Authors:Yi Yang; Yufeng Cheng; Weidong Zhu Pages: 1229 - 1241 Abstract: Stress concentration caused by holes can be investigated by numerical and analytical methods. Current analytical methods can only solve two-dimensional problems. This paper proposes an analytical study on a three-dimensional stress concentration problem that involves a rectangular cuboid hole in a three-dimensional elastic body under tension loading. Based on the finite element method and U-transformation method, the problem can be expressed as a set of uncoupled equations with cyclic periodicity. Displacements of the three-dimensional elastic body are derived in analytical form to study stress distribution in it. Numerical simulation is conducted using ABAQUS to verify the analytical solution. Stress concentration factors in cases of uniaxial, biaxial, and triaxial tensions and the effect of the side ratio of the hole on them are discussed. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1369-7 Issue No:Vol. 88, No. 8 (2018)

Authors:H. Roy; S. Chandraker Pages: 1243 - 1261 Abstract: In the past, many researchers developed rotor models using either lump system or finite element approach, where material damping played a crucial role in dynamic behaviour. Such damping in any rotating structure triggers instability at the supercritical range. In most of the literatures, material damping has been incorporated either by frequency-independent hysteretic damping or frequency-dependent viscous damping, but these models are insufficient to estimate the dynamic characteristics of the system. The motivation for using general viscoelastic model arises from a need to capture the influence of both types of damping. Such type of modelling is done through operator-based constitutive relationship. The numerator and denominator of material modulus are a polynomial of differential time operator, and polynomial coefficients are known as a viscoelastic parameter. The operator-based constitutive relationship is further utilized to bring down higher-order equations of motion by using two different techniques, i.e. (a) analytical approach and (b) finite element approach.The shaft damping is tackled in such a manner that the dissipation effects can be considered through all coordinates. The significance of both approaches is explained with the help of stability and response analysis at various disc positions. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1370-1 Issue No:Vol. 88, No. 8 (2018)

Authors:Jia-Hao He; Hsin-Haou Huang Pages: 1263 - 1274 Abstract: This paper presents a metamaterial plate (metaplate) consisting of a periodic array of holes on a homogeneous thin plate with slot-embedded resonators. The study numerically proves that the proposed model can generate a complete vibrational bandgap in the low-frequency range. A simplified analytical model was proposed for feasibly and accurately capturing the dispersion behavior and first bandgap characteristics in the low-frequency range, which can be used for initial design and bandgap study of the metaplate. A realistic and practical unit metaplate was subsequently designed to verify the analytical model through finite element simulations. The metaplate not only generated a complete vibrational bandgap but also exhibited excellent agreement in both analytical and finite element models for predicting the bandgap characteristics. This study facilitates the design of opening and tuning bandgaps for potential applications such as low-frequency vibration isolation and stress wave mitigation. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1371-0 Issue No:Vol. 88, No. 8 (2018)

Authors:George A. Gazonas; Raymond A. Wildman; David A. Hopkins; Michael J. Scheidler Pages: 1275 - 1304 Abstract: We consider several one-dimensional impact problems involving finite or semi-infinite, linear elastic flyers that collide with and adhere to a finite stationary linear viscoelastic target backed by a semi-infinite linear elastic half-space. The impact generates a shock wave in the target which undergoes multiple reflections from the target boundaries. Laplace transforms with respect to time, together with impact boundary conditions derived in our previous work, are used to derive explicit closed-form solutions for the stress and particle velocity in the Laplace transform domain at any point in the target. For several stress relaxation functions of the Wiechert (Prony series) type, a modified Dubner–Abate–Crump algorithm is used to numerically invert those solutions to the time domain. These solutions are compared with numerical solutions obtained using both a finite-difference method and the commercial finite element code, COMSOL Multiphysics. The final value theorem for Laplace transforms is used to derive new explicit analytical expressions for the long-time asymptotes of the stress and velocity in viscoelastic targets; these results are useful for the verification of viscoelastic impact simulations taken to long observation times. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1372-z Issue No:Vol. 88, No. 8 (2018)

Authors:Chuanzong Sun; Yushu Chen; Lei Hou Pages: 1305 - 1324 Abstract: In this paper, the nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact are investigated. A novel framework is proposed, in which the sophisticated geometrical structure is considered by finite solid element method and efficient model order reduction is applied to the model. The validity and efficiency of the reduced-order model are verified through critical speed and eigen problems. Its stable and unstable solutions are calculated by means of the assembly technique and the multiple harmonic balance method combined with the alternating frequency/time domain technique (MHB–AFT). The accurate frequency amplitudes are obtained accordingly for each harmonic component. The stabilities of the solutions are checked by the Floquet theory. Through the numerical computations, some complex nonlinear phenomena, such as combined frequency vibration, hysteresis, and resonant peak shifting, are discovered when the rub-impact occurs. The results also show that the control parameters of mass eccentricity, rub-impact stiffness, and rotational speed ratio make significant but different influences on the dynamical characteristics of the system. Therefore, a key innovation of this paper is the marriage of a hybrid modeling method—accurate modeling technique combined with model order reduction and solution method—highly efficient semi-analytic method of MHB–AFT. The proposed framework is benefit for parametric study and provides a better understanding of the nonlinear dynamical behaviors of the real complicated dual-rotor aero-engine with rub-impact. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1373-y Issue No:Vol. 88, No. 8 (2018)

Authors:Carmine M. Pappalardo; Domenico Guida Pages: 1325 - 1347 Abstract: This paper is focused on the development of a numerical procedure for solving the system identification problem of linear dynamical models that mathematically describe multibody mechanical systems. To this end, an input–output representation of the time evolution of a general mechanical system based on a sequence of matrices referred to as Markov parameters is employed. The set of Markov parameters incorporate the state-space matrices that allow for describing the dynamic behavior of a general mechanical system considering the assumption of structural linearity. The system Markov parameters are defined by means of a discretization process applied to the analytical description of a mechanical system, and therefore, they are difficult to obtain directly from observable measurements. However, a state observer can be introduced in order to define a set of observer Markov parameters that can be readily recovered from input–output experimental data. The observer Markov parameters obtained by using a least-square approach allow for computing in a recursive manner the system Markov parameters as well as another discrete sequence of matrices referred to as observer gain Markov parameters. Subsequently, the system and observer gain Markov parameters identified from observable input–output data are used for constructing a sequence of generalized Hankel matrices from which a state-space model of the mechanical system of interest can be extracted. This fundamental step of the identification procedure is performed in the algorithm elaborated in this work employing a numerical procedure which relies on the use of the Moore–Penrose pseudoinverse matrix obtained by means of the singular value decomposition. In the paper, the principal analytical and numerical aspects of the proposed identification algorithm are described in detail. Furthermore, a numerical example based on a simple vehicle model is discussed in order to verify by means of numerical experiments the effectiveness of the identification procedure developed in this work. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1374-x Issue No:Vol. 88, No. 8 (2018)

Authors:H. S. Bauomy; A. T. EL-Sayed Pages: 1349 - 1368 Abstract: This study focused on the vibration behavior of a modified vertical conveyor system. The calculated system is exhibited by 2-degree-of-freedom counting quadratic and cubic nonlinearities among both external and parametric forces. Technique of multiple scales connected to gain approximate solutions and study stability of measured structure. All resonances from mathematical solution are extracted. The performance of the system is measured by means of Runge–Kutta fourth-order process (e.g., ode45 in MATLAB). Moreover, two simultaneous resonance cases of this system have been studied analytically and numerically. Stability of acquired numerical solution discovered via frequency response equations. Influences contained by important coefficients scheduled frequency response curves of the considered structure are studied inside numerical results. Methodical results obtained in this work agreed well through the numerical outcome. The description outcome is matched up to available recently published articles. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1375-9 Issue No:Vol. 88, No. 8 (2018)

Authors:Nguyen Van Khang; Nguyen Sy Nam; Nguyen Van Quyen Pages: 1369 - 1384 Abstract: A computer algebraic approach for linearization of the equations of constrained multibody systems is discussed in this paper. Based on linearized differential equations, the Newmark method is applied to calculate steady-state periodic vibrations of the parametric vibration of constrained dynamical models. The numerical calculation is also demonstrated on a model of a mechanism with elastic connecting link. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1376-8 Issue No:Vol. 88, No. 8 (2018)

Authors:Alla V. Ilyashenko; Sergey V. Kuznetsov Pages: 1385 - 1394 Abstract: The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed ( \(c_2\) ) all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree wave can propagate at \(c_2\) phase speed. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1377-7 Issue No:Vol. 88, No. 8 (2018)

Authors:Emmanuel Rigaud; Pierre-Henri Cornuault; Benoît Bazin; Emmanuel Grandais-Menant Pages: 1395 - 1410 Abstract: This paper focuses on the numerical analysis of the vibroacoustic behavior of an electric window-lift gear motor for automotive vehicle which consists of a DC motor and a worm gear. A dynamic modeling of the gear motor is proposed. The excitation sources correspond to radial electromagnetic forces applied to steel stator, electromagnetic input torque fluctuation, rotor mechanical imbalance, worm gear static transmission error and mesh stiffness fluctuations and gear wheel eccentricity. Parametric equations of motion are solved using an iterative spectral method. It allows the computing of the vibroacoustic response of the system, taking account of the interaction between the mesh stiffness fluctuation and the other excitations. The simulation results are validated from comparison with experimental vibroacoustic measurements performed with a specific test bench. Spectrograms of the dynamic response show components corresponding to the harmonics of the excitation spectra, as well as lateral components arising around the mesh frequency and the input torque fluctuation frequency. This spectral enrichment is generated by the interaction between the mesh stiffness fluctuation and the other excitations. The lateral components contribute little to the overall level of the vibroacoustic response, but they may have a significant impact on the quality of noise radiated directly by the gear motor or indirectly by its supporting structure. Finally, the weights of the different excitation sources to the spatial-average mean-square velocity of the radiating surface and the equivalent global dynamic force transmitted to the supporting structure are compared. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1378-6 Issue No:Vol. 88, No. 8 (2018)

Authors:Ehsan Torkan; Mostafa Pirmoradian; Mohammad Hashemian Pages: 1411 - 1428 Abstract: Elastodynamic behavior analysis of structures under moving loads is of great interest in most engineering fields. In this study, dynamic instability due to parametric and external resonances of simply supported thin rectangular plates on an elastic foundation under successive moving masses is investigated as a linear time-periodic problem. Effects of all components of moving mass inertia are considered in the analysis. The governing partial differential equation of motion is transformed to a set of ordinary differential equations using the Galerkin method. A comprehensive study of resonance conditions is carried out for two cases: (1) the masses move on a rectilinear path parallel to the longitudinal edges of the plate, and (2) a sequence of moving masses along the diagonal of the plate. Homotopy perturbation method (HPM) is employed as a semi-analytical method to obtain stable and unstable zones in a parameters space in additions to external resonance curves. In order to validate the HPM results, Floquet theory is applied to the state-space equations. A good agreement between two methods is observed. The results of this study are useful for the design of road pavements resting on foundation soil, slab-type bridges, airport pavements, and decks of ships on which aircrafts land. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1379-5 Issue No:Vol. 88, No. 8 (2018)

Authors:Sandipan Nath Thakur; Chaitali Ray; Subrata Chakraborty Pages: 1429 - 1459 Abstract: Laminated composite shells are widely used as structural components in important aerospace, marine, automobile engineering structures. Thus, appropriate evaluation of sensitivities of responses like deflection, frequency, buckling etc. due to changes in design variables is of great importance for efficient and safe design of such structures. The present paper deals with a comprehensive sensitivity analysis of laminated composite shells using \({C}^{0 }\) finite element with more accurate theoretical model based on higher-order shear deformation theory (HSDT). The sensitivity analysis of deflection and natural frequency with respect to important design parameters such as material parameters, angle of fiber orientation, radius of curvature, density of materials and external load is presented. Furthermore, sensitivity-based importance factor for each parameter is obtained so that the most important parameters affecting the shell responses can be readily identified. The response sensitivities obtained by the proposed formulation are compared with those obtained by the finite difference procedure. An extensive parametric study has been carried out considering different variables to understand the performance of laminated shell. PubDate: 2018-08-01 DOI: 10.1007/s00419-018-1380-z Issue No:Vol. 88, No. 8 (2018)

Authors:Antonios I. Arvanitakis Abstract: Internal variables in continuous media with a microstructure of multiple phases spatially distributed within its volume are discussed in this paper. However, in our analysis phase transition boundaries are represented implicitly under the use of the level-set formulation. Each level-set function representing an interface corresponds to an internal variable of state. Employing the general thermodynamic theory of internal variables within the framework of canonical thermomechanics, we derive the evolution equations for the level-set functions describing the motion of the interfaces inside a material. Finally, the concept of two internal variables and both dissipative and non-dissipative cases is discussed. PubDate: 2018-07-12 DOI: 10.1007/s00419-018-1424-4

Authors:Simon Schnabl; Igor Planinc Abstract: This paper focuses on development of a new mathematical model and its analytical solution for the buckling analysis of elastic longitudinally cracked columns with finite axial adhesion between the cracked sections. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated for different crack lengths and various degrees of the contact adhesion. It is shown that the critical buckling loads can be greatly affected by the crack length and degree of the connection between the cracked sections. Finally, the presented results can be used as a benchmark solution. PubDate: 2018-07-12 DOI: 10.1007/s00419-018-1426-2

Authors:K. C. Le; Y. Piao Abstract: The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. Taking into account the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict stress–strain curves and dislocation densities. PubDate: 2018-07-10 DOI: 10.1007/s00419-018-1425-3

Authors:Yinggang Miao; Bing Du; Muhammad Zakir Sheikh Abstract: Metallic materials are mostly rate dependent in mechanical behavior, but their elastic modulus under high strain rate is hard to measure accurately. In this paper, two methodologies are proposed based on stress wave theory in hope of accurate measurement for metallic materials, for example Ti6Al4V alloy. One is based on the one-dimension stress wave propagation in a long Ti6Al4V bar, and the elastic modulus under a high strain rate is obtained from the calculated stress wave speed. The other technique is to utilize the integrated Hopkinson pressure bar made of Ti6Al4V material. The obtained elastic moduli from these methods are compared and analyzed, and the results are consistent with each other. The numerical simulations with cylindrical and dogbone-shaped specimens are conducted to show the influence of bar indentation on measurement accuracy. An alternative method is introduced based on the vertical split Hopkinson pressure bar, which can extend the integrated Hopkinson pressure bar method for most metallic materials with small bulk. The verification experiments are also conducted. Finally, the limiting strain rate is estimated for potential measurement problems. PubDate: 2018-07-06 DOI: 10.1007/s00419-018-1422-6

Authors:Vipin Sukumara Pillai; Athanasios Kolios; Seng Tjhen Lie Abstract: This paper covers the validation of standard safety assessment procedure in the new BS 7910:2013+A1:2015 for cracked uni-planar square hollow section (SHS) T-, Y- and K-joints using the finite element analyses. The procedure is based on the failure assessment diagram (FAD) method. A completely new and robust finite element mesh generator is developed, and it is validated using the full-scale experimental test results. FAD curves are constructed using the elastic J-integral ( \(J_{\mathrm{e}}\) ), the elastic-plastic J-integral ( \(J_{\mathrm{ep}}\) ) and the plastic collapse load ( \(P_{\mathrm{c}}\) ) values calculated using the 3D cracked models of the joints. The results reveal that the standard Option 1 FAD curve of the new BS code is not always safe in assessing the safety and integrity of cracked uni-planar SHS joints. Therefore, a penalty factor of 1.2 for plastic collapse load is recommended to move all the constructed Option 3 FAD curves above the standard Option 1 curve. The new Option 3 FAD curves are found to generate optimal solutions for cracked uni-planar SHS T-, Y- and K-joints. PubDate: 2018-07-06 DOI: 10.1007/s00419-018-1423-5

Authors:P. F. Pelz; M. M. G. Kuhr Abstract: The interface of two normal colliding media is always unstable. This is true even for both media showing the same density. The common precondition for a Rayleigh–Taylor instability “the lighter medium pushes the heavier” is generalised for the case that two media experience different accelerations in a short period after colliding. The arithmetic average of the accelerations determines the evolution of the wavy interface shape. The theory is applicable for various technologies of impact welding, such as explosion and magnetic pulse welding. PubDate: 2018-07-04 DOI: 10.1007/s00419-018-1420-8

Authors:Peter F. Pelz; Ferdinand-J. Cloos; Jörg Sieber Abstract: This paper investigates the energetic advantage of the embedded propulsion compared to a state-of-the-art propulsion of an aircraft. Hereby, the integral method of boundary layer theory together with the potential theory is applied to analyze the boundary layer thickness and the impact of the flow acceleration due to the embedded propulsion. The aircraft body is treated as a flat plate and the engine as a momentum disk. For an embedded propulsion, there is a trade-off of the engine size, since the propulsion efficiency is affected by the boundary layer. On the one hand, the propulsion inlet momentum is noticeably reduced for a small engine size and the viscous friction is reduced due to boundary layer ingestion. On the other hand, a slow jet speed, i.e., a large engine size, increases the propulsion efficiency as known. The outcome of the energetic assessment is the following: the propulsion efficiency is increased and the drag of the aircraft body is reduced by the embedded propulsion compared to a conventional propulsion. The optimized aircraft engine size depending on Reynolds number is given as well as the dimensionless cost function. PubDate: 2018-07-02 DOI: 10.1007/s00419-018-1417-3

Authors:J. Papuga; R. Halama Abstract: The paper deals with evaluating the mean stress effect in multiaxial criteria for fatigue limit estimation, with special emphasis on the mean shear stress effect. The usual practice of accepting the mean normal stress effect and neglecting the effect of static torsion is scrutinized. Two methods—two critical plane criteria, PCr (Papuga Criterion) and QCP (Quadratic parameter on the Critical Plane)—are described, and additional local stress parameters representing the mean torsion effect are implemented. The efficiency of the new implementations is evaluated on a large data set of 407 fatigue limits. Additionally, outputs of two other well-known methods—the Crossland method and the Dang Van method—are provided for comparison. The positive outcome of including the mean shear stress effect is evident not only in cases of applied mean torsion load, but also in cases with purely axial loading or with biaxial configurations. PubDate: 2018-07-02 DOI: 10.1007/s00419-018-1421-7