Archive of Applied Mechanics

Basohbatnovinzad, Mohammadreza; Shams, Mahdi; Pouryoussefi, Sohrab Gholamhosein; Doostmahmoudi, Alireza

doi: 10.1007/s00419-022-02284-1pmid: N/A

This work experimentally and numerically studies a high Reynolds number flow around an inline configuration of three square cylinders exposed to a cross stream. The wind tunnel experiments include the measurement of drag coefficients for the cylinders at the Reynolds number of 5.06 × 104. The pressure distribution on the surface of the cylinders was measured by transducers, and the pressure distribution method was exploited to calculate the drag coefficients. Furthermore, we used a turbulence model based on the k-ω SST model to perform the numerical investigation. For validating our scheme, the results pertaining to the single cylinder configuration were compared with those available in the literature, indicating a well agreement. Finally, the effect of different cylinder spacing ratios (widely ranging from 1.5 to 5.5) on flow characteristics underwent analysis through the identification of flow patterns and pressure distributions. Our findings suggest that the variation in spacing ratio can strongly affect the flow pattern around the cylinders as well as the aerodynamic coefficients. Nevertheless, for the spacing ratio larger than 3, the flow interference between the cylinders is attenuated to a great extent.

Zhao, Li-Cai; Chen, Shi-Shuenn; Cheng, Jiaxing

doi: 10.1007/s00419-022-02289-wpmid: N/A

Although the thermal buckling behavior of thin plates has received great attention, only a limited number of studies have reported the thermal buckling analysis of damaged rectangular plates. A long-term loading can induce material damage on such plates, resulting in the premature failure. The present work addresses the thermal buckling of thin rectangular plates with damage. The continuum damage mechanics approach is used to represent material damage, which is accordance with the stiffness reduction. Stability equilibrium equations of rectangular plates with damage under thermal loads are derived based on classical plate theory. Take a concrete rectangular plate with damage on four edges simply supported under pressure as an example, the analytical solutions of temperature variation function and the effects of geometry size on the buckling temperature are obtained. The numerical results indicate that considering material damage in thermal buckling analysis is more in line with engineering practice and improves the design requirements of reliability. The correctness of the present numerical results through a comparison of the present results and the existing results.

Liu, Chao; Chen, Jin-Hong

doi: 10.1007/s00419-022-02290-3pmid: N/A

In this technical note, we add to the literature the analytical solution of the heat equation with radiation boundary conditions for an instantaneous point source in a hollow sphere. Instead of using the conventional method of the Laplace transfer and inverse Laplace transfer that requires intricate integral in the complex plane, we present a new approach to derive the analytical solution in the time domain. First, we express the instantaneous point source as the initial condition in terms of Dirac delta, e.g., Eq. (2), which is further expressed in the form of the general solution, i.e., Eq. (18). Subsequently, we determine the solution coefficients and obtain the analytical solution. Two special cases with prescribed surface temperature and no-flux boundaries are presented to demonstrate the solution. This solution is of practical importance in many scientific and engineering applications, such as pore pressure prediction in reservoir engineering, thermal analysis of casing in drilling engineering, and determining the relaxation process in nuclear magnetic resonance (NMR).

Rabindran, R.; Karhausen, K.; Hirt, G.; Teller, M.; Hojda, S.

doi: 10.1007/s00419-022-02238-7pmid: N/A

The rolling process induces a heterogeneous deformation over the rolling stock height. The causes are the frictional shear stress between the contacting surfaces and the roll gap geometry. They induce a complex material flow within the rolling stock describable by the shear evolution. The shear evolution has a significant impact on rolling values like grain size and crystallographic texture and therefore on the final material properties of the rolled product. Industry and academia use fast rolling models for flat rolling processes to predict the material properties due to their short computation time. The time advantage enables online applicability to adapt processes in real time or to evaluate the influence of different process conditions several times within seconds. However, these models have a limitation regarding the shear evolution. They do not consider all relevant influences or apply simplifying assumptions, valid only for specific rolling cases. This work presents a general approach to extend fast rolling models to consider the shear evolution without any restrictions to specific rolling cases. The approach derives the shear evolution as shear angle α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document} evolution based on FE simulations. The shear angle α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha$$\end{document} is a geometrical description and not influenced by rotations, which occur during the rolling process. This enables an enhanced and simple analysis of the material flow. The outcome is an extended model that completely describes the deformation along a deformation path and enables the calculation of each desired deformation value (strain, deformation gradient, velocity gradient, etc.).

Yang, Zhenghao; Naumenko, Konstantin; Altenbach, Holm; Ma, Chien-Ching; Oterkus, Erkan; Oterkus, Selda

doi: 10.1007/s00419-022-02245-8pmid: N/A

Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these equations are available. The aim of this paper is to formulate governing equations for buckling of beams and to derive analytical solutions for critical buckling loads based on the nonlinear peridynamic beam theory. For three types of boundary conditions, explicit expressions for the buckling loads are presented. The results are compared with the classical results for buckling loads. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the current approach. The results show that with an increase of the horizon size the critical buckling load slightly decreases for the fixed overall stiffness of the beam.

Moatimid, Galal M.; Amer, T. S.

doi: 10.1007/s00419-022-02246-7pmid: N/A

To suppress the nonlinearity of an excited Van der Pol–Duffing oscillator (VdPD), time-delayed position and velocity are used throughout this study. The time delay is supplemental to prevent the nonlinear vibration of the considered system. The topic of this work is extremely current because technologies with a time delay have been the subject of several studies in the latest days. The classical homotopy perturbation method (HPM) is utilized to extract an approximate systematic explanation for the system at hand. Furthermore, a modification of the HPM reveals a more accurate approximate solution. This accuracy is tested through a comparison with the numerical solution. The practical approximate analytical methodology makes the work possible to qualitatively evaluate the results. The time histories of the obtained solutions are drawn for various values of the natural frequency and the time delay parameters. Discussion of the results is presented in light of the plotted curves. On the other hand, the multiple scale procedure examines the organized nonlinear prototypical approach. The influence of the diverse regulatory restrictions on the organization’s vibration performances is explored. Two important cases of resonance, the sub-harmonic and super-harmonic, are examined according to the cubic nonlinearity. The modulation equations achieved for these cases are examined graphically according to the impact of the used parameters.

Jin, Miao; Wang, Ai-lun; Wang, Qingshan; Wang, Longkai; Zhang, Haibiao

doi: 10.1007/s00419-022-02247-6pmid: N/A

The Hirth couplings are the basic connection structure of the central tie rod rotor-blade-bearing (CTRRBB) coupling system for turboshaft engine. Those connecting structures tend to loosen when the decrease of the pre-tightening forces, the looseness behaviors can reduce the local stiffness of the rotor system and further affect its dynamic characteristics. In this paper, a novel mechanical model of the assembled stiffness of the Hirth couplings is derived based on the force balance and deformation compatibility of each tooth; then, the dynamic model of the CTRRBB with Hirth couplings is established based on the Timoshenko beam theory and Galerkin method. Then, assembled stiffness method of the Hirth couplings is incorporated in the system. The proposed model is verified by the results of the ANSYS model. Finally, the effects of the pre-tightening forces and rotational speed on the natural frequencies, three-dimensional mode shapes of the CTRRBB with Hirth couplings are further discussed. The results show that reduction of assembled stiffness of the Hirth couplings at contact interface becomes significant as the decrease of the pre-tightening forces, which lead to the decrease of the modal frequencies in the system. The analysis of the Campbell diagram indicates that frequency veering, intersection and instability phenomena occur in the system as the decrease of the pre-tightening forces. When the pre-tightening forces reach the 60 kN, the dynamic characteristics of the system make no difference with the integral rotor. The proposed methodology makes an important contribution to the further understanding of the rotor system considering the Hirth couplings connection structure in rotating machinery.

Alic, Fikret

doi: 10.1007/s00419-022-02248-5pmid: N/A

A vortex velocity field of nanofluid (Al2O3/water) is generated inside the cylindrical metal vessel (A) and heated at the bottom. A second hollow metal cylinder (B) filled with secondary fluid (ethanol) is concentrically placed in the center of the nanofluid vortex field. Vessel B is so technically designed that the active convective surface is equal to the current height of the secondary fluid in vessel B. The magnetic stirrer in the bottom of the vessel A causes a complex movement of the nanofluid. In the conducted analysis, nanofluid temperatures of 80 °C, 85 °C, and 90 °C were established, which enabled heating and evaporation of the secondary fluid inside vessel B. By combining the volume fraction of Al2O3 nanoparticles in amounts of 0.1%, 0.5%, 0.9%, and the angular velocity of the stir bar (at the bottom of the vessel A), the efficiency of secondary fluid evaporation is variable. Vessel B is open, the secondary fluid decreases its height due to evaporation. At the same time, the moving hollow heat-insulating cylinder inside vessel B continuously touches the surface of this fluid. Two cases, first when the temperature of the nanofluid is kept constant and second when the temperature is variable during the process of evaporation of the secondary fluid, are analyzed in this paper. The paper established an analytical model of the transient change in the height of the secondary fluid, the flux of the heat source, and the thermal entropy of the nanofluid. The transient process is analyzed until the complete volume of the secondary fluid evaporates, up to a maximum time of 1000 s.

Mukherjee, Soumya

doi: 10.1007/s00419-022-02251-wpmid: N/A

In this paper, we develop several limited chain extensible (LCE) models using fractional powers of certain forms. The fractional powers provide an alternative functional framework similar to the logarithmic function. The present models exhibit limited extensibility when the arbitrary exponent is less than unity, and reduce to well-posed parent models when the exponent is unity or the stiffening parameter tends to infinity. When the exponent approaches zero, the proposed model reduces to the logarithm-based existing LCE models. Using these arbitrary fractional powers, we construct suitable strain energy functions based on (a) I1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$I_1$$\end{document}, (b) both I1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$I_1$$\end{document} and I2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$I_2$$\end{document}, (c) principal stretches as well as for transversely isotropic materials. The developed functions also generalizes existing limited chain extensible models. We also further modify the Ogden model to deduce a pair of limited extensible models which reduce to existing models as the exponents approach zero. We next apply various inequalities of solid mechanics, viz. (a) Baker–Ericksen inequality, (b) strong ellipticity, (c) polyconvexity, (d) Hill’s constitutive inequality to the proposed models. We observe that sufficient conditions for satisfying the above inequalities match exactly with the condition for exhibiting limiting stretchable behavior. We further employ the models for investigating homogeneous and inhomogeneous deformation characteristics. In the sphere inflation characteristics, we observe that these models display a wider range of strain-stiffening and stability patterns. While the critical stiffening parameter is a constant for the Gent model, it can assume any positive value for the present model depending on the exponent. As a result, the proposed models can exhibit stable inflation or an inflation-jump instability in the sphere for any given maximum stretch limit, or the stiffening parameter. The critical values of maximum allowable stretch or stiffening parameters can assume any value in the present framework to fit the experimental results. Since the stability characteristics depend completely on stiffening parameter it is diversified using the present model. We observe inflation-jump instability for a stiffening parameter as low as 2.30. Since the present models involve arbitrary exponents and exhibit limited elasticity, they nicely exhibit the real deformation characteristics of spheres. As a result, they adequately capture the mechanical response of inflating rubber-like spheres. We demonstrate excellent agreements of these theoretical models with the experimental responses of inflation of monkey bladder and rubber balloon.

Wang, Yong; Wang, Peili; Meng, Haodong; Chen, Li-Qun

doi: 10.1007/s00419-022-02252-9pmid: N/A

Motivated by the demand of improving the multi-directional vibration dynamic performance, an inerter-based multi-directional (IMD) vibration isolator is proposed in this paper, which is composed of the inerter, damper and spring structures in multiple directions. The dynamic equation of the IMD vibration isolator is established using the Lagrange theory, its dynamic response under base harmonic excitation is obtained using the harmonic balance method and pseudo-arc-length method, and the stability of the dynamic response is considered. The dynamic performance of the IMD vibration isolator under harmonic and shock excitations is studied and compared with those of the conventional multi-directional (MD) vibration isolator consist of the damper and spring structure, and the effect of structural parameters on its dynamic performance is investigated in detail. The results show that the IMD vibration isolator has nonlinear inertial, damping and stiffness characteristics, and it further reduces the dynamic displacement and absolute displacement transmissibility peaks, widens the isolation frequency band than the MD vibration isolator and also has better shock performance in the middle severity parameter range. In order to obtain better isolation and shock performance, the vertical and horizontal inertance-to-mass ratios are chosen as larger values, and the stiffness ratio and the horizontal spring compression ratio are chosen as smaller values. Therefore, the design of the proposed IMD vibration isolator exhibits the advantages of applying the inerter and provides excellent isolation and shock performance in multiple directions.