# Volume 12, number 1 (2018)

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Item On the level of computational model of a human skull: a comparative study(University of West Bohemia, 2018) Chamrad, Jakub; Marcián, Petr; Borák, LiborShow more In this study, different patient-specific computational models of the skull, which are often used in literature, were investigated, analysed and compared.The purpose of this studywas to demonstrate the differences in computational model creation and results in case different computationalmodels based on same computed tomography (CT) dataset are used. The selection of computationalmodel directly influences the values of investigated parameters. The effort is to demonstrate, how the selection of the computational model influences the results of biomechanically relevant parameters. The comparison was based on total displacement of the skull and von Mises strain investigated around predefined paths around the skull. The strain values were evaluated according to criterion from literature. The results were obtained using finite element method. The values of the displacement of the skull were higher in case of considering cancellous bone tissue due to its poor material properties or heterogeneous material properties. The same situation occurred during the evaluation of strain. The values were higher in models which include cancellous bone tissue in the structure.Show more Item Identification of several non-stationary loads applied to an elastically deformed structure(University of West Bohemia, 2018) Lachmayer, Roland; Yanchevskyi, Igor V.; Mozgova, Iryna; Gottwald, PhillipShow more The technique has been presented for time-dependence identification of several independent beetwen each other loads distributed over a given area of a structure with arbitrary topology by using quantity values more convenient for measurements. In the assumption that the structure’s response linearly depends on the loads, the considered problem,which belongs to the class of boundary inverse problems in the mechanics of solids, is reduced to a system of linear algebraic equations for coefficients that approximate the sought-for influences. The system is solved using a regularizing algorithm providing stability of results to random errors in initial data and calculation errors.Concrete calculations, substantiating the efficiency of the presented technique, have been performed as with theoretical data to identify two non-stationary loads applied to a wheel carrier of a race car as with experimental data to restore an impact force applied to a round plate with fixed boundary. To calculate values of a system’s elements corresponding to values of measured quantities under unit loads, the finite elementmethod was used. The suggested technique can be used for designing structures with complex geometry based on criterias of their dynamic (fatigue) strength, etc.Show more Item Lateral force effects of three-axle locomotive bogie on track(University of West Bohemia, 2018) Michálek, Tomáš; Haupt, Lukáš; Zelenka, Jaromír; Kohout, Martin; Liberová, StanislavaShow more This paper deals with guiding behaviour of a diesel-electric locomotive equipped with new three-axle bogies which were developed in co-operation of the company CZ LOKO and the Faculty of Transport Engineering of the University of Pardubice. At first, the design of the new bogie intended for the track gauge 1520 mm is shortly introduced. Then, the attention is paid to three different variants of secondary suspension design and their influence on lateral force effects of the locomotive on track in curves. The assessment is performed by means of the multibody simulation tool “SJKV” and it takes into account GOST standards. Possibilities of application of a system of active elements for bogie steering are also evaluated.Show more Item On the application of Sturm's theorem to analysis of dynamic pull-in for a graphene-based MEMS model(University of West Bohemia, 2018) Omarov, Daniyar; Nurakhmetov, Daulet; Wei, Dongming; Skrzypacz, PiotrShow more A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementationswith Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.Show more Item Torsion dissipated energy of hard rubbers as function of hyperelastic deformation energy of the Yeoh model(University of West Bohemia, 2018) Šulc, Petr; Pešek, Luděk; Bula, Vítězslav; Košina, Jan; Cibulka, JanShow more In this paper, we are proposing a new formulation of dissipated energy of hard rubbers as a function of the deformation energy expressed by the Yeoh hyperelastic model. Torsion deformation is considered as a planar deformation of a simple shear on the surface of a cylinder. Thus the deformation energy is dependent only on the first invariant of strain. Based on the experiment, a “hyperelastic proportional damping” (HPD) is proposed for hard rubbers under finite strains. Such damping is analogical to the model of proportional damping in the linear theory of viscoelasticity, i.e. the dissipated energy is proportional to the deformation energymultiplied by the frequency of dynamic harmonic loading. To obtain the experimental data, samples of hard EPDM rubbers of different harnesses were dynamically tested on a torsional test rig for different frequencies and amplitudes. The Yeoh model is chosen since the deformation function is dependent only on the first strain invariant for the description of the simple shear of a surface cylinder. The Yeoh constants are evaluated by curve fitting of the analytical stress function to the experimental torsion stress-deformation curve. The constants are used to express the deformation energy of the Yeoh model for specific cases of tested rubbers. The coefficients of hyperelastic proportional damping are evaluated on the basis of experimental results.Show more Item Dynamic analysis of planar rigid multibody systems modeled using natural absolute coordinates(University of West Bohemia, 2018) Pappalardo, Carmine Mariar; Guida, DomenicoShow more This paper deals with the dynamic simulation of rigid multibody systems described with the use of two-dimensional natural absolute coordinates. The computational methodology discussed in this investigation is referred to as planar Natural Absolute Coordinate Formulation (NACF). The kinematic representation used in the planar NACF is based on a vector of generalized coordinates that includes two translational coordinates and four rotational parameters. In particular, the set of natural absolute coordinates is employed for describing the global location and the geometric orientation relative to the general configuration of a planar rigid body. The kinematic description utilized in the planar NACF is based on the separation of variable principle. Therefore, a constant symmetric positive-definite mass matrix and a zero inertia quadratic velocity vector associated with the centrifugal and Coriolis inertia effects enter in the formulation of the equations of motion. However, since a redundant set of rotational parameters is used in the kinematic description of the planar NACF for defining the geometric orientation of a rigid body, the introduction of a set of intrinsic normalization conditions is necessary for the mathematical formulation of the algebraic constraint equations. Thus, the intrinsic constraint equations associated with the natural absolute coordinates must be properly taken into account in addition to the extrinsic constraint equations that model the kinematic pairs which form the mechanical joints. This investigation discusses in details the mathematical derivation and the numerical implementation of the multibody system differential-algebraic equations of motion elaborated in the context of the planar NACF. For this purpose, simple geometric considerations are employed in the paper to develop the algebraic equations associated with the intrinsic and extrinsic constraints, whereas the fundamental principles of classical mechanics are utilized for the formal deduction of the dynamic equations. By using the augmented formulation, the index-three form of the differential-algebraic equations of motion is reduced to the corresponding index-one counterpart in order to be able to apply the Udwadia-Kalaba approach for the analytical calculation of the multibody system generalized acceleration vector. Furthermore, in the numerical implementation of the equations of motion based on the planar NACF, the direct correction method is utilized for stabilizing the algebraic constraint equations at both the position and velocity levels. The direct correction approach represents a new methodology recently developed in the field of multibody system dynamics for treating the algebraic constraint equations leading to physically correct and numerically stable dynamic simulations. A standard numerical integration algorithm is employed for obtaining an approximate solution of the nonlinear dynamic equations derived by using the planar NACF. The numerical implementation of a general-purpose multibody computer program based on the planar NACF is demonstrated in the paper considering four simple benchmark examples of rigid multibody systems.Show more Item Semi-analytical stochastic analysis of the generalized van der Pol system(University of West Bohemia, 2018) Náprstek, Jiří; Fischer, CyrilShow more The paper is motivated by a series of wind tunnel experiments, which deal with aeroelastic Single Degree of Freedom (SDOF) and Two Degrees of Freedom (TDOF) section models. Most of them can be mathematically expressed by van der Pol-Duffing type equations or their combination. Excitation due to aeroelastic forces consists mostly of a deterministic periodic part and random components, both of them are applied as additive processes. The lock-in state represents an auto-synchronization of the vortex shedding and basic eigen-frequency of the system. This problem seems to be very polymorphous and, therefore, several isolated regimes have been outlined together with their characterization. Parameter setting with solely random excitation is further investigated in the paper. The strategy of stochastic averaging is then employed to formulate normal form of stochastic system for partial amplitudes of harmonic approximates of the response. The random part of excitation is considered as a Gaussian process with significantly variable spectral density. Hence, a conventional way of investigation based on an idea of white noise excitation is no more applicable. Therefore, the general formulation of diffuse and drift coefficients should be used to construct the relevant Fokker-Planck equation (FPE). Semi-analytical solution of FPE is deduced in the exponential form by means of a probability potential. It is later used for stochastic stability investigation together with consideration about the stationary probability distribution existence. Open problems and further research steps are outlined.Show more