Authors:M. R. Behnam; M. M. Khatibi; A. Malekjafarian Pages: 837 - 853 Abstract: Frequency response functions (FRFs) can be estimated only from responses of structures without knowledge of input forces. Mode shapes identified from operational modal analysis (OMA) methods are unscaled, and the unscaled mode shapes provide unscaled FRFs. In this paper, mass change and mass–stiffness methods are employed to construct FRFs from the response-only measurements. A numerical case study of a cantilever beam is investigated using the finite element method. It is shown that the mass–stiffness change method provides more accurate results compared to the mass change method in the low-frequency range. A laboratory-scale steel beam is also tested using an OMA method and conventional hammer test. The experimental results show better accuracy of the identified FRFs in the low-frequency range when the mass–stiffness method is used. PubDate: 2018-06-01 DOI: 10.1007/s00419-018-1345-2 Issue No:Vol. 88, No. 6 (2018)

Authors:Kai Zhou; Jinpeng Su; Hongxing Hua Pages: 855 - 873 Abstract: This paper investigates the free and forced vibration of moderately thick orthotropic plates under thermal environment and resting on elastic supports. Three kinds of elastic supports, namely non-homogeneous elastic foundations, point elastic supports and line elastic supports, are considered in the present study. The first-order shear deformation theory is employed to formulate the strain and kinetic energy functions of the structures, and then the stiffness and mass matrices can be obtained by applying the Hamilton’s principle. The modified Fourier method is adopted to solve the dynamic problems of moderately thick orthotropic plates with different combinations of temperature variations, elastic supports and boundary conditions. The accuracy and reliability of the proposed formulation are validated by comparing the obtained results with the finite element method results. Finally, the effects of some key parameters including temperature variation and stiffness values of the elastic supports on the modal and dynamic characteristics of the plates are analyzed in detail. In views of the versatility of the developed method, it offers an efficient tool for the structural analysis of moderately thick orthotropic plates under thermal environment and resting on elastic supports. PubDate: 2018-06-01 DOI: 10.1007/s00419-018-1346-1 Issue No:Vol. 88, No. 6 (2018)

Authors:A. Alijani; M. Mastan Abadi; A. Darvizeh; M. Kh. Abadi Pages: 875 - 895 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: 2018-06-01 DOI: 10.1007/s00419-018-1347-0 Issue No:Vol. 88, No. 6 (2018)

Authors:Wei Sun; Rong Liu; Yunfei Fan Pages: 897 - 912 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: 2018-06-01 DOI: 10.1007/s00419-018-1348-z Issue No:Vol. 88, No. 6 (2018)

Authors:Tianya Bian; Zhidong Guan; Faqi Liu Pages: 913 - 932 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: 2018-06-01 DOI: 10.1007/s00419-018-1349-y Issue No:Vol. 88, No. 6 (2018)

Authors:Mohammad Sahlabadi; Naser Soltani Pages: 933 - 942 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: 2018-06-01 DOI: 10.1007/s00419-018-1350-5 Issue No:Vol. 88, No. 6 (2018)

Authors:Michał Opala Pages: 943 - 953 Abstract: This paper investigates the influence of the models of dry friction suspension component used in the numerical simulation of freight car dynamics on the possible predictions related to safety against derailment. Moreover, the performance of the models is compared on the basis of simulation runtime. Three groups of static and dynamic models of friction are selected as three different approaches which are often utilized in popular multibody simulation tools. The models are used for the centre bowl friction joint between the car body and bogies. The friction torque in the centre bowl affects the rotational resistance of the bogie in motion relative to the car body and consequently influences the interaction forces between the wheels and rails. Simulation results of safety against derailment index obtained from the vehicle curving scenario suggest noticeable differences in predictions of the selected models of friction. PubDate: 2018-06-01 DOI: 10.1007/s00419-018-1351-4 Issue No:Vol. 88, No. 6 (2018)

Authors:Meilong Chen; Shuying Li; Hongliang Li; Tao Peng; Siyuan Liu Pages: 955 - 979 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: 2018-06-01 DOI: 10.1007/s00419-018-1352-3 Issue No:Vol. 88, No. 6 (2018)

Authors:Farhad Adel; Majid Jamal-Omidi Pages: 981 - 997 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: 2018-06-01 DOI: 10.1007/s00419-018-1353-2 Issue No:Vol. 88, No. 6 (2018)

Authors:Daniel Fernández Caballero; Juan Manuel Muñoz Guijosa; Víctor Rodríguez de la Cruz Pages: 999 - 1008 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: 2018-06-01 DOI: 10.1007/s00419-018-1354-1 Issue No:Vol. 88, No. 6 (2018)

Authors:Igor I. Andrianov; Jan Awrejcewicz; Alexander A. Diskovsky Pages: 1027 - 1039 Abstract: In this work we consider an optimal design of corrugated cylindrical shells. The functionally graded (FG) corrugation with amplitude following a given shape is defined. The problem is solved as a linear one assuming the axially symmetric loading. The method of estimation of the stress–strain state and, consequently, the shell optimal design based on homogenization approach is proposed. The illustrative examples of the optimal FG corrugation shell subjected to hydrostatic load have demonstrated high efficiency of the employed method. PubDate: 2018-06-01 DOI: 10.1007/s00419-018-1356-z Issue No:Vol. 88, No. 6 (2018)

Authors:Y. W. Yang; Y. Zhang; W. Q. Chen; B. Yang; Q. Q. Yang Abstract: Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The expressions of the mid-plane displacements of the plate are constructed to meet the clamped boundary conditions in which the unknown constants are determined from the governing equations. The expressions of four analytic functions \(\alpha (\zeta )\) , \(\beta (\zeta )\) , \(\phi (\zeta )\) and \(\psi (\zeta )\) corresponding to this problem are then obtained using the complex variables method. As a result, the three-dimensional elasticity solution of a functionally graded elliptical plate with clamped boundary subject to uniform load is derived. Finally, numerical examples are presented to verify the proposed method and discuss the effects of different factors on the deformation and stresses in the plate. PubDate: 2018-06-09 DOI: 10.1007/s00419-018-1407-5

Authors:Bin Zhou; Bin Zi; Sen Qian; Weidong Zhu Abstract: Deterministic kinematic modeling and stochastic luffing angular response field prediction of the dual automobile cranes system (DACS) are studied in this paper. For the response analysis of the DACS with deterministic information, the inverse kinematics are analyzed. For the prediction of luffing angular response field of the DACS with narrowly random payload parameters, a narrowly random model is introduced. In the narrowly random model, the payload parameters with certain probability distribution are modeled as random variables. Based on the narrowly random model, the equilibrium equation of luffing angular response vector of the DACS with random parameters is derived. Then a perturbation-based random composite function method (PRCFM) is proposed. Based on the PRCFM, the first-order Neumann series expansion and the proposed random variable functional moment method, a modified hybrid random method (MHRM) for the luffing angular response field prediction of the DACS with narrowly random payload parameters is proposed. In the MHRM, the statistical characteristics of luffing angular response vector are determined. Numerical results show the feasibility and efficiency of the MHRM for solving the narrowly stochastic DACS problems compared with the Monte Carlo method. The effects of different random parameters (y, z, \(\theta \) ) on the DACS luffing angular response field are also investigated deeply, and numerical results indicate the impact on the variances made by the randomness in the random payload parameter y is larger than those made by random payload parameters z and \(\theta \) . PubDate: 2018-06-09 DOI: 10.1007/s00419-018-1402-x

Abstract: A closed finite-dimensional system of dynamical equations for an unbounded periodic set of edge dislocations obtained previously from homogenization reasoning (Berdichevsky in J Mech Phys Solids 106:95–132, 2017) is rederived in this paper using some elementary means. PubDate: 2018-06-07 DOI: 10.1007/s00419-018-1408-4

Abstract: In this article, the size-dependent stress intensity factors in an elastic double cantilever beam (DCB) are obtained using strain gradient theory. The surface effects are included, while the DCB is assumed to undergo large deformation. Both cracked and uncracked parts (root effect) of the DCB are incorporated in modeling and analyses. The Variational principle is employed to obtain the governing equation and the corresponding boundary conditions. The deflections along the beam axis and stress intensity factors are obtained and plotted. Results exhibit large deformation to be influential for slender beams at small scale. Strain gradient effect tends to increase beam stiffness though reverse holds true for the root effect of the DCB. These effects on structure stiffness are conspicuous when the beam thickness is less than the material characteristic length. Due to positive surface residual stress, beam exhibits less stiff behavior in comparison with the negative surface residual stress. This softening behavior may be credited to the sign of curvature that causes an additional distributed load and alters beam stiffness. It is shown that even with the root effect, negative surface residual stress causes the DCB to display stiffer response by lowering the stress intensity factors and vice versa. PubDate: 2018-06-07 DOI: 10.1007/s00419-018-1406-6

Abstract: We study three different 1D continuous models (extensional rods, Euler and Timoshenko beams) for addressing the dynamic properties of those microstructural materials containing a density of resonators. These models correspond to metamaterials which show interesting properties: In particular, the property that is the objective of this paper is the capacity of eliminating the vibration amplitude in a specific frequency range, which is called hereinafter band gap. The simplicity of these models emphasizes those microstructural properties having a relation with the band gap. We show that the rigidity of the hosting structure does not affect the values of the frequency band gap; it affects only the distance between the load-source of vibration and those points where the amplitude attenuation is visible. We also study, from a numerical point of view and using the Euler beam as the hosting structure, the case of a finite number of resonators. In particular, we study the minimum number of resonators which provides the same band gap as in the case of the presence of a density of resonators. We finally perform a numerical study on a periodic 2D elastic structure, which behaves like the Timoshenko beam model and for which an identification procedure is given. PubDate: 2018-06-06 DOI: 10.1007/s00419-018-1399-1

Authors:Ali Nili; Saeed Adibnazari; Ardavan Karimzadeh Abstract: The thermoelastic rolling contact problem for an FGM-coated half plane under the plane strain deformation is studied in this paper. A rigid roller rolls over the surface of coating with constant translational velocity generating frictional heating in the slip zones of the contact patch. The material properties of the FGM vary exponentially along the thickness direction. It is assumed that the contact area consists of a central stick zone and two slip zones of the same sign. The transfer matrix method and Fourier integral transform technique are used to achieve a system of two Cauchy singular integral equations. The coupling effect of tangential traction is eliminated by adapting the conventional Goodman approximation. The associated governing equations are discretized by applying the Gauss–Chebyshev integration method gaining a system of linear algebraic equations. The effects of moving velocity, thermal conductivity and expansion coefficients’ ratios on through the thickness stress distribution are studied. PubDate: 2018-06-05 DOI: 10.1007/s00419-018-1405-7

Authors:Evgeniya V. Goloveshkina; Leonid M. Zubov Abstract: The equilibrium problem of a nonlinearly elastic medium with a given dislocation distribution is considered. The system of equations consists of the equilibrium equations for the stresses, the incompatibility equations for the distortion tensor, and the constitutive equations. Deformations are considered to be finite. For a special distribution of screw and edge dislocations, an exact spherically symmetric solution of these equations is found. This solution is universal in the class of isotropic incompressible elastic bodies. With the help of the obtained solution, the eigenstresses in a solid elastic sphere and in an infinite space with a spherical cavity are determined. The interaction of dislocations with an external hydrostatic load was also investigated. We have found the dislocation distribution that causes the spherically symmetric quasi-solid state of an elastic body, which is characterized by zero stresses and a nonuniform elementary volumes rotation field. PubDate: 2018-06-05 DOI: 10.1007/s00419-018-1403-9

Authors:Guanxixi Jiang; Zailin Yang; Cheng Sun; Baitao Sun; Yong Yang Abstract: Dynamic response of a shallow circular inclusion under incident SH wave in radially inhomogeneous half-space is researched by applying complex function theory and multipolar coordinate system. Considering that the mass density of the half-space varies along with the radius direction, the governing equation is expressed as a Helmholtz equation with a variable coefficient. Based on the conformal mapping method, the Helmholtz equation with a variable coefficient is transformed into its normalized form. Then, the expressions of incident wave, reflected wave and scattering wave are obtained, and the standing wave function is deduced by considering the circular inclusion subsequently. According to displacement and stress continuous condition of the inclusion, the undetermined coefficients in scattering wave and standing wave are solved. Finally, dynamic stress concentration factor around the inclusion is calculated and discussed. Numerical results demonstrate the validity of the method and influential factors of dynamic stress concentration factor. PubDate: 2018-06-05 DOI: 10.1007/s00419-018-1404-8

Authors:Amin Ghadami; Mehdi Behzad; Hamid Reza Mirdamadi Abstract: Damage detection in uniform structures has been studied in numerous previous researches. However, damage detection in non-uniform structures is less studied. In this paper, a damage detection algorithm for identifying rectangular notch parameters in a stepped waveguide using Lamb waves is presented. The proposed algorithm is based on mode conversion and scattering phenomena because of interaction of Lamb wave modes with defects. The analysis is divided into two steps: notch localization and notch geometry detection. The main advantage of this method is its ability to detect all of the notch parameters in a waveguide with arbitrary number of step discontinuities. The method is applied to a numerical example and the results show that it can successfully identify the notch location, depth, and width in a multi-step plate. PubDate: 2018-04-06 DOI: 10.1007/s00419-018-1355-0