Table of Content

01 January 2024, Volume 45 Issue 1

Previous Issue    Next Issue

Articles

A novel efficient energy absorber with free inversion of a metal foam-filled circular tube

Jianxun ZHANG, Jinwen BAI

2024, 45(1):  1-14.  doi:10.1007/s10483-024-3068-9

Abstract ( 200 )   HTML ( 11)   PDF (7415KB) ( 121 )  

Figures and Tables | References | Related Articles | Metrics

In this paper, a novel efficient energy absorber with free inversion of a metal foam-filled circular tube (MFFCT) is designed, and the axial compressive behavior of the MFFCT under free inversion is studied analytically and numerically. The theoretical analysis reveals that the energy is mainly dissipated through the radial bending of the metal circular tube, the circumferential expansion of the metal circular tube, and the metal filled-foam compression. The principle of energy conservation is used to derive the theoretical formula for the minimum compressive force of the MFFCT over free inversion under axial loading. Furthermore, the free inversion deformation characteristics of the MFFCT are analyzed numerically. The theoretical steady values are found to be in good agreement with the results of the finite element (FE) analysis. The effects of the average diameter of the metal tube, the wall thickness of the metal tube, and the filled-foam strength on the free inversion deformation of the MFFCT are considered. It is observed that in the steady deformation stage, the load-carrying and energy-absorbing capacities of the MFFCT increase with the increase in the average diameter of the metal tube, the wall thickness of the metal tube, or the filled-foam strength. The specific energy absorption (SEA) of free inversion of the MFFCT is significantly higher than that of the metal tube alone.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

Xiaoye MAO, Jiabin WU, Junning ZHANG, Hu DING, Liqun CHEN

2024, 45(1):  15-38.  doi:10.1007/s10483-024-3066-7

Abstract ( 227 )   HTML ( 8)   PDF (4717KB) ( 108 )  

Figures and Tables | References | Related Articles | Metrics

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method (HBM) is utilized to solve coupled ordinary differential equations (ODEs) of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method (DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations; nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Effect of boundary conditions on shakedown analysis of heterogeneous materials

Xiuchen GONG, Yinghao NIE, Gengdong CHENG, Kai LI

2024, 45(1):  39-68.  doi:10.1007/s10483-024-3073-9

Abstract ( 170 )   HTML ( 1)   PDF (9608KB) ( 117 )  

Figures and Tables | References | Related Articles | Metrics

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field (SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force (NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements (RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions (DBCs), uniform traction boundary conditions (TBCs), and periodic boundary conditions (PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit (EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs. Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

Effects of layer interactions on instantaneous stability of finite Stokes flows

Chen ZHAO, Zhenli CHEN, C. T. MUTASA, Dong LI

2024, 45(1):  69-84.  doi:10.1007/s10483-024-3067-8

Abstract ( 177 )   HTML ( 1)   PDF (517KB) ( 65 )  

Figures and Tables | References | Related Articles | Metrics

The stability analysis of a finite Stokes layer is of practical importance in flow control. In the present work, the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow. The oscillations of two plates can have different velocity amplitudes, initial phases, and frequencies. The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed. The growth rates of two most unstable modes when δ < 0.12 are almost equal, and δ = δ^*/h^*, where δ^* and h^* are the Stokes-layer thickness and the half height of the channel, respectively. However, their vorticities are different. The vorticity of the most unstable mode is symmetric, while the other is asymmetric. The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ < 0.68, and have a stabilizing effect when δ > 0.68. However, the interactions always have a stabilizing effect on the other unstable mode. It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong. We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile. The effects of inconsistent velocity-amplitude, initial phase, and frequency of the oscillations on the stability are analyzed. The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency. The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

Yong WANG, Peili WANG, Haodong MENG, Liqun CHEN

2024, 45(1):  85-110.  doi:10.1007/s10483-024-3070-7

Abstract ( 203 )   HTML ( 3)   PDF (1476KB) ( 145 )  

Figures and Tables | References | Related Articles | Metrics

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink (IX-NES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method (HBM) and the pseudo-arc-length method (PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square (RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger. When the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%, respectively, and the other dynamic performance indices are within the reasonable ranges. Thus, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.

Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

Zhiyuan WU, Linchuan ZHAO, Han YAN, Ge YAN, Ao CHEN, Wenming ZHANG

2024, 45(1):  111-136.  doi:10.1007/s10483-024-3071-5

Abstract ( 177 )   HTML ( 6)   PDF (20536KB) ( 209 )  

Figures and Tables | References | Related Articles | Metrics

Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing (SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multi-blade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness, and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed, which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

Galerkin-based quasi-smooth manifold element (QSME) method for anisotropic heat conduction problems in composites with complex geometry

Pan WANG, Xiangcheng HAN, Weibin WEN, Baolin WANG, Jun LIANG

2024, 45(1):  137-154.  doi:10.1007/s10483-024-3072-8

Abstract ( 236 )   HTML ( 4)   PDF (5689KB) ( 130 )  

Figures and Tables | References | Related Articles | Metrics

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method (FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element (QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional (2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity. The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom (DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

N. SHAHVEISI, S. FELI

2024, 45(1):  155-178.  doi:10.1007/s10483-024-3074-6

Abstract ( 195 )   HTML ( 1)   PDF (1482KB) ( 276 )  

Figures and Tables | References | Related Articles | Metrics

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate (GRL) layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact (LVI) are investigated. The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity. For the layer analysis, the high-order shear deformation theory (HSDT) and Frostig's second model for the displacement fields of the core layer are used. The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time. In order to validate the analytical method, the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI. Finite element (FE) simulations are conducted by means of the ABAQUS software. The effects of the parameters such as foam modulus, layer material, fiber angle, impactor mass, and its velocity on the generated voltage are reviewed.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Yali ZHANG, Yueting ZHOU, Shenghu DING

2024, 45(1):  179-196.  doi:10.1007/s10483-024-3075-7

Abstract ( 157 )   HTML ( 1)   PDF (1396KB) ( 148 )  

Figures and Tables | References | Related Articles | Metrics

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear, optimize lubrication, and enhance the overall performance and durability of mechanical systems. The sliding friction contact problem between a thermoelectric (TE) half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation. To simplify the problem, we utilize mixed boundary conditions, leading to a set of singular integral equations (SIEs) with the Hilbert kernels. The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field. The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials. Notably, the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress, and ensures that it remains free at the contact edge. Based on the plane strain theory of elasticity, the analysis primarily examines the correlation between the applied load and the effective contact area. The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients. Furthermore, the obtained results indicate that the in-plane stress decreases behind the trailing edge, while it increases ahead of the trailing edge when subjected to TE loads.

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fln exposed to magnetic fleld in the presence of a shape-dependent trihybrid nanofluid

C. G. PAVITHRA, B. J. GIREESHA, M. L. KEERTHI

2024, 45(1):  197-216.  doi:10.1007/s10483-024-3069-6

Abstract ( 225 )   HTML ( 212)   PDF (4356KB) ( 333 )  

Figures and Tables | References | Related Articles | Metrics

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid (Fe₃O₄-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical (Fe₃O₄), cylindrical (Au), and platelet (Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method (ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.