is devoted to the kinematic analysis of the robot, including solving its inverse and forward kinematic problems. To demonstrate the developed techniques, we consider two numerical examples. In the first one, we solve the inverse kinematics and determine the actuator displacements required to realize a spatial trajectory of the output link. The forward kinematic analysis, presented in the second example, results in six different assembly modes of the robot for the given set of the actuator displacements. The proposed algorithms represent the basis for subsequent velocity, acceleration, and dynamic analysis of the robot, and they can be adapted to other Delta-type parallel robots.

A program of basic tests and a method for identifying a three-dimensional model of the elastoplastic behavior of an isotropic porous or powdery consolidated medium experiencing arbitrary quasi-static loading under compressive medium stress at room temperature are proposed. The medium under consideration under compressive medium stresses is compacted with increasing effective stress, which leads to a nonlinear change in elastic modules, hardening and dilatancy (coupling of shear and volumetric components of deformations) in the yield region. To describe this behavior, the cap model of DiMaggio and Sandler, which is present in application software packages, is considered. As basic tests, the free and constrained compression of a cylindrical sample is considered according to a special program containing the stages of loading and unloading with a sequential increase in the amplitude voltage. Samples with a given porosity for free compression tests are manufactured using a tight compression test rig. According to the initial slope of the discharge curves, the values of the elastic modulus for free and constrained compression are determined in a certain range of porosity changes, according to which the Poisson’s ratio is determined. The five constants of the cap model are correctly and explicitly determined by the deformation curve of the material under constrained compression over a wide range of changes in axial deformation (and density), the flow stress under free compression of the sample at some density, and the assumption that the coefficient of transverse deformation in the yield region is equal to the Poisson’s ratio. The elastic and plastic constants were determined according to the test data of powdered paraffin grade T1 with a fraction of 0.63 mm. The corresponding model is applicable for numerical simulation of extrusion processes and mold filling for casting by melting models, processes for manufacturing blanks of non-melting polymer composites by powder technology, stamping sealing elements from flexible graphite and other pressure treatment processes of non-compact media.

In this paper, considering the dual-functionally graded carbon nanotube reinforced composite (DFG-CNTRC) cylindrical shells with stepped variable thicknesses, the free vibration characteristics of the shell under arbitrary boundary conditions are investigated. To begin with, based on the improvement law of the mixtures, the effective material properties of DFG-CNTRC are obtained. Then, the artificial spring technique is used to simulate the continuous coupling between the shell segments and the boundary conditions at both ends of the shell. Further, based on the first-order shear deformation theory (FSDT), the dynamics equations of DFG-CNTRC stepped cylindrical shells are derived by the Rayleigh–Ritz method using Chebyshev polynomials as admissible functions. Therefore, the dynamic differential equation of the shell with arbitrary boundary conditions is solved. Finally, compared with the data from existing literature, the results indicate that the proposed method has excellent validity and reasonable convergence. Moreover, the effects of carbon nanotubes (CNTs) volume fraction, CNTs distribution types, matrix volume fraction, geometric parameters, and spring stiffness value on the vibration characteristics of DFG-CNTRC stepped cylindrical shells are assessed.