Authors:Friedrich Pfeiffer; Johannes Mayet Pages: 1411 - 1426 Abstract: Abstract Chain fountains are known since long time, and many efforts have been taken to model and to explain the dynamics of such a chain fountain. A chain consists of many small elements starting from an inertial container, forms this specific arc and comes to an inertial position again after a rather long vertical distance. As the chain elements are all connected by a bearing-type structure, they all have to move with the same velocity v. In the following we shall consider only the stationary case and not the evolution from a state of rest to the fountain with velocity v. Most models known use the idea of a continuous model. In the following we shall apply multibody theory in addition by modeling each bead with its connections separately. Results confirm the approach. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1260-y Issue No:Vol. 87, No. 9 (2017)

Authors:Guoqi Zhao; Wenfeng Hao; Xixuan Sheng; Yin Luo; Guangping Guo Pages: 1427 - 1438 Abstract: Abstract In this study, the interactions of matrix crack with inclusions of different shapes were investigated using the method of caustic. First, the specimens with inclusions of different shapes were prepared, where glass was used as inclusion and epoxy was used as matrix. Then, caustic experiments were conducted, and the typical caustic spots at the crack tip with varied distances from three different shapes of inclusions were obtained. Ultimately, the stress intensity factors of the cracks shielded by different shapes of inclusions were extracted from the caustic spots, and finite element simulations were conducted to verify the experimental results using the ABAQUS software. The results show that the stress intensity factors measured by the caustic method are in good agreement with the finite element simulation results. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1261-x Issue No:Vol. 87, No. 9 (2017)

Authors:Jialin Tian; Yinglin Yang; Lin Yang Pages: 1439 - 1451 Abstract: Abstract For the nonlinear vibration of the drill string in the drilling process, vibration characteristics analysis and experimental study of the drill string are conducted, which are to analyze the drill string dynamic characteristics with wellbore random friction force on the basis of the horizontal well. Firstly, considering the wellbore random friction force, the analysis models of the drill string vibration and the drilling efficiency of the horizontal well are established. Then, the establishment method of the random wellbore friction field is also obtained. With the combination of solution expressions of each force in the vibration equation, the discrete method of the dynamic model is established. According to the experimental test, the key input parameters are determined, and then, the example analysis of the vibration model is conducted. With the comparison of the experimental test and theoretical calculation, the influences of key parameters on the dynamic characteristics of the drill string are analyzed to verify the accuracy of the analysis model. The results can provide a new insight to the researches of the drill string dynamics, especially for the complex well, such as ultra-deep well, branch well and directional well, in which the wellbore friction has a significant influence on the result of the drill string kinetics. Moreover, the results can offer an important guidance for the design and application of new downhole tools. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1262-9 Issue No:Vol. 87, No. 9 (2017)

Authors:Xuhui Liao; Shunming Li; Lianying Liao; Haodong Meng Pages: 1453 - 1463 Abstract: Abstract An important procedure in transfer path analysis (TPA) is to measure the frequency response functions (FRFs) of the decoupled passive subsystem. The classical TPA method obtains the passive subsystem’s FRFs by direct measuring when the system is disassembled. The main shortcoming of the classical method to measure the FRFs is that it is time-consuming due to the necessity to dismount the active part. In this paper, a novel method is proposed to estimate the passive subsystem’ FRF matrix without disassembling the coupled mechanical structure. The key idea of this method is that the effect of a coupled subsystem will be canceled out if the links which connect this subsystem with the other one have no deformation, since the coupled systems influence each other only through the links which can be regarded as combinations of connecting springs and dampers. Following this idea, the expression of the passive subsystem’s FRF matrix can be deduced from the entire system’s FRF matrix directly. The proposed method in this paper is called the virtual decoupling method, since the decoupling is not ‘real’ but ‘virtual’. Obviously, the actual decoupling procedure is avoided so that the shortcoming mentioned above is overcome. The method is validated by a numerical model and a finite element model. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1264-7 Issue No:Vol. 87, No. 9 (2017)

Authors:S. H. Mirtalaie; M. A. Hajabasi Pages: 1465 - 1494 Abstract: Abstract The nonlinear axial-lateral-torsional free vibration of the rotating shaft is analyzed by employing the Rayleigh beam theory. The effects of lateral, axial and torsional deformations, gyroscopic forces and rotary inertia are taken into account, but the shear deformations are neglected. In the new developed dynamic model, the nonlinearities are originated from the stretching of beam centerline, nonlinear curvature and twist and inertial terms which leads to the coupling between the axial, lateral and torsional deformations. The deformed configuration of the cross section of the beam is represented by the axial and lateral deformations, also the geometry of the beam in the deformed configuration is represented by Euler angles. A system of coupled nonlinear differential equations is obtained which is examined by the method of multiple scales and the nonlinear natural frequencies are determined. The accuracy of the solutions is inspected by comparing the free vibration response of the system with the numerical integration of the governing equations. The effect of the spin speed and radius-to-length ratio of the rotating shaft on the free vibrational behavior of the system is inspected. The study demonstrates the effect of axial-lateral-torsional coupling on the nonlinear free vibrations of the rotating shaft. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1265-6 Issue No:Vol. 87, No. 9 (2017)

Authors:B. Emek Abali; Wolfgang H. Müller; Francesco dell’Isola Pages: 1495 - 1510 Abstract: Abstract In continuum mechanics, there exists a unique theory for elasticity, which includes the first gradient of displacement. The corresponding generalization of elasticity is referred to as strain gradient elasticity or higher gradient theories, where the second and higher gradients of displacement are involved. Unfortunately, there is a lack of consensus among scientists how to achieve the generalization. Various suggestions were made, in order to compare or even verify these, we need a generic computational tool. In this paper, we follow an unusual but quite convenient way of formulation based on action principles. First, in order to present its benefits, we start with the action principle leading to the well-known form of elasticity theory and present a variational formulation in order to obtain a weak form. Second, we generalize elasticity and point out, in which term the suggested formalism differs. By using the same approach, we obtain a weak form for strain gradient elasticity. The weak forms for elasticity and for strain gradient elasticity are solved numerically by using open-source packages—by using the finite element method in space and finite difference method in time. We present some applications from elasticity as well as strain gradient elasticity and simulate the so-called size effect. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1266-5 Issue No:Vol. 87, No. 9 (2017)

Authors:Arpita Mandal; Chaitali Ray; Salil Haldar Pages: 1511 - 1523 Abstract: Abstract The present paper deals with free vibration analysis of laminated composite skew plates with and without cut-outs. The experimental investigation along with numerical simulation has been presented in this paper for complete understanding of the dynamic behaviour of laminated skew plates with cut-out. Glass fibre-reinforced laminated composite plates have been prepared by resin infusion process using vacuum bagging technique in the laboratory for experimental analysis. The experimental studies have been carried out on skew composite plates with varying size of cut-out placed at the centre. The numerical analysis has been carried out by developing a computer code in MATLAB. Special attention is drawn on the formulation of mass matrix by considering effect of rotary inertia. The results obtained by the finite element formulation using nine-noded isoparametric plate-bending elements are validated by comparing the results from relevant published literature. The numerical and experimental data are then compared for experimental verification of present investigation. The consistency of mode shapes between experimental and numerical investigations is checked by using modal assurance criteria. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1267-4 Issue No:Vol. 87, No. 9 (2017)

Authors:Shaowei Hu; Jiang Yu; Congjie Wei; Zhaoguang Zhang Pages: 1525 - 1539 Abstract: Abstract Due to non-uniform distribution of structural deformation along its transverse width direction, shear lag behavior widely exists in composite structure with multi-box and leads to structural instability and destruction. To in-depth explore its mechanical mechanism, a type of steel–concrete composite structure with double-box (the DBSCCS model) is proposed, and its longitudinal warping shape functions are set up. Based on the minimum potential energy principle, governing differential equations of the DBSCCS model and its boundary conditions are deduced by means of the variational method. And then, its strain functions and shear lag coefficients are also obtained under concentrated loading and symmetrical loading, respectively. What is more, experimental verification and its related parametric sensitivity analysis are launched based on deduced longitudinal strain functions and shear lag coefficients. Through this analysis, it shows that this method can be used to illustrate and predict shear lag characteristics for this type of the DBSCCS model. That further suggests that it provides a more reference value for engineering design and structure optimization in some extent for the composite structures. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1268-3 Issue No:Vol. 87, No. 9 (2017)

Authors:Pei Zhu; Xingmin Ren; Weiyang Qin; Yongfeng Yang; Zhiyong Zhou Pages: 1541 - 1554 Abstract: Abstract In this paper, we study the characteristics of a tri-stable energy harvester (TEH) that is realized by the effect of magnetic attractive forces. The electromechanical model is established, and the corresponding coupling equations are derived by Euler–Lagrange equation. The potential energy indicates that the TEH’s potential well depths are the determinant factors for performance and can be designed such that the snap-through is easy to be elicited. We find that the TEH exhibits the best performance when the three potential well’s depths are nearly identical. To highlight the advantage of the TEH in harvesting energy, the comparisons between the tri-stable energy harvester and the bi-stable energy harvester (BEH) are carried out in simulations and experiments. The results prove that the TEH is preferable to the BEH in energy harvesting. The validation experiments show that the TEH owns a wide range of frequency of snap-through and high output voltage. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1270-9 Issue No:Vol. 87, No. 9 (2017)

Authors:Abdolrasoul Ranjbaran; Mohammad Ranjbaran Pages: 1555 - 1565 Abstract: Abstract Beam, column, plate, and any other structure, under full or partial compressive loading, are prone to failure by the buckling phenomenon. At the instant of failure, the structure may be in unpredictable elastic, elastic–plastic, full plastic, cracked, or other forms of deterioration state. Therefore, in spite of so much study, there is no definite solution to the problem. In this paper a unified, simple, and exact theory is proposed where buckling is considered as the change of state of structure between intact and collapsed states, and then the buckling capacity is innovatively expressed via states and phenomena functions, which are explicitly defined as functions of state variable. The state variable is determined by calibration of the structure slenderness ratio. The efficacy of the work is verified via concise mathematical logics, and comparison of the results with those of the others via seven examples. PubDate: 2017-09-01 DOI: 10.1007/s00419-017-1273-6 Issue No:Vol. 87, No. 9 (2017)

Authors:Sonia Parvanova; Georgi Vasilev; Petia Dineva Abstract: Abstract The paper deals with numerical evaluation of the scattered wave and dynamic stress concentration fields in a finite anisotropic solid containing multiple nano-cavities. 2D plane-strain state and in-plane wave motion are assumed. The proposed mechanical model combines classical elastodynamic theory for the bulk general anisotropic solid and the Gurtin–Murdoch theory of surface elasticity assuming localized constitutive equation for the infinitely thin interface between the cavity and the matrix. The developed computational methodology is based on the following: (a) displacement boundary integral equations along existing boundaries using the analytically derived through Radon transform fundamental solution of the equation of motion of the bulk anisotropic solid; (b) non-classical boundary conditions of the Gurtin–Murdoch model along the interface between the matrix and cavities taking into consideration a jump in the stresses as one moves from the bulk material to the cavity due to the presence of surface elasticity; and (c) elastic-viscoelastic correspondence principle. The accuracy of the developed software is proven by comparisons of the obtained results solved by boundary element method and finite element method. A detailed parametric study reveals the sensitivity of the wave field to different key factors such as size, number and configuration of the cavities, surface and bulk material properties. PubDate: 2017-09-13 DOI: 10.1007/s00419-017-1303-4

Authors:R. Bagheri Abstract: Abstract A piezoelectric half-plane weakened by several horizontal cracks is investigated under anti-plane mechanical and in-plane electrical impacts. The distributed dislocation and integral transform techniques are employed to construct integral equations of the multiple dynamic cracks embedded in the piezoelectric half-plane. At first, the stress and the electric fields in the piezoelectric half-plane are calculated by using pattern. Then, by determining distributed dislocation density on the crack surface, a system of singular integral equations with Cauchy-type singularity is derived. The dynamic field stress intensity factors are determined by using the numerical Laplace inversion and dislocation densities. Finally, several examples are solved and the effects of the geometrical parameters and cracks configuration are graphically obtained upon the dynamic field intensity factors. PubDate: 2017-09-12 DOI: 10.1007/s00419-017-1305-2

Authors:Włodzimierz Kurnik; Piotr M. Przybyłowicz; Roman Bogacz Abstract: Abstract The paper is inspired by recent experiment with a two-member discrete column subjected to dry friction force of interaction between the moving column and a moving plane. The experiment was presented in the form of a YouTube film and recommended as an experimental evidence for flutter in the Ziegler column. We show that the tested mechanism cannot be identified with the original Ziegler column. PubDate: 2017-08-31 DOI: 10.1007/s00419-017-1294-1

Authors:Airong Liu; Mark Andrew Bradford; Yong-Lin Pi Abstract: Abstract Nonlinear in-plane multiple equilibria and buckling of pinned–fixed shallow circular arches under an arbitrary radial concentrated load are investigated. Analytical solutions for the multiple nonlinear equilibria, buckling and limit points are derived. New findings are: (1) pinned–fixed shallow arches under the arbitrary concentrated load have multiple stable and unstable equilibria; (2) the position of the arbitrary concentrated load and the modified slenderness of the arch influence the number of multiple equilibria and limit points as well as the first buckling load significantly; (3) a pinned–fixed arch under the arbitrary concentrated load can buckle in a limit point instability mode, but not in a bifurcation mode; (4) when the load is located between the crown and the pinned end, the buckling load is lower than that when the load is located between the crown and the fixed end, and (5) in addition to limit points, the nonlinear equilibria of pinned–fixed arches under the arbitrary concentrated load have inflexion points, which corresponds to specific modified slenderness switching the number of equilibria and limit points or switching buckling and no buckling behaviour. The analytical solutions for inflexion points and specific modified slenderness, and for the corresponding load, axial force and displacement are also derived for the first time in the literature. Comparisons with the finite element results have shown that the analytical solutions can accurately predict the multiple equilibria, limit points, inflexion points, and buckling load of shallow pinned–fixed arches under the arbitrary concentrated load. PubDate: 2017-08-31 DOI: 10.1007/s00419-017-1300-7

Authors:Sebastian Korczak Abstract: Abstract This contribution presents some nonlinear behaviors of an underactuated mechanical system under the trajectory tracking task. Presented hovercraft model is fully controlled by the computed torque algorithm with the pseudoinverse operation and proportional-derivative feedback. General form of errors dynamic equation gives possibility to analyze their behavior. These errors present irregular behaviors because of the input force limitations. Positive values of highest Lyapunov exponent and Fourier spectrum shape prove chaotic behavior of the system. PubDate: 2017-08-30 DOI: 10.1007/s00419-017-1297-y

Authors:Chang-Sheng Lin Abstract: Abstract The topic of this paper is the accuracy improvements in parametric estimation of systems with modal interference. A channel-expansion technique has been previously used in the Ibrahim time domain method to well perform the modal identification. However, the error involved in the determination of system order from the frequency response function or the Fourier spectrum associated with each of the response channels would generally lead to a distortion in the modal identification, especially for a system with modal interference. In the present paper, the singular value decomposition in conjunction with least-squares analysis is introduced in the procedure of Ibrahim time domain method to obtain the system matrix and determine the system order. Also, the phase angle diagram of frequency response function can be employed to distinguish the structural modes influenced by modal interference and then avoid the phenomenon of omitted modes from the distortion of system order determined by frequency response function. Numerical simulations, including two examples of a model of the motor vehicle, and a linear two-dimensional model of one-half of a railway vehicle, confirm the validity of the proposed method for modal identification of a system with modal interference. PubDate: 2017-08-21 DOI: 10.1007/s00419-017-1292-3

Authors:Alireza Ebrahimi; Mahdi Heydari; Mehdi Behzad Abstract: Abstract In this paper, the forced vibration of a cracked rotor with an open edge crack has been studied by a new continuous model for flexural vibration of cracked rotors proposed in Ebrahimi et al. (J Sound Vib 333:3522–3535, 2014). The cracked rotor behavior under the external excitation of gravity and unbalance forces is presented. Since the governing equation is linear, using the superposition principle the responses of the cracked rotor to the gravity and unbalance forces are calculated separately. Then, the total response is calculated by summing these two responses. Each of these two responses is found by using a modified Galerkin method. The effect of the crack in the presence of the gravity and unbalance forces on the time response, frequency spectrum, frequency response curve and orbit diagram of the rotor is analyzed. Results can be used for the crack identification of rotors. PubDate: 2017-08-19 DOI: 10.1007/s00419-017-1295-0

Authors:S. Suresh Kumar; H. Ashwin Clement; R. Karthik Abstract: Abstract In real time, aircraft panels are mainly subjected to fatigue loading induced by the pressurization cycle. When two cracks approach one another, their stress fields influence each other and produce enhancing or shielding effect depending on the position of the cracks. In the present work, an attempt has been made to determine the effect of plate curvature on mixed mode stress intensity factor (SIF) of multiple cracks in a riveted joint using numerical and experimental methods. Diametrically opposite surface cracks of various crack depth ratios [(a / t); ‘a’ crack length and ‘t’ thickness of the plate] were considered for a typical longitudinal splice joint. ‘Frictional contact interaction’ was defined between rivet hole, rivet head-sheet, between sheet surfaces and stringer to sheet interfaces in order to simulate the service conditions. At lower crack depths, [ \(({a}/{t}) =2\) ] higher SIF was observed for biaxial loading compared to uniaxial loading. Marginal influence of loading condition was observed for deep cracks [ \(({a}/{t})=5\) ]. SIF values of curved panels were observed to be higher than that of flat panel irrespective of the crack depths considered the present work. This is mainly due to ‘flattening’ of curved plate when loading. It was also noticed that, the presence of stiffener reduces the in plane (mode-II) and out of plane (mode-III) shear fracture considerably for curved panel as it exerts compressive force on the joint. To validate the numerical observations, experiments were conducted on a Al 2024-T3 specimens to determine the fatigue crack growth rate and it showed a good correlation with numerical methods. The experimental results also indicated a higher crack growth rate for curved panel compared to flat panel which is mainly due to additional bending stress at the rivet hole region caused by eccentric loading. PubDate: 2017-08-17 DOI: 10.1007/s00419-017-1289-y

Authors:V. I. Fabrikant Abstract: Abstract A general solution is obtained for a magneto-electro-elastic half-space \(x_{3}\ge 0\) subjected to arbitrary point forces or arbitrary point dislocations, as well as electric and magnetic influence by using two-dimensional Fourier transform. The final results are presented as single integrals over a unit circle. Using the theory of generalized functions, all basic parameters at the half-space boundary are defined in a finite form, and no computation of any integral is needed. Knowledge of Green’s functions in finite form allows us to derive the governing integral equations for the normal and tangential contact and crack problems, as well as to establish certain relationship between the kernels of the relevant integral equations. We also established some interesting general properties of the determinants, which might be new. PubDate: 2017-08-16 DOI: 10.1007/s00419-017-1293-2

Authors:Stefan Kaessmair; Paul Steinmann Abstract: Abstract In the present contribution, we consider species diffusion coupled to finite deformations in strongly heterogeneous microstructures. A semi-dual energy formulation parameterized in terms of the chemical potential is obtained by Legendre transformation of the free energy. Doing so avoids the presence of higher gradients of the deformation field. The constitutive response at the macroscopic level is obtained using variationally consistent homogenization (Larson et al. in Int J Numer Method Eng 81(13):1659–1686, 2010. doi:10.1002/nme.2747). This approach allows to treat transient microscale problems on a representative volume element which has a finite size, i.e., the scales are not clearly separated. Full details of the implementation are provided. A series of numerical examples compares the homogenization results to single-scale formulations which fully resolve all microstructural features. PubDate: 2017-08-12 DOI: 10.1007/s00419-017-1287-0