Nonlinear vibration analysis of a circular composite plate harvester via harmonic balance

Alumped parameter transversevibration model of a composite plate harvester is analyzed via harmonic balance approaches. The harvester is mainly composed of a piezoelectriccircular composite clamped by two steel rings and a proof mass on the plate.The lumped parameter model is a 1.5 degree-of-freedom strongly nonlinear system with a higher order polynomial stiffness. Aharmonic balance approach is developed to analyze the system, and the resulting algebraic equations are numerically solved by adopting an arc-length continuation technique. Anincremental harmonic balance approach is also developedfor the lumped parameter model. The two approaches yieldthe same results.The amplitude-frequency responses produced by the harmonic balance approach are validated by the numericalintegrations and the experimental data. The investigation reveals that there coexist hardening and softening characteristics in the amplitude-frequency response curves under sufficiently large excitations. The harvester with thecoexistenceof hardening and softening nonlinearitiescan outperform not only linear energy harvesters but also typical hardening nonlinear energy harvesters.

Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the effects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial dif- ferential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge-Kutta method. Moreover, the effects of different truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.

Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink

Nonlinear behaviors are investigated for a structure coupled with a nonlinear energy sink. The structure is linear and subject to a harmonic excitation, modeled as a forced single-degree-of-freedom oscillator. The nonlinear energy sink is modeled as an oscillator consisting of a mass,a nonlinear spring, and a linear damper. Based on the numerical solutions, global bifurcation diagrams are presented to reveal the coexistence of periodic and chaotic motions for varying nonlinear energy sink mass and stiffness. Chaos is numerically identified via phase trajectories, power spectra,and Poincaré maps. Amplitude-frequency response curves are predicted by the method of harmonic balance for periodic steady-state responses. Their stabilities are analyzed.The Hopf bifurcation and the saddle-node bifurcation are determined. The investigation demonstrates that a nonlinear energy sink may create dynamic complexity.

Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

Broadband energy harvesting based on one-to-one internal resonance

We design an electromechanical transducer harvesting system with one-to-one internal resonance that can emerge a broader spectrum vibrations. The novel harvester is composed of a Duffing electrical circuit coupled to a mobile rod, and the coupling between both components is realized via the electromagnetic force. Approximate analytical solutions of the electromechanical system are carried out by introducing the multiple scales analysis, also the nonlinear modulation equation for one-to-one internal resonance is obtained. The character of broadband harvesting performance are analyzed, the two peaks and one jump phenomenon bending to the right for variation of control parameters are observed. It is shown that an advanced bandwidth over a corresponding linear model that does not possess a modal energy interchange.

Elastodynamic analysis at an interface of viscous fluid/thermoelastic micropolar honeycomb medium due to inclined load

In this paper, the effect of angle inclination at the interface of a viscous fluid and thermoelastic micropolar honeycomb solid due to inclined load is investigated. The inclined load is assumed to be a linear combination of normal load and tangential load. Laplace transform with respect to time variable and Fourier transform with respect to space variable are applied to solve the problem. Expressions of stresses, temperature distribution, and pressures in the transformed domain are obtained by introducing potential functions. The numerical inversion technique is used to obtain the solution in the physical domain. The frequency domain expressions for steady state are also obtained with appropriate change of variables. Graphic representations due to the response of different sources and changes of angle inclination are shown. Some particular cases are also discussed.

Mechanical Characteristics of a Thrust Magnetic Bearing

Static and dynamic mechanical characteristics of a thrust magnetic bearing are studied owing to the inclination of the runner disk. The application refers to a thrust magnetic bearing for a turbo expander/compressor. The static tilt of the runner disk has remarkable influence on the mechanical characteristics of thrust magnetic bearing, it can change the static load distribution between two radial magnetic bearings and will exert violent coupling effect among a thrust magnetic bearing and two radial magnetic bearings. Such a finding can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks

Nonlinear vibration absorbers have been widely used for vibration suppression of elastic structures,but they were usually placed within the structures.However,designing such a vibration damping device within an engineering structure is possibly difficult.In this paper,an inertial nonlinear energy sinks(NES)is mounted on the boundaries of the elastic beam to suppress its vibration.Although this vibration suppression approach is more in line with engineering requirements,it introduces nonlinear oscillators at boundaries.This brings certain difficulties to the structural vibration analysis and the optimal absorber design.An approximate analytical approach for the steady-state response is developed in this work and verified by numerical solutions.The comparison with the uncontrolled system demonstrates the high-efficiency vibration suppression of the inertial NES installed on the boundary.Besides,the optimization of the NES parameters is performed.Resonance amplitude of the elastic structure can be reduced by 98%with the optimized NES.In summary,this paper proposes a novel approach to suppress the bending vibration of elastic structures through boundary NESs.The vibration reduction effect is very significant,and it is more feasible to implement.Therefore,this work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers.

GNOM-LIKE 2, Encoding an Adenosine Diphosphate-Ribosylation Factor-Guanine Nucleotide Exchange Factor Protein Homologous to GNOM and GNL1, is Essential for Pollen Germination in Arabidopsis

In flowering plants, male gametes are delivered to female gametophytes by pollen tubes. Although it is important for sexual plant reproduction, little is known about the genetic mechanism that controls pollen germination and pollen tube growth. Here we report the identification and characterization of two novel mutants, gnom-like 2-1 （gnl2-1） and gn12-2 in Arabidopsis thaliana, in which the pollen grains failed to germinate in vitro and in vivo. GNL2 encodes a protein homologous to the adenosine diphosphate-ribosylation factor-guanine nucleotide exchange factors, GNOM and GNL1 that are involved in endosomal recycling and endoplasmic reticulum-Golgi vesicular trafficking. It was prolifically expressed in pollen grains and pollen tubes. The results of the present study suggest that GNL2 plays an important role in pollen germination.

MARIS plays important roles in Arabidopsis pollen tube and root hair growth

In flowering plants, male gametes are delivered to female gametes for double fertilization through pollen tubes. Therefore, pollen tube growth is crucial for double fertilization. Despite its importance to sexual reproduction, genetic mechanisms of pollen tube growth remain poorly understood. In this study, we characterized the receptor-like cytoplasmic protein kinase （RLCK） gene, MARLS （MRI） that plays critical roles in pollen tube growth. MRI is preferentially expressed in pollen grains, pollen tubes and roots. Mutation in MRI by a Ds insertion led to a burst of pollen tubes after pollen germination. Pollen-rescue assay by pollen and pollen tubespecific expression of MRI in the mri-4 mutant showed that loss of MRI function also severely affected root hair elongation. MRI protein interacted with the protein kinase OXIDATIVE SIGNAL INDUCIBLEI （OXII） in the in vitro and in vivo assays, which functions in plant defence and root hair development, and was phosphorylated by OXII in vitro. Our results suggest that MRI plays important roles in pollen tube growth and may function in root hair elongation through interaction with OXII.

3D printed collagen/silk fibroin scaffolds carrying the secretome of human umbilical mesenchymal stemcells ameliorated neurological dysfunction after spinal cord injury in rats

Although implantation of biomaterials carrying mesenchymal stem cells(MSCs)is considered as a promising strategy for ameliorating neural function after spinal cord injury(SCI),there are still some challenges including poor cell survival rate,tumorigenicity and ethics concerns.The performance of the secretome derived from MSCs was more stable,and its clinical transformation was more operable.Cytokine antibody array demonstrated that the secretome of MSCs contained 79 proteins among the 174 proteins analyzed.Three-dimensional(3D)printed collagen/silk fibroin scaffolds carrying MSCs secretome improved hindlimb locomotor function according to the Basso–Beattie–Bresnahan scores,the inclined-grid climbing test and electrophysiological analysis.Parallel with locomotor function recovery,3D printed collagen/silk fibroin scaffolds carrying MSCs secretome could further facilitate nerve fiber regeneration,enhance remyelination and accelerate the establishment of synaptic connections at the injury site compared to 3D printed collagen/silk fibroin scaffolds alone group according to magnetic resonance imaging,diffusion tensor imaging,hematoxylin and eosin staining,Bielschowsky’s silver staining,immunofluorescence staining and transmission electron microscopy.These results indicated the implantation of 3D printed collagen/silk fibroin scaffolds carrying MSCs secretome might be a potential treatment for SCI.

Pollen-Expressed Transcription Factor 2 Encodes a Novel Plant-Specific TFIIB-Related Protein that Is Required for Pollen Germination and Embryogenesis in Arabidopsis

Pollen germination and embryogenesis are important to sexual plant reproduction. The processes require a large number of genes to be expressed. Transcription of eukaryotic nuclear genes is accomplished by three conserved RNA polymerases acting in association with a set of auxiliary general transcription factors （GTFs）, including B-type GTFs. The roles of B-type GTFs in plant reproduction remain poorly understood. Here we report functional characterization of a novel plant-specific TFIIB-related gene PTF2 in Arabidopsis. Mutation in PTF2 caused failure of pollen germination. Pollen-rescue revealed that the mutation also disrupted embryogenesis and resulted in seed abortion. PTF2 is expressed prolifically in developing pollen and the other tissues with active cell division and differentiation, including embryo and shoot apical meristem. The PTF2 protein shares a lower amino acid sequence similarity with other known TFIIB and TFIIB-related proteins in Arabidopsis. It can interact with TATA-box binding protein 2 （TBP2） and bind to the double- stranded DNA （dsDNA） as the other known TFIIB and TFIIB-related proteins do. In addition, PTF2 can form a homodimer and interact with the subunits of RNA polymerases （RNAPs）, implying that it may be involved in the RNAPs transcription. These results suggest that PTF2 plays crucial roles in pollen germination and embryogenesis in Arabidopsis, possibly by regulating gene expression through interaction with TBP2 and the subunits of RNAPs.

Subharmonic and Combination Resonance of Rotating Pre-deformed Blades Subjected to High Gas Pressure

The present paper deals with the investigation of dynamic responses of a rotating pre-deformed blade in four cases of resonance,including two subharmonic resonances and two combination resonances.The dimensionless gas excitation amplitude is assumed to share the same order with the dimensionless vibration displacement.Four cases of resonance are confirmed by examining the secular terms.The theoretical analysis framework is established for each resonance case based on the method of multiple scales.The original dynamic system is integrated numerically by the Runge–Kutta method.The frequency components and phases obtained from fast Fourier transform of the numerical response are used to verify the theoretical results.For the purpose of contrast,modulation equations are also integrated numerically.In all four resonance cases,the theoretical results agree well with the numerical simulation.Parameter studies are conducted to clarify the effects of system parameters on the perturbation curves.Various results are obtained for the rotating blade.A quasi-saturation phenomenon occurs in both combination resonances of summed type and difference type,and the corresponding limit value of the second-mode response can be reduced by decreasing the external detuning parameter.The quasi-saturation phenomenon of rotating blade only appears with high gas pressure.The subharmonic resonance of second mode and the combination resonance of summed type are hard to excite in practice compared with the other two cases.

Forced vibration control of an axially moving beam with an attached nonlinear energy sink

This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.

AtTMEM18 plays important roles in pollen tube and vegetative growth in Arabidopsis

In flowering plants, pollen tube growth is essential for delivery of male gametes into the female gametophyte or embryo sac for double fertilization. Although many genes have been identified as being involved in the process, the molecular mechanisms of pollen tube growth remains poorly understood. in this study, we identified that the Arabidopsis Transmembrane Protein 18 （AtTMEM18） gene played important roles in pollen tube growth. The AtTMEM18 shares a high similarity with the Transmembrane 18 proteins （TMEM18s） that are conserved in most eukaryotes and may play important roles in obesity in humans. Mutation in the AtTMEM18 by a Ds insertion caused abnormal callose deposition in the pollen grains and had a significant impact on pollen germination and pollen tube growth. AtTMEM18 is expressed in pollen grains, pollen tubes, root tips and other vegetative tissues. The pollen-rescued assays showed that the mutation in AtTMEM18 also caused defects in roots, stems, leaves and transmitting tracts. AtTMEM18-GFP was located around the nuclei. Genetic assays demonstrated that the localization of AtTMEM18 around the nuclei in the generative cells of pollen grains was essential for the male fertility.Furthermore, expression of the rice TM EM18-homologous protein （OsTMEM18） driven by LAT52 promoter could recover the fertility of the Arabidopsis attmem18 mutant. These results suggested that the TMEM18 is important for plant growth in Arabidopsis.

利用强非线性减振器的模态能量再分配缓解大型结构的冲击响应

采用一种轻型几何非线性附件,强非线性减振器(SNA),以抑制线性大型九层结构的冲击响应.SNA的作用不仅是耗散能量,而且重新分配结构模态之间的冲击能量.本文研究单自由度(SDOF)和双自由度(Two-DOF)的SNAs.冲击能量再分配的定量结果表明,在强几何非线性的情况下,这种结构可以实现从低频到高频的非线性单向能量传递.具体而言,在锁定SNA、单自由度SNA和双自由度SNA的情况下,较高结构模态耗散的冲击能量百分比分别为0.08%,0.43%和30.04%.结果表明,与单自由度SNA相比,双自由度SNA能够将更多的能量快速散射到更高的频域,从而更快地降低主结构的冲击响应.还研究了在不同冲击强度下SNA性能的鲁棒性,其中双自由度SNA在从低频到高频散射冲击能量时表现出更强的鲁棒性.最后,采用等效阻尼技术来验证和量化主结构中模态能量的重新分布,并讨论这种新型被动减震方法的潜在应用.

The Scheme to Determine the Convergence Term of the Galerkin Method for Dynamic Analysis of Sandwich Plates on Nonlinear Foundations

The vibration of a plate resting on elastic foundations under a moving load is of great significance in the design of many engineering fields,such as the vehicle-pavement system and the aircraft-runway system.Pavements or runways are always laminated structures.The Galerkin truncation method is widely used in the research of vibration.The number of truncation terms directly affects the convergence and accuracy of the response results.However,the selection of the number of truncation terms has not been clearly stated.A nonlinear viscoelastic foundation model under a moving load is established.Based on the natural frequency of linear undisturbed derivative systems,the truncation terms are used to determine the convergence of vibration response.The criterion for the convergence of the Galerkin truncation term is presented.The scheme is related to the natural frequency with high efficiency and practicability.Through the dynamic response of the sandwich beam under a moving load,the feasibility of the scheme is verified.The effects of different system parameters on the scheme and the truncation convergence of dynamic response are presented.The research in this paper can be used as a reference for the study of the vibration of elastic foundation plates.Especially,the model established and the truncation analysis method proposed are helpful for studying the vibration of vehicle-pavement system and related systems.

WBC27,an Adenosine Tri-phosphate-binding Cassette Protein,Controls Pollen Wall Formation and Patterning in Arabidopsis

In flowering plants, the exine components are derived from tapetum. Despite its importance to sexual plant reproduction, little is known about the translocation of exine materials from tapetum to developing microspores. Here we report functional characterization of the arabidopsis WBC27 gene. WBC27 encodes an adenosine tri-phosphate binding cassette （ABC） transporter and is expressed preferentially in tapetum. Mutation of WBC27 disrupted the exine formation. The wbc27 mutant microspores began to degenerate once released from tetrads and most of the microspores collapsed at the uninucleate stage. Only a small number of wbc27-1 microspores could develop into tricellular pollen grains. These survival pollen grains lacked exine and germinated in the anther before anthesis. All of these results suggest that the ABC transporter, WBC27 plays important roles in the formation of arabidopsis exine, possibly by translocation of lipidic precursors of sporopollenin from tapetum to developing microspores.

ABORTED GAMETOPHYTE 1 is required for gametogenesis in Arabidopsis

In flowering plants, the male and female gameto- genesis is a crucial step of sexual reproduction. Although many genes have been identified as being involved in the gametogenesis process, the genetic mechanisms underlying gametogenesis remains poorly understood. We reported here characterization of the gene, ABORTED GAMETOPHYTE 1 （AOGI） that is newly identified as essential for gametogenesis in Arabidopsis thaliana. AOG1 is expressed predominantly in reproductive tissues including the developing pollen grains and ovules. The AOG1 protein shares no significant amino acid sequence similarity with other documented proteins and is located mainly in nuclei of the cells. Mutation in AOG~ caused degeneration of pollen at the uninucleate microspore stage and severe defect in embryo sacs, leading to a significant reduction in male and female fertility.Furthermore, the molecular analyses showed that the aogl mutant significantly affected the expression of several genes, which are required for gametogenesis. Our results suggest that AOG1 plays important roles in gameto- genesis at the stage prior to pollen mitosis 1 （PMI） in Arabidopsis, possibly through collaboration with other genes.

Stability and Nonlinear Response Analysis of Parametric Vibration for Elastically Constrained Pipes Conveying Pulsating Fluid

Usually,the stability analysis of pipes with pulsating flow velocities is for rigidly constrained pipes or cantilevered pipes.In this paper,the effects of elastic constraints on pipe stability and nonlinear responses under pulsating velocities are investigated.A mechanical model of a fluid-conveying pipe under the constraints of elastic clamps is established.A partial differentialintegral nonlinear equation governing the lateral vibration of the pipe is derived.The natural frequencies and mode functions of the pipe are obtained.Moreover,the stable boundary and nonlinear steady-state responses of the parametric vibration for the pipe are established approximately.Furthermore,the analytical solutions are verified numerically.The results of this work reveal some interesting conclusions.It is found that the elastic constraint stiffness in the direction perpendicular to the axis of the pipe does not affect the critical flow velocity of the pipe.However,the constraint stiffness has a significant effect on the instability boundary of the pipe with pulsating flow velocities.Interestingly,an increase in the stiffness of the constraint increases the instable region of the pipe under parametric excitation.However,when the constraint stiffness is increased,the steady-state response amplitude of the nonlinear vibration for the pipe is significantly reduced.Therefore,the effects of the constraint stiffness on the instable region and vibration responses of the fluid-conveying pipe are different when the flow velocity is pulsating.