Table of Content

01 July 2019, Volume 40 Issue 7

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Articles

Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

Hu DING, Minhui ZHU, Liqun CHEN

2019, 40(7):  911-924.  doi:10.1007/s10483-019-2493-8

Abstract ( 515 )   HTML   PDF (404KB) ( 168 )  

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Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

Yuda HU, Bingbing MA

2019, 40(7):  925-942.  doi:10.1007/s10483-019-2496-7

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The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and the kinetic energy of the circular plate, the Hamilton principle is used to induce the magnetoelastic coupling transverse vibration dynamical equation of the ferromagnetic circular plate. Based on the basic electromagnetic theory, the expressions of the magnet force and the Lorenz force of the circular plate are presented. A displacement function satisfying clamped-edge combined with the Galerkin method is used to derive the Duffing vibration differential equation of the circular plate. The amplitude-frequency response equations of the system under various combined resonance forms are obtained by means of the multi-scale method, and the stability of the steady-state solutions is analyzed according to the Lyapunov theory. Through examples, the amplitude-frequency characteristic curves with different parameters, the amplitude of resonance varying with magnetic field intensity and excitation force, and the time-course response diagram, phase diagram, Poincaré diagram of the system vibration are plotted, respectively. The effects of different parameters on the amplitude and stability of the system are discussed. The results show that the electromagnetic parameters have a significant effect on the multi-valued attribute and stability of the resonance solutions, and the system may exhibit complex nonlinear dynamical behavior including multi-period and quasi-periodic motion.

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

Yun CUI, Yafei YIN, Chengjun WANG, K. SIM, Yuhang LI, Cunjiang YU, Jizhou SONG

2019, 40(7):  943-952.  doi:10.1007/s10483-019-2495-8

Abstract ( 592 )   HTML   PDF (473KB) ( 465 )  

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Thermally responsive liquid crystal elastomers (LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultra-thin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.

Analytical solutions for buckling of size-dependent Timoshenko beams

Xiaojian XU, Mulian ZHENG

2019, 40(7):  953-976.  doi:10.1007/s10483-019-2494-8

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The inconsistences of the higher-order shear resultant expressed in terms of displacement(s) and the complete boundary value problems of structures modeled by the nonlocal strain gradient theory have not been well addressed. This paper develops a size-dependent Timoshenko beam model that considers both the nonlocal effect and strain gradient effect. The variationally consistent boundary conditions corresponding to the equations of motion of Timoshenko beams are reformulated with the aid of the weighted residual method. The complete boundary value problems of nonlocal strain gradient Timoshenko beams undergoing buckling are solved in closed forms. All the possible higher-order boundary conditions induced by the strain gradient are selectively suggested based on the fact that the buckling loads increase with the increasing aspect ratios of beams from the conventional mechanics point of view. Then, motivated by the expression for beams with simply-supported (SS) boundary conditions, some semiempirical formulae are obtained by curve fitting procedures.

Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables' external excitations

Yunyue CONG, Houjun KANG, Tieding GUO

2019, 40(7):  977-1000.  doi:10.1007/s10483-019-2497-8

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The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin's method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin's integration are conducted. The analysis shows that the two results have a slight difference; however, they both have sufficient accuracy to solve the proposed dynamic system.

Postbuckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach

S. BLOORIYAN, R. ANSARI, A. DARVIZEH, R. GHOLAMI, H. ROUHI

2019, 40(7):  1001-1016.  doi:10.1007/s10483-019-2498-8

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An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von Kármán nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.

Rotating electroosmotic flows in soft parallel plate microchannels

Yongbo LIU, Yongjun JIAN

2019, 40(7):  1017-1028.  doi:10.1007/s10483-019-2501-8

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We present a theoretical investigation of rotating electroosmotic flows (EOFs) in soft parallel plate microchannels. The soft microchannel, also called as the polyelectrolyte-grafted microchannel, is denoted as a rigid microchannel coated with a polyelectrolyte layer (PEL) on its surface. We compare the velocity in a soft microchannel with that in a rigid one for different rotating frequencies and find that the PEL has a trend to lower the velocities in both directions for a larger equivalent electrical double layer (EDL) thickness λ_FCL (λ_FCL=0.3) and a smaller rotating frequency ω (ω < 5). However, for a larger rotating frequency ω (ω=5), the main stream velocity u far away from the channel walls in a soft microchannel exceeds that in a rigid one. Inspired by the above results, we can control the EOF velocity in micro rotating systems by imparting PELs on the microchannel walls, which may be an interesting application in biomedical separation and chemical reaction.

Bio-fluid flow analysis based on heat transfer and variable viscosity

H. SADAF

2019, 40(7):  1029-1040.  doi:10.1007/s10483-019-2499-8

Abstract ( 342 )   HTML   PDF (2854KB) ( 415 )  

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This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T₀, and the leftward wall has a temperature of T₁. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

Qingxiang LI, Ming PAN, Quan ZHOU, Yuhong DONG

2019, 40(7):  1041-1052.  doi:10.1007/s10483-019-2500-8

Abstract ( 379 )   HTML   PDF (1413KB) ( 323 )  

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The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.