Table of Content

03 January 2025, Volume 46 Issue 1

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Bandgap characteristics analysis and graded design of a novel metamaterial for flexural wave suppression

Fan YANG, Zhaoyang MA, Xingming GUO

2025, 46(1):  1-24.  doi:10.1007/s10483-025-3204-7

Abstract ( 172 )   HTML ( 5)   PDF (8659KB) ( 103 )  

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A novel elastic metamaterial is proposed with the aim of achieving low-frequency broad bandgaps and bandgap regulation. The band structure of the proposed metamaterial is calculated based on the Floquet-Bloch theorem, and the boundary modes of each bandgap are analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the metamaterials with a low elastic modulus of ligaments can generate flexural wave bandgaps below 300 Hz. Multi-frequency vibrations can be suppressed through the selective manipulation of bandgaps. The dual-graded design of metamaterials that can significantly improve the bandgap width is proposed based on parametric studies. A new way that can regulate the bandgap is revealed by studying the graded elastic modulus in the substrate. The results demonstrate that the nonlinear gradient of the elastic modulus in the substrate offers better bandgap performance. Based on these analyses, the proposed elastic metamaterials can pave the way for multi-frequency vibration control, low-frequency bandgap broadening, and bandgap tuning.

Modification of Maxwell model for conductivity prediction of carbon nanotubes-filled polymer composites with tunneling effect

Jue ZHU, Longyuan LI, Ningtao ZHU

2025, 46(1):  25-36.  doi:10.1007/s10483-025-3210-9

Abstract ( 119 )   HTML ( 4)   PDF (861KB) ( 51 )  

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Carbon nanotubes (CNTs) have garnered great attention in recent years due to their outstanding electrical, thermal, and mechanical properties. The incorporation of small amounts of CNTs in polymers can substantially improve the sensitivity of the polymer's electrical conductivity. This paper presents a modified Maxwell model to evaluate the electrical conductivity of CNTs-filled polymer composites by introducing a transition zone to account for the tunneling effect. In this modified Maxwell model, the CNTs-filled polymer composite is modeled as a three-phase composite, consisting of a matrix (polymer), inclusions (CNTs), and a transition zone (tunneling zone). The effective electrical conductivity (EEC) of the composite is calculated based on the volume fractions and electrical conductivities of the matrix, inclusions, and transition zone. The model's validity is confirmed through the use of available test data, which demonstrates its capability to accurately capture the nonlinear conductivity behavior observed in CNTs-polymer composites. This study offers valuable insights into the design of high-performance conductive polymer nanocomposites, and enhances the understanding of electrical conduction mechanisms in CNT-dispersed polymer composites.

Free vibration and transient response of double curved beams connected by intermediate straight beams

R. A. JAFARI-TALOOKOLAEI, H. GHANDVAR, E. JUMAEV, S. KHATIR, T. CUONG-LE

2025, 46(1):  37-62.  doi:10.1007/s10483-025-3197-8

Abstract ( 117 )   HTML ( 0)   PDF (2261KB) ( 71 )  

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This paper investigates the free vibration and transient response of interconnected structures including double curved beams and intermediate straight beams, which are all constructed from functionally graded porous (FGP) materials. The strain potential and kinetic energies of each beam along with the work done by the external force are calculated. Additionally, a higher-order beam element is introduced to derive stiffness and mass matrices, along with the force vector. The curved and straight beams are discretized, and their assembled stiffness, mass matrices, and force vectors, are obtained. Continuity conditions at the joints are used to derive the total matrices of the entire structure. Subsequently, the natural frequencies and transient response of the system are determined. The accuracy of the mathematical model and the self-developed computer program is validated through the comparison of the obtained results with those of the existing literature and commercial software ANSYS, demonstrating excellent agreement. Furthermore, a comprehensive study is conducted to investigate the effects of various parameters on the free vibration and transient response of the considered structure.

Dynamic behaviors of graphene platelets-reinforced metal foam piezoelectric beams with velocity feedback control

Jie CHEN, Xinyue ZHANG, Mingyang FAN

2025, 46(1):  63-80.  doi:10.1007/s10483-025-3209-8

Abstract ( 138 )   HTML ( 2)   PDF (10589KB) ( 33 )  

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Graphene platelets (GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams. Further bonding piezoelectric actuator and sensor layers on the surfaces of GPLs-reinforced metal foam beams enables active vibration control, greatly expanding their applications in the aerospace industry. For the first time, this paper investigates the vibration characteristics and active vibration control of GPLs-reinforced metal foam beams with surface-bonded piezoelectric layers. The constant velocity feedback scheme is used to design the closed-loop controller including piezoelectric actuators and sensors. The effects of the GPLs on the linear and nonlinear free vibrations of the beams are numerically studied. The Newmark-β method combined with Newton's iteration technique is used to calculate the nonlinear responses of the beams under different load forms including harmonic loads, impact loads, and moving loads. Additionally, special attention is given to the vibration reduction performance of the velocity feedback control on the responses of the beam.

A comprehensive investigation on nonlinear vibration andbending characteristics of bio-inspired helicoidallaminated composite structures

S. SAURABH, R. KIRAN, D. SINGH, R. VAISH, V. S. CHAUHAN

2025, 46(1):  81-100.  doi:10.1007/s10483-025-3200-7

Abstract ( 133 )   HTML ( 4)   PDF (5066KB) ( 49 )  

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Bio-inspired helicoidal composite laminates, inspired by the intricate helical structures found in nature, present a promising frontier for enhancing the mechanical properties of structural designs. Hence, this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates. The inverse hyperbolic shear deformation theory (IHSDT) of plates is employed to characterize the displacement field, with the incorporation of Green-Lagrange nonlinearity. The problem is modeled using the C⁰ finite element method (FEM), and an in-house code is developed in the MATLAB environment to solve it numerically. Various helicoidal layup configurations including helicoidal recursive (HR), helicoidal exponential (HE), helicoidal semi-circular (HS), linear helicoidal (LH), and Fibonacci helicoidal (FH) with different layup sequences and quasi-isotropic configurations are studied. The model is validated, and parametric studies are conducted. These studies investigate the effects of layup configurations, side-to-thickness ratio, modulus ratios, boundary conditions, and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates. The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors. Moreover, this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.

Nonlinear forced vibration in a subcritical regime of a porous functionally graded pipe conveying fluid with a retaining clip

M. GHOLAMI, M. EFTEKHARI

2025, 46(1):  101-122.  doi:10.1007/s10483-025-3206-9

Abstract ( 109 )   HTML ( 0)   PDF (3336KB) ( 38 )  

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This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material (FGM) that conveys fluids and is equipped with a retaining clip, focusing on primary resonance and subcritical dynamics. The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle, and subsequently discretized through the application of the Galerkin method. The direct method of multi-scales is then used to solve the derived equations. A thorough analysis of various parameters, including the clip stiffness, the power-law index, the porosity, and the clip location, is conducted to gain a comprehensive understanding of the system's nonlinear dynamics. Through the analysis of the first natural frequency, the study highlights the influence of the flow velocity and the clip stiffness, while the comparisons with metallic pipes emphasize the role of FGM composition. The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index, offering valuable insights into the system's nonlinear resonant behavior. Furthermore, the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness, revealing nuanced effects on the system response and resonance characteristics. This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip, providing key insights for practical engineering applications in system design and optimization.

Dynamic modeling of a three-dimensional braided compositethin plate considering braiding directions

Chentong GAO, Huiyu SUN, Jianping GU, W. M. HUANG

2025, 46(1):  123-138.  doi:10.1007/s10483-025-3205-8

Abstract ( 120 )   HTML ( 2)   PDF (4832KB) ( 23 )  

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Currently, there are a limited number of dynamic models available for braided composite plates with large overall motions, despite the incorporation of three-dimensional (3D) braided composites into rotating blade components. In this paper, a dynamic model of 3D 4-directional braided composite thin plates considering braiding directions is established. Based on Kirchhoff's plate assumptions, the displacement variables of the plate are expressed. By incorporating the braiding directions into the constitutive equation of the braided composites, the dynamic model of the plate considering braiding directions is obtained. The effects of the speeds, braiding directions, and braided angles on the responses of the plate with fixed-axis rotation and translational motion, respectively, are investigated. This paper presents a dynamic theory for calculating the deformation of 3D braided composite structures undergoing both translational and rotational motions. It also provides a simulation method for investigating the dynamic behavior of non-isotropic material plates in various applications.

Dynamic stress concentration in an infinitely long cylindrical cavity due to a point spherical source embedded within a fluid-saturated poroelastic formation of infinite extent

H. HOSSEINI, O. BALILASHAKI

2025, 46(1):  139-156.  doi:10.1007/s10483-025-3203-6

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The effects of a harmonically exciting monopole source on an infinitely long cylindrical cavity embedded entirely within a fluid-saturated poroelastic formation of infinite extent are examined theoretically. It is assumed that the source is located outside the cavity at a specified distance from the borehole axis. The magnitudes of the hoop and radial stresses beside the pore pressures exerted on the interface and inside the porous medium surrounding the borehole are calculated and discussed. Biot's poroelastic modeling along with three types of boundary conditions for the cylindrical interface including the ideal fluid, empty borehole, and rigid inclusion with a hard boundary is employed for the analysis. Utilizing a proper translational addition theorem for expressing the incident spherical wave in terms of cylindrical wave expansions, the proposed boundary conditions at the interface are satisfied. Stresses are formulated by means of wave potential functions in a three-dimensional (3D) manner. The effects of the frequency and the radial distance between the source and borehole on the induced stresses are examined for the first cylindrical modes over frequency spectra. Two permeability conditions for the interface and three types of soils for the porous formation are considered throughout the analysis. To give an overall outline of the study, a numerical example is presented. The results clearly indicate that the distance is a key parameter and has considerable effects on the induced stress values. In addition, the interface permeability condition and soil characteristics play an important role in determining the dynamic response of the borehole. Finally, the obtained results are compared with the relevant analyses existing in the literature for some limit cases, and good agreement is achieved.

A six-variable quasi-3D isogeometric approach for free vibration of functionally graded graphene origami-enabled auxeticmetamaterial plates submerged in a fluid medium

Wei CHEN, Zhihong TANG, Yufen LIAO, Linxin PENG

2025, 46(1):  157-176.  doi:10.1007/s10483-025-3207-6

Abstract ( 110 )   HTML ( 0)   PDF (4232KB) ( 83 )  

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This paper presents, for the first time, an effective numerical approach based on the isogeometric analysis (IGA) and the six-variable quasi-three dimensional (3D) higher-order shear deformation theory (HSDT) to study the free vibration characteristics of functionally-graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) plates submerged in a fluid medium. The plate theory incorporates the thickness stretching and the effects of transverse shear deformation without using any shear correction factors. The velocity potential function and Bernoulli's equation are used to derive the hydrodynamic pressure acting on the plate surface. Both horizontally and vertically immersed plate configurations are considered here in the form of inertia effects. The plates are composed of multilayer GOEAMs, with the GOri content varying through the plate's thickness in a layer-wise manner. This design results in graded auxetic growth. The material properties are evaluated by mixing rules and a genetic programming (GP)-assisted micromechanical model. The governing equations of motion for the FG-GOEAM plates immersed in a fluid medium are derived by Hamilton's principle. After validating the convergence and accuracy of the present model, a comprehensive parametric study is carried out to examine the effects of the GOri content, GOri distribution pattern, GOri folding degree, fluid level, immersed depth, and geometric parameter on the natural frequencies of the FG-GOEAM plates. The results show that the natural frequencies for the four GOri distribution patterns increase with the increase in the layer number when the lay number is fewer than 10, and then stabilize after the layer number reaches 10. Besides, in general, the natural frequency of the FG-GOEAM plate in a vacuum or fluid increases when the GOri content increases, while decreases when the GOri folding degree increases. Some additional findings related to the numerical results are presented in the conclusions. It is believed that the present results are useful for the precise design and optimization of FG-GOEAM plates immersed in a fluid medium.

Transport mechanism in chemically reactive hybrid nanofluidflow containing gyrotactic micro-organisms overa curved oscillatory surface

M. NAVEED, M. IMRAN, T. ASGHAR, Z. ABBAS

2025, 46(1):  177-192.  doi:10.1007/s10483-025-3208-7

Abstract ( 112 )   HTML ( 5)   PDF (419KB) ( 39 )  

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This paper examines the transport analysis, including both heat transfer and mass transfer, in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory surface. The influence of magnetic fields is also inspected in terms of their physical characteristics. To depict the phenomena of transport, modified versions of both Fick's and Fourier's laws are used. Additionally, the characteristics of both heterogeneous and homogeneous chemical reactions are also incorporated. Utilizing a curvilinear coordinate system, the flow problem is formulated as partial differential equations (PDEs) for momentum, concentration, microorganism field, and energy. An analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method (HAM). The effects of significant flow parameters on the pressure and microorganism fields, velocity, oscillation velocity, concentration, and temperature distributions are shown via graphs. Furthermore, the variations in skin friction, mass transfer rate, heat transfer rate, and local motile number due to different involved parameters are presented in tables and are analyzed in detail. Graphical results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables increase. It is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase, and it increases with the Schmidt number and the heterogeneous reaction strength parameter. Tabular outcomes show a favorable response of the motile number to advanced values of the Peclet number, the Schmidt number, the microorganism difference parameter, and the bio-convective Lewis number.

Regression analysis of squeezing-induced hybrid nanofluid flow in Darcy-Forchheimer porous medium

K. MUHAMMAD, M. SARFRAZ

2025, 46(1):  193-208.  doi:10.1007/s10483-025-3202-9

Abstract ( 119 )   HTML ( 1)   PDF (302KB) ( 80 )  

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This article presents a mathematical model addressing a scenario involving a hybrid nanofluid flow between two infinite parallel plates. One plate remains stationary, while the other moves downward at a squeezing velocity. The space between these plates contains a Darcy-Forchheimer porous medium. A mixture of water-based fluid with gold (Au) and silicon dioxide (SiO₂) nanoparticles is formulated. In contrast to the conventional Fourier's heat flux equation, this study employs the Cattaneo-Christov heat flux equation. A uniform magnetic field is applied perpendicular to the flow direction, invoking magnetohydrodynamic (MHD) effects. Further, the model accounts for Joule heating, which is the heat generated when an electric current passes through the fluid. The problem is solved via NDSolve in MATHEMATICA. Numerical and statistical analyses are conducted to provide insights into the behavior of the nanomaterials between the parallel plates with respect to the flow, energy transport, and skin friction. The findings of this study have potential applications in enhancing cooling systems and optimizing thermal management strategies. It is observed that the squeezing motion generates additional pressure gradients within the fluid, which enhances the flow rate but reduces the frictional drag. Consequently, the fluid is pushed more vigorously between the plates, increasing the flow velocity. As the fluid experiences higher flow rates due to the increased squeezing effect, it spends less time in the region between the plates. The thermal relaxation, however, abruptly changes the temperature, leading to a decrease in the temperature fluctuations.