Authors:Wenxue Zhang; Ying Chen; Wenqi Kou; Xiuli Du Pages: 329 - 339 Abstract: It is important to estimate the longitudinal fundamental period of cable-stayed bridges accurately in the selecting of structure system and evaluating of seismic response of a cable-stayed bridge. A reverse double-mass model to compute the longitudinal fundamental period of a floating cable-stayed bridge is proposed based on the transfer paths of seismic horizontal inertia forces under longitudinal seismic. The simplified calculation formula of the longitudinal fundamental period has been developed using rigidity-based method. In addition, another simplified calculation formula was proposed based on Rayleigh method, in which the coupling of the vertical vibration of the main girder and longitudinal vibration of the bridge can be accounted together. The accuracy of the proposed calculating expressions was verified by finite element analysis using SAP2000 with ten constructed cable-stayed bridges. It indicated that the two formulae developed in this study, especially the formula based on rigidity-based method, were more reliable than single-mass model commonly used and could be effectively applied in simplified calculation of the longitudinal fundamental period of cable-stayed bridges. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1311-4 Issue No:Vol. 88, No. 3 (2018)

Authors:H. M. Mobarak; Helen Wu; Joseph P. Spagnol; Keqin Xiao Pages: 341 - 372 Abstract: In this paper, a new analytical model (unbalanced one), which considers the coupling effects of unbalance force, rotor weight, and rotor physical and dimensional properties, is developed to study the actual breathing mechanisms of the transverse fatigue crack in a cracked rotor system. The results are also compared with those of the existing balanced model, where only rotor weight is considered. It has been identified that a crack in the unbalanced model breathes differently from the one in the balanced model. A crack’s breathing mechanism in the unbalanced model depends strongly on its location along shaft length. At some special locations, a crack in the unbalanced model may remain fully closed or open during the shaft rotation, which will never occur in a balanced model. It may also behave completely like the one in the balanced shaft. Depending on the crack location, unbalance force magnitude and orientation, the unbalanced shaft may be stiffer or more flexible than the balanced counterpart. It is also demonstrated that the unbalanced model will progressively approach balanced one as unbalance force decreases. Further, different crack breathing mechanisms between two models lead to a large difference along shaft length in the second area moment of inertia, which forms the elements of local stiffness matrix at crack location. It is expected that more accurate prediction of the vibration response of a cracked rotor can be achieved when the effect of unbalance force and rotor properties on the crack breathing has been taken into account. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1312-3 Issue No:Vol. 88, No. 3 (2018)

Authors:Zhixin Zhan; Weiping Hu; Qingchun Meng; Zhidong Guan Pages: 373 - 390 Abstract: In this paper, a new method is proposed to calculate the fatigue life and defect tolerance for a 30CrMnSiA steel specimen with foreign object impact damage and scratch damage. First, the processes of foreign object impact and scratch are simulated. Then, the Lemaitre’s plasticity damage model is adopted to calculate the initial damage field arising from the impact process and scratch process. Second, the Chaudonneret’s damage model is applied to calculate the fatigue damage for the specimen with a defect under multiaxial fatigue loading. Then, the FE implementation of the damage mechanics model is presented in the platform of ANSYS, in which the coupling effect between the stress and damage fields is considered. Finally, this proposed method is applied to fatigue life and defect tolerance calculation for the 30CrMnSiA steel specimen with an impact defect and a scratch defect. The experiments were conducted to evaluate the approach mentioned above. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1313-2 Issue No:Vol. 88, No. 3 (2018)

Authors:Tingting Zhang; Hans True; Huanyun Dai Pages: 391 - 404 Abstract: In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness \(K_{1x}\) as bifurcation parameters the first and second Lyapunov coefficients are calculated to determine which kind of Hopf bifurcation can happen and how the system states change with the variance of the bifurcation parameters. It is found that multiple solution branches both stable and unstable coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit cycles both stable and unstable near the Hopf bifurcation point. With a further reduction in the bifurcation parameters two saddle-node bifurcation points emerge, resulting in the loss of the stable limit cycle between these two bifurcation points. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1314-1 Issue No:Vol. 88, No. 3 (2018)

Authors:Asghar Najafi Pages: 405 - 418 Abstract: Nonlinear behavior of a rotating bladed disk system is investigated at the critical speed, where the rotor internal damping starts to destabilize the rotor vibrations. A simple bladed Jeffcott model is suggested to study the Hopf bifurcation around the critical speed. The Euler–Bernoulli theory is employed to model the flexible blades, which bend in the plane of the motion. Duffing’s type nonlinearity is considered for the bearing stiffness. The equations of motion are derived using the Lagrange equations, and the bifurcation equation is obtained by the multiple scales method. The characteristics of the limit cycle are studied through the bifurcation equation near the critical speed. The nonlinear analysis results are validated by a numerical simulation. The results show that the blade dynamic can deteriorate the asynchronous vibrations and even widen the instability region. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1316-z Issue No:Vol. 88, No. 3 (2018)

Authors:Carmine M. Pappalardo; Domenico Guida Pages: 419 - 451 Abstract: This paper deals with the Lagrange multipliers corresponding to the intrinsic constraint equations of rigid multibody mechanical systems. The intrinsic constraint equations are algebraic equations that are associated with nonminimal sets of orientation parameters employed for the kinematic representation of large finite rotations. Two coordinate formulations are analyzed in this investigation, namely the reference point coordinate formulation (RPCF) with Euler parameters and the natural absolute coordinate formulation (NACF). While the RPCF with Euler parameters employs the four components of a unit quaternion as rotational coordinates, the NACF directly uses the orthonormal set of nine direction cosines for describing the orientation of a rigid body in the three-dimensional space. In the multibody approaches based on the RPCF with Euler parameters and on the NACF, the use of a nonminimal set of rotational coordinates facilitates a general and systematic formulation of the differential–algebraic equations of motion. Considering the basic equations of classical mechanics, the fundamental problem of constrained motion is formalized and solved in this paper by using a special form of the Udwadia–Kalaba method. By doing so, the Udwadia–Kalaba equations are employed for obtaining closed-form analytical solutions for the Lagrange multipliers associated with the intrinsic constraint equations that appear in the differential–algebraic dynamic equations developed by using the RPCF with Euler parameters and the NACF multibody approaches. Two simple numerical examples support the analytical results found in this paper. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1317-y Issue No:Vol. 88, No. 3 (2018)

Authors:F. D. Fischer; G. A. Zickler; J. Svoboda Pages: 453 - 460 Abstract: The ensemble of interstitial atoms as C attracted to a dislocation is well established as “Cottrell cloud” phenomenon. The deposition of the interstitial atoms in octahedral or tetrahedral positions in a bcc lattice may yield a remarkable internal stress state according to their anisotropic misfit eigenstrains. The stress fields of the atoms may then lead to a significant change in the stress field, e.g., around a dislocation. In such a case, the interstitial atoms are situated near the dislocation core in cylindrical volume elements along the dislocation line. As the occupancy of the sites in each cylinder by interstitial atoms can be considered as constant, also the eigenstrain state tensor is constant in the cylinder. A complete set of analytical expressions for the eigenstress state inside and outside of the cylinder is presented. The resultant stress field is then given by superposition, which allows also the determination of the interaction energy between the Cottrell cloud and the dislocation. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1318-x Issue No:Vol. 88, No. 3 (2018)

Authors:M. Beerhorst; M. Seibel; C. Mittelstedt Pages: 461 - 476 Abstract: This paper presents approximate solutions for the postbuckling behavior of a plate consisting of laminated composites with symmetrical, balanced lay-up loaded in longitudinal compression. The transversal edges of the plate are simply supported, one longitudinal edge is free and the opposite one is rotationally restrained. Key to obtain an explicit and thus highly computational efficient solution is the use of a shape function with only few variables. First, the shape function is inserted into the compatibility condition of in-plane strains to derive a closed-form solution of Airy’s stress function. Then, the equilibrium condition is approximated with the Galerkin procedure yielding a load–deflection relationship. Subsequently, other state variables such as in-plane displacements and stresses can be obtained. Overall, results for displacements and strains show very good agreement with detailed nonlinear finite element analyses. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1319-9 Issue No:Vol. 88, No. 3 (2018)

Authors:V. I. Fabrikant Pages: 477 - 478 Abstract: The following text should be changed in the abstract: Using the theory of generalized functions, some basic parameters at the half-space boundary are defined in a finite form, and no computation of any integral is needed. Knowledge of some of the Green’s functions in finite form allows us to derive the governing integral equations for the normal contact and crack problems, as well as to establish certain relationship between the integrands in Fourier transforms of the kernels of the relevant integral equations. PubDate: 2018-03-01 DOI: 10.1007/s00419-017-1331-0 Issue No:Vol. 88, No. 3 (2018)

Authors:Sebastian Korczak Pages: 111 - 120 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: 2018-02-01 DOI: 10.1007/s00419-017-1297-y Issue No:Vol. 88, No. 1-2 (2018)

Authors:C. B. Silbermann; J. Ihlemann Pages: 141 - 173 Abstract: Continuum dislocation theory (CDT) allows the consideration of dislocation ensembles by introducing the dislocation density tensor. Though the kinematics of geometrically linear CDT are well established, the closure of governing field equations is not finished yet. The present study now brings together different principles for such a closure: It is shown how the field equations for the CDT can be obtained from potential energy minimization and from the phase field approach. These two energetic methods are integrated into a generic thermodynamic framework with twofold benefit: First, the rigorous thermodynamic treatment allows clarifying physical consequences of the energetic methods, among them the proof of thermodynamic consistency. Second, the framework provides a basis for consistent extensions of CDT. In this way, a new dynamic formulation of CDT is presented, which enables the analysis of the evolution of dislocation structures during plastic deformation. Moreover, a variety of possible dissipative phenomena is considered and the mechanical balance laws are deduced. For two special cases, the field equations are derived in the strong form and the stability of the solution is analyzed. Next, a flexible numerical solution algorithm is presented using the finite difference method. Solutions of various initial boundary value problems are presented for the case of plane deformations. Therefore, some of the dissipative phenomena are further investigated and two distinct sources of the Bauschinger effect are identified. Special attention is also given to different boundary conditions and their effect on the solution. For the case of uniaxial compression, the numerical results are confronted with experimental data. Thus, the simulations are validated and a new consistent interpretation of the experimental results is achieved. PubDate: 2018-02-01 DOI: 10.1007/s00419-017-1296-z Issue No:Vol. 88, No. 1-2 (2018)

Authors:Xueyan Chen; Huifeng Tan; Jianzheng Wei Abstract: In this paper, an energy coefficient method is presented to predict the nonlinear constitutive relations of stretching dominated lattice materials. The proposed method adopts a process based on boundary coefficient and energy calculation to obtain the effective elastic stiffness of lattice truss materials. Furthermore, the Ramberg–Osgood relationship and the geometrical coefficient is introduced to establish the nonlinear relationship between macro-stress and macro-strain. The method is used to determine the stiffness matrix of the pyramid lattice material and the nonlinear constitutive relationships of the octet lattice material and the 3D Kagome core sandwich panels under uniaxial compression and pure shear, respectively. The obtained results agree well with the related experimental results. This agreement validates the energy coefficient method. PubDate: 2018-02-26 DOI: 10.1007/s00419-018-1343-4

Authors:Daniel Fernández Caballero; Juan Manuel Muñoz Guijosa; Víctor Rodríguez de la Cruz Abstract: Torsional springs or coil springs are used to apply a torque and obtain a rotation of its shaft. They are usually manufactured with flat steel. Recommended maximum operating stresses in static applications are given as a percentage of tensile strength. These values could be consulted in an experimental table with an appropriate stress correction factor. An energetic model for torsional spiral springs is presented in this work. First of all a parametric study analyzes different variables which affect the spring performance. Main variables analyzed have been the length of the spring strip, strip thickness and height, housing diameter, shaft diameter, variation of bending stiffness and curvature along the length of the spring strip. Afterward, the analysis of energy storage in coil spring is carried out. There are two causes why energy storage is less than the maximum of the model developed. The first one is energy wasted in coil contact and in spring blocking and unblocking process. The second cause is that the torque applied to spin is less than the one which reached the yield strength in spring section. Both of them are quantified and incorporated in the model. At the end the energetic model is used to calculate the torque–angle turned curve, framework deformation and the spring-framework contact force. Model developed is validated with test on a monolithic fiberglass spiral spring. PubDate: 2018-02-22 DOI: 10.1007/s00419-018-1354-1

Authors:Farhad Adel; Majid Jamal-Omidi Abstract: This paper investigates the vibrational behavior of a system which consists of two free–free Timoshenko beams interconnected by a nonlinear joint. To model the bolted lap joint interface, a combination of the linear translational spring, linear and nonlinear torsional springs, and a linear torsional damper is used. The governing equations of motion are derived using the Euler–Lagrange equations. The reduced-order model equations are obtained based on Galerkin method. The set of coupled nonlinear equations are then analytically solved using the harmonic balance approach and numerical simulation. A parametric study is carried out to reveal the influence of different parameters such as linear and nonlinear torsional spring, linear translational spring, and linear torsional damper on the vibration and stability of the bolted lap joint structure. It is shown that the effect of the nonlinear torsional spring on the response of the system is significant. Interestingly, it is observed that in the presence of the nonlinear spring the softening behavior could be changed to hardening behavior. In addition, the effects of the different engineering beam theories on the modeling of the substructures are studied and it is observed that considering the effect of the rotary inertia and shear deformations is significant. In addition, it is observed that neglecting each of them can yield completely wrong interpretations of the system behavior and incorrect results. PubDate: 2018-02-20 DOI: 10.1007/s00419-018-1353-2

Authors:Tianya Bian; Zhidong Guan; Faqi Liu Abstract: Experiments and finite element analysis were carried out for the problem of open-hole sensitivity of 3D carbon/carbon composite material plates. Finite element models of the representative volume element and open-hole plates of 3D carbon/carbon composite were established. Transition method between macro-level stress and meso-level stress was given, and numerical simulation on the compressive failure of open-hole plates was implemented based on this method. By uniaxial compressive tests of 3D carbon/carbon composite open-hole plates, good agreement between numerical results and experiments was observed. In addition, the influence of width-to-diameter ratio (WTDR) on the compressive strength was analyzed. The results show that the compressive strength of the WTDR-6 open-hole plate is larger than that of the WTDR-4 open-hole plate. It can be considered that the carbon/carbon composite plate is insensitive to the opening hole when the WTDR reaches to 6. And the result of the investigation provides insight into the design of carbon/carbon composite open-hole plates. PubDate: 2018-02-15 DOI: 10.1007/s00419-018-1349-y

Authors:Mohammad Sahlabadi; Naser Soltani Abstract: High-density polyethylene (HDPE) is widely used in the production of fuel tanks and natural gas distribution systems, and therefore better understanding its fractural behavior under different loading conditions is essential. The present study is an extension of our previous work, in which J–Q theory was applied to study elastic–plastic fracture in HDPE. In this study, we explore the mixed-mode ductile fracture in HDPE using Brazilian disk samples. Brazilian disk test is commonly used to create different modes of fracture; however, its application has been limited to the linear elastic fracture mechanics. This work has merit to characterize mixed-mode ductile fracture from the experimental data. The combined experimental finite element (CEFE) method introduced in our previous studies was employed to calculate ductile fracture parameters. To validate experimental results, the CEFE results were compared to finite element results, and the difference was less than 7%. The effects of the factors like crack angle and sample’s thickness on Q values were also investigated. PubDate: 2018-02-12 DOI: 10.1007/s00419-018-1350-5

Authors:Meilong Chen; Shuying Li; Hongliang Li; Tao Peng; Siyuan Liu Abstract: Free torsional vibration analysis of a shaft with multiple disks and elastic supports is important in mechanical engineering. As is well known, many numerical methods have been proposed to solve the problem, but exact analytic solutions are rarely reported in the literature. In this paper, a successful method is presented to solve this problem by combining the Hamilton’s principle and integral transform. The analysis results from the proposed method agree well with the results published in the studies. Compared with lumped-mass method, it shows that with lumped-mass method, the accuracy of computation of natural frequencies and modes very much depends on the numbers of simplified inertia and the structures simplified. The results demonstrate that the proposed method is superior to the lumped-parameter method in accuracy. The proposed method is used to verify the finite element method while modeling shafting. The results indicate that when using finite element modeling shaft, the principle is that the order of interpolation functions should be chosen as high as possible, the elements chosen as many as possible and the discrete finite elements of shaft divided as even as possible in a reasonable range. PubDate: 2018-02-12 DOI: 10.1007/s00419-018-1352-3

Authors:A. Alijani; M. Mastan Abadi; A. Darvizeh; M. Kh. Abadi Abstract: The purpose of the present study is to investigate the static behavior of cracked Euler–Bernoulli beams resting on an elastic foundation through implementing analytical, approximate and numerical approaches. Among common approximate and numerical approaches, Galerkin’s and the finite element methods, respectively, are selected to solve the governing equations. The crack-caused imperfection is simulated by two discrete spring models whose stiffness factors are determined in terms of the stress intensity factor and the geometric parameters. In the analytical solution, a Dirac’s delta function is used to define the singularity in the flexural stiffness and to derive an improved governing equation. In the Galerkin solution, two deflection functions corresponding to the right- and left-hand sides of the crack point are offered to satisfy the governing equation. In the finite element method by introducing a novel technique, a modified stiffness matrix whose components are enriched by material and geometric parameters of the crack is proposed. This study focuses on the effect of various parameters including the crack depth and position, boundary conditions, elastic foundation as well as the discrete spring models on the beam deflection through aforementioned theoretical approaches. Lastly, results from these three theoretical solutions are verified through comparison with each other and Abaqus software. PubDate: 2018-02-06 DOI: 10.1007/s00419-018-1347-0

Authors:Wei Sun; Rong Liu; Yunfei Fan Abstract: Finding the best coating location with the fixed shape of the hard coating is an urgent need for the engineering application of the hard-coating damping. In this paper, a study on optimal placement of hard-coating damping treatment for vibration reduction in the cantilever plate was presented. Based on the energy method and the assumed mode method, the analytical model was derived for free vibration analysis of the thin plate partially covered with hard coating, and the modal loss factors of the coating structure were determined by the modified modal strain energy method. The damping optimization model of the hard-coating thin plate was described with the maximum modal loss factor of single order or multi-orders as the objective function and the coating position as the design variable. Moreover, a method named multiple population genetic algorithms was proposed to search for the optimal coating position. Finally, a cantilever titanium plate with a single side partially deposited with NiCrAlCoY+YSZ hard coating was taken as an example to carry out a case study. The correctness of the analytical results was verified by ANSYS software and experiment, and the rationality of the damping optimization results for the hard-coating plate was also verified by experiment. PubDate: 2018-02-05 DOI: 10.1007/s00419-018-1348-z