Modeling and motion simulation of a three-wheeled mobile robot with front wheel driven and steered taking into account wheels�� slip

The problem of modeling of dynamics of a three-wheeled mobile robot with front wheel driven and steered is analyzed in this paper. Kinematical structure and kinematics of the robot are described. A universal methodology of analytical modeling of robot??s dynamics is applied. This methodology takes into account wheel-ground contact conditions and wheels?? slip. Its essence is the use of a contact model of deformable tire with rigid ground and division of the robot??s dynamics model into parts connected with wheels, including tire model, and with the mobile platform. The tire model used in this paper results from empirical dependencies determined during investigations of car tires. Ground geometry and type are specified in the environment model. Tire-ground interface is characterized by coefficients of friction and rolling resistance. The robot model takes into account the presence of friction in kinematical pairs. The model of servomotors is included as well. The important part of this work is simulation research performed using Matlab/Simulink package. Simulation research includes solving of the forward and inverse dynamics problems as well as the tracking control task. During simulations, the robot was moving on concrete and on a piece of ice. The simulation research enabled verification of the elaborated solutions.     

Optimum Young��s Modulus of a Homogeneous Cylinder Energetically Equivalent to a Functionally Graded Cylinder

For a functionally graded (FG) circular cylinder loaded by uniform pressures on the inner and the outer surfaces and Young??s modulus varying in the radial direction, we find lower and upper bounds for Young??s modulus of the energetically equivalent homogeneous cylinder. That is, the strain energies of the FG and the homogeneous cylinders are equal to each other. For a typical power law variation of Young??s modulus in the FG cylinder, it is shown that taking only two series terms, yields good values for bounds of the equivalent modulus. We also study two inverse problems. First, an investigation is made to find the radial variation of Young??s modulus in the FG cylinder, having a constant Poisson??s ratio, that gives the maximum value of the equivalent modulus. Second, the complementary problem of finding the radial variation of Poisson??s ratio in the FG cylinder, having a constant stiffness, that gives the maximum value of the equivalent modulus, is considered. It is found that the spatial variation of the elastic properties, that maximizes the equivalent modulus, depends strongly upon the external loading on the cylinder.     

Extrema of Young’s modulus for cubic and transversely isotropic solids

For a homogeneous anisotropic and linearly elastic solid, the general expression of Young’s modulus E(n), embracing all classes that characterize the anisotropy, is given. A constrained extremum problem is then formulated for the evaluation of those directions n at which E(n) attains stationary values. Cubic and transversely isotropic symmetry classes are dealt with, and explicit solutions for such directions n are provided. For each case, relevant properties of these directions and corresponding values of the modulus are discussed as well. Results are shown in terms of suitable combinations of elements of the elastic tensor that embody the discrepancy from isotropy. On the basis of such material parameters, for cubic symmetry two classes of behavior can be distinguished and, in the case of transversely isotropic solids, the classes are found to be four. For both symmetries and for each class of behavior, some examples for real materials are shown and graphical representations of the dependence of Young’s modulus on direction n are given as well.     

Evaluation of the effective elastic moduli of tetragonal fiber-reinforced composites based on Maxwell’s concept of equivalent inhomogeneity

Maxwell’s concept of an equivalent inhomogeneity is employed for evaluating the effective elastic properties of tetragonal, fiber-reinforced, unidirectional composites with isotropic phases. The microstructure induced anisotropic effective elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic, circular cylindrical fibers embedded in an infinite isotropic matrix with that for the problem of a single, tetragonal, circular cylindrical equivalent inhomogeneity embedded in the same isotropic matrix. The former solutions precisely account for the interactions between all fibers in the cluster and for their geometrical arrangement. The solutions to several example problems that involve periodic (square arrays) composites demonstrate that the approach adequately captures microstructure induced anisotropy of the materials and provides reasonably accurate estimates of their effective elastic properties.     

Elastic fields and effective moduli of particulate nanocomposites with the Gurtin–Murdoch model of interfaces

A complete solution has been obtained for periodic particulate nanocomposite with the unit cell containing a finite number of spherical particles with the Gurtin–Murdoch interfaces. For this purpose, the multipole expansion approach by Kushch et al. [Kushch, V.I., Mogilevskaya, S.G., Stolarski, H.K., Crouch, S.L., 2011. Elastic interaction of spherical nanoinhomogeneities with Gurtin–Murdoch type interfaces. J. Mech. Phys. Solids 59, 1702–1716] has been further developed and implemented in an efficient numerical algorithm. The method provides accurate evaluation of local fields and effective stiffness tensor with the interaction effects fully taken into account. The displacement vector within the matrix domain is found as a superposition of the vector periodic solutions of Lamé equation. By using local expansion of the total displacement and stress fields in terms of vector spherical harmonics associated with each particle, the interface conditions are fulfilled precisely. Analytical averaging of the local strain and stress fields in matrix domain yields an exact, closed form formula (in terms of expansion coefficients) for the effective elastic stiffness tensor of nanocomposite. Numerical results demonstrate that elastic stiffness and, especially, brittle strength of nanoheterogeneous materials can be substantially improved by an appropriate surface modification.     

Clarifications of Certain Ambiguities and Failings of?Poisson��s Ratios in Linear Viscoelasticity

Detailed new analytical investigations are presented describing the behavior of Class I, II and III viscoelastic Poisson??s ratios (PR). Their previously demonstrated dependence on stress-time histories, which lead to the inability to consider them as universal viscoelastic material properties and the incapacity to produce a general elastic?Cviscoelastic correspondence principle (EVCP) based, is expanded. A new Class VI PR is analytically derived from the viscoelastic constitutive relations in the Fourier transform (FT) space to achieve the proper FT form of the elastic/viscoelastic correspondence principle, i.e., the elastic-viscoelastic analogy. However, even though this PR Class is a pure universal material property function, it still fails to provide a convenient and useful path to a correspondence principle due to its inopportune constitutive form in real time space vis-à-vis a thermodynamic model with equivalent attributes. Consequently, no general EVCP involving PRs can be formulated. The derived Class VI PRs are equivalent to the defined Class III PRs with 1-D loadings (stresses).     

A Modified Poincaré Method for the Persistence of Periodic Orbits and Applications

This paper is devoted to the persistence of periodic orbits under perturbations in dynamical systems generated by evolutionary equations, which are not smoothing in finite time, but only asymptotically smoothing. When the periodic orbit of the unperturbed system is non-degenerate, we show the existence and uniqueness of a periodic orbit (with a minimal period near the minimal period of the unperturbed problem) by using “modified” Poincaré methods. Examples of applications, including the perturbed hyperbolic Navier–Stokes equations, systems of damped wave equations and the system of second grade fluids, are given.     

Young’s modulus prediction of hexagonal nanosheets and nanotubes based on dimensional analysis and atomistic simulations

The present work investigates Young’s modulus of hexagonal nanosheets and nanotubes based on dimensional analysis and molecular mechanics. Using second derivatives of the strain energy density revealed from molecular dynamics simulations at 0 K (i.e., molecular mechanics) with harmonic potentials for various combinations of force constants, Young’s modulus have been computed for single-walled armchair and zigzag nanotubes of different radii. This parametric study with the aid of dimensional analysis allows explicitly establishing Young’s modulus of (n, n) armchair and (n, 0) zigzag nanotubes as functions of the force constants, bond length and chiral index n. Proposed formulae are applied to estimate Young’s modulus of graphene, boron nitride, silicon carbide sheets and their nanotubes. The accuracy of the proposed formulae are verified and discussed with available data in the literature for these three sheets and their nanotubes.     

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio is proposed. Effects of thermo-oxidative aging and viscoelastic Poisson’s ratio are considered in this comprehensive constitutive equation with two sets of reduced time system coping with the time and temperature dependence. In order to simulate the single and combined effects of aging and viscoelastic Poisson’s ratio, constitutive equation is rewritten into an incremental form and implemented in the user subroutine UMAT at the platform of finite element code ABAQUS. Detailed procedure for acquiring the parameters in constitutive equation is introduced and conducted for the subsequent applied analysis. Two typical loading cases during the service life of solid rocket motor and four sets of combined constitutive models are simulated. Von Mises strain and stress distribution and their changes versus time are utilized as the main analysis index. The results show that the effects of aging and viscoelastic Poisson’s ratio or their combinations will improve or decrease the level and change the distribution of Von Mises strain and stress in varying degrees.     

An inverse problem in film/substrate indentation: extracting both the Young’s modulus and thickness of films

In an indentation test, the effective Young’s modulus of a film/substrate bilayer heterostructure varies with the indentation depth, a phenomenon known as the substrate effect. In previous studies investigating this, only the Young’s modulus of the film was unknown. Once the effective Young’s modulus of a film/substrate structure is determined at a given contact depth, the Young’s modulus of the film can be uniquely determined, i.e., there is a one-to-one relation between the Young’s modulus of the film and the film/substrate effective Young’s modulus. However, at times it is extremely challenging or even impossible to measure the film thickness. Furthermore, the precise definition of the layer/film thickness for a two-dimensional material can be problematic. In the current study, therefore, the thickness of the film and its Young’s modulus are treated as two unknowns that must be determined. Unlike the case with one unknown, there are infinite combinations of film thickness and Young’s modulus which can yield the same effective Young’s modulus for the film/substrate. An inverse problem is formulated and solved to extract the Young’s modulus and thickness of the film from the indentation depth-load curve. The accuracy and robustness of the inverse problem-solving method are also demonstrated.     

Deflection Measurement and Determination of Young’s Modulus of Micro-cantilever Using Phase-shift Shadow Moiré Method

The deflection of micro-structures have been previously measured using optical interferometry methods. In this study, the classical phase-shift shadow moiré method (PSSM) was applied to measure the deflection of a silicon micro-cantilever and to determine the Young’s modulus of the cantilever material. The modulus value was determined from the profile based on deflection equation. A normal white light source and a grating of 40 line pairs per mm were used to generate the moiré fringes. Since the use of white light and high-resolution grating produces low contrast moiré fringes, the fringe visibility was enhanced by applying contrast enhancement and filtering techniques. The Young’s modulus of the silicon cantilever material was estimated to be 165.9 GPa with an uncertainty of ±11.3 GPa (6.8%). The experimental results show that the PSSM method can be successfully applied for characterizing micro-cantilevers. Comparison of the deflection profile from the proposed method and a commercial 3-D optical profiler showed that the measurement range and sensitivity of PSSM are not affected by the poor contrast images.     

Large In-plane Deformation Mapping and Determination of Young’s Modulus of Rubber Using Scanner-Based Digital Image Correlation

Experimental Techniques - We propose a novel scanner-based digital image correlation (DIC) method to determine the full-field in-plane displacement as well as the Young’s modulus of...     

Micromechanics Characterization on the Lower Bound Young’s Moduli of Composite Materials Measured from Nanoindentation

Experimental Mechanics - The measurements of the through-thickness Young’s moduli of composite materials are important, but they were not systematically reported because of the complexity. In...     

Identification of Damping and Dynamic Young’s Modulus of a Structural Adhesive Using Radial Basis Function Neural Networks and Modal Data

In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model, an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work, in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved by repeating the identification process for several times. The validity of results is proved by comparing the results with those identified in a previous work.     

Integration of the journal Prikladnaya Mekhanika (International Applied Mechanics) into the world’s scientific community

Two new tendencies in the integration of the journal Prikladnaya Mekhanika (International Applied Mechanics) into the world’s scientific community are discussed. One tendency is that representatives of the world’s scientific community publish their articles in the journal. The other tendency is positioning of this journal in the world’s scientific information environment. The number of full-text article requests as per the document Springer—the Language of Science: International Applied Mechanics, Publisher’s Report, July 1 (2011) is discussed.Anew publication evaluation criterion based on this metric is offered     

The monotonicity and critical periods of periodic waves?of?the �� 6 field model

In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the ?? ⁶ field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.     

Measuring the dependence of the local Young’s modulus on the porosity of isotropic composite materials by a pulsed acoustic method using a laser source of ultrasound

A laser optoacoustic method for analyzing the effect of porosity on the local isotropic Young’s modulus of composite materials was proposed and experimentally implemented. Using as an example samples of a metal matrix composite based on silumin with reinforcing microparticles of silicon carbide, SiC, in various concentrations, it is shown that to provide an effective increase in Young’s modulus with increasing concentration of SiC, the porosity of the final sample should not exceed 2%.