Working condition recognition of sucker rod pumping system based on 4-segment time-frequency signature matrix and deep learning

High-precision and real-time diagnosis of sucker rod pumping system(SRPS)is important for quickly mastering oil well operations.Deep learning-based method for classifying the dynamometer card(DC)of oil wells is an efficient diagnosis method.However,the input of the DC as a two-dimensional image into the deep learning framework suffers from low feature utilization and high computational effort.Additionally,different SRPSs in an oil field have various system parameters,and the same SRPS generates different DCs at different moments.Thus,there is heterogeneity in field data,which can dramatically impair the diagnostic accuracy.To solve the above problems,a working condition recognition method based on 4-segment time-frequency signature matrix(4S-TFSM)and deep learning is presented in this paper.First,the 4-segment time-frequency signature(4S-TFS)method that can reduce the computing power requirements is proposed for feature extraction of DC data.Subsequently,the 4S-TFSM is constructed by relative normalization and matrix calculation to synthesize the features of multiple data and solve the problem of data heterogeneity.Finally,a convolutional neural network(CNN),one of the deep learning frameworks,is used to determine the functioning conditions based on the 4S-TFSM.Experiments on field data verify that the proposed diagnostic method based on 4S-TFSM and CNN(4S-TFSM-CNN)can significantly improve the accuracy of working condition recognition with lower computational cost.To the best of our knowledge,this is the first work to discuss the effect of data heterogeneity on the working condition recognition performance of SRPS.

A matrix metalloproteinase-responsive hydrogel system controls angiogenic peptide release for repair of cerebral ischemia/reperfusion injury

Vascular endothelial growth factor and its mimic peptide KLTWQELYQLKYKGI(QK)are widely used as the most potent angiogenic factors for the treatment of multiple ischemic diseases.However,conventional topical drug delivery often results in a burst release of the drug,leading to transient retention(inefficacy)and undesirable diffusion(toxicity)in vivo.Therefore,a drug delivery system that responds to changes in the microenvironment of tissue regeneration and controls vascular endothelial growth factor release is crucial to improve the treatment of ischemic stroke.Matrix metalloproteinase-2(MMP-2)is gradually upregulated after cerebral ischemia.Herein,vascular endothelial growth factor mimic peptide QK was self-assembled with MMP-2-cleaved peptide PLGLAG(TIMP)and customizable peptide amphiphilic(PA)molecules to construct nanofiber hydrogel PA-TIMP-QK.PA-TIMP-QK was found to control the delivery of QK by MMP-2 upregulation after cerebral ischemia/reperfusion and had a similar biological activity with vascular endothelial growth factor in vitro.The results indicated that PA-TIMP-QK promoted neuronal survival,restored local blood circulation,reduced blood-brain barrier permeability,and restored motor function.These findings suggest that the self-assembling nanofiber hydrogel PA-TIMP-QK may provide an intelligent drug delivery system that responds to the microenvironment and promotes regeneration and repair after cerebral ischemia/reperfusion injury.

High quality repair of osteochondral defects in rats using the extracellular matrix of antler stem cells

BACKGROUND Cartilage defects are some of the most common causes of arthritis.Cartilage lesions caused by inflammation,trauma or degenerative disease normally result in osteochondral defects.Previous studies have shown that decellularized extracellular matrix(ECM)derived from autologous,allogenic,or xenogeneic mesenchymal stromal cells(MSCs)can effectively restore osteochondral integrity.AIM To determine whether the decellularized ECM of antler reserve mesenchymal cells(RMCs),a xenogeneic material from antler stem cells,is superior to the currently available treatments for osteochondral defects.METHODS We isolated the RMCs from a 60-d-old sika deer antler and cultured them in vitro to 70%confluence;50 mg/mL L-ascorbic acid was then added to the medium to stimulate ECM deposition.Decellularized sheets of adipocyte-derived MSCs(aMSCs)and antlerogenic periosteal cells(another type of antler stem cells)were used as the controls.Three weeks after ascorbic acid stimulation,the ECM sheets were harvested and applied to the osteochondral defects in rat knee joints.RESULTS The defects were successfully repaired by applying the ECM-sheets.The highest quality of repair was achieved in the RMC-ECM group both in vitro(including cell attachment and proliferation),and in vivo(including the simultaneous regeneration of well-vascularized subchondral bone and avascular articular hyaline cartilage integrated with surrounding native tissues).Notably,the antler-stem-cell-derived ECM(xenogeneic)performed better than the aMSC-ECM(allogenic),while the ECM of the active antler stem cells was superior to that of the quiescent antler stem cells.CONCLUSION Decellularized xenogeneic ECM derived from the antler stem cell,particularly the active form(RMC-ECM),can achieve high quality repair/reconstruction of osteochondral defects,suggesting that selection of decellularized ECM for such repair should be focused more on bioactivity rather than kinship.

Strengthening of reinforced concrete beams using fiberreinforced cementitious matrix systems fabricated with custom-designed mortar and fabrics

The performance of a new fiber-reinforced cementitious matrix(FRCM)system developed using custom-designed mortar and fabrics is investigated in this study.The behavior of this system is evaluated in terms of both the flexural and shear strengthening of reinforced concrete beams.Eight beams are designed to assess the effectiveness of the FRCM system in terms of flexural strengthening,and four specimens are designed to investigate their shear behavior.The parameters investigated for flexural strengthening are the number of layers,span/depth ratio,and the strengthening method.Unlike previous studies,custom fabrics with similar axial stiffness are used in all strengthening methods in this study.In the shear-strengthened specimens,the effects of the span/depth ratio and strengthening system type(fiberreinforced polymer(FRP)or FRCM)are investigated.The proposed FRCM system exhibits desirable flexural and shear strengthening for enhancing the load capacity,provides sufficient bonding with the substrate,and prevents premature failure modes.Considering the similar axial stiffness of fabrics used in both FRCM and FRP systems and the higher load capacity of specimens strengthened by the former,cement-based mortar performs better than epoxy.

Tree-based ecosystem services supply and multifunctionality of church forests and their agricultural matrix near Lake Tana,Ethiopia

Ecosystem services(ES)are the connection between nature and society,and are essential for the well-being of local communities that depend on them.In Ethiopia,church forests and the surrounding agricultural matrix supply numerous ES.However,the ES delivered by both land use types have not yet been assessed simultaneously.Here we surveyed both church forests and their agricultural matrices,aiming to quantify,compare and unravel the drivers underlying tree-based ES supply,density and multifunctionality.We found that almost all church forests and half of the agricultural matrices provided high ES densities.ES multifunctionality was higher in the agricultural matrices,suggesting that people deliberately conserve or plant multifunctional tree species.Furthermore,the supply of all categories of ES was positively correlated with church forest age(p-value<0.001)in the agricultural matrix,while the extent of church forest was positively correlated with the density of all categories ecosystem services score in the church forests(p-value<0.001).Our results can be used to prioritize conservation efforts at sites that provide high levels of ES supply,ES density and ES multifunctionality,and to prioritize restoration efforts at sites with low levels thereof.

Attribute Reduction for Information Systems via Strength of Rules and Similarity Matrix

An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction problems,but they all require a common categorization.The selection of features in most scientific studies is a challenge for the researcher.When working with huge datasets,selecting all available attributes is not an option because it frequently complicates the study and decreases performance.On the other side,neglecting some attributes might jeopardize data accuracy.In this case,rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information;nonetheless,investigating all available combinations of attributes will result in some problems.Furthermore,because attribute reduction is primarily a mathematical issue,technical progress in reduction is dependent on the advancement of mathematical models.Because the focus of this study is on the mathematical side of attribute reduction,we propose some methods to make a reduction for information systems according to classical rough set theory,the strength of rules and similarity matrix,we applied our proposed methods to several examples and calculate the reduction for each case.These methods expand the options of attribute reductions for researchers.

Philosophical Matrix as a System of Categories of Pure Mind

The article is a study devoted to the development of the concept of the philosophical matrix as a system of categories of pure reason.The author proposes a new approach to understanding the philosophical system of categories by putting forward unambiguous comparative concepts that serve as the basis for natural sciences.While the foundations of specific sciences are the concepts of“practical reason”,the author finds the categories of“pure reason”to be the foundations of philosophy,understood as“knowledge of the universal”.The article shows that relying on the senses and the concepts of“practical reason”allows for the verification of knowledge,while their generalization,removed from knowledge obtained empirically,gives categories of“pure reason”,which are accepted as the building material of the matrix.In this way,the author proposes a new system of philosophical categories that describes the fundamental aspects of human reasoning and its interaction with the world.At the same time,the categories of the philosophical matrix are not related to such ambiguous classificatory concepts as space,time,being,existence,consciousness,and others.The article draws attention to the fact that the matrix can be used not only to analyze philosophical theories but also to develop new concrete scientific approaches,for example,for the intellectual development of children.In addition,the article suggests the possibility of applying the philosophical matrix in other areas of the humanities,including psychology,linguistics,and sociology.As a result of the conducted research,the human intellect is divided into three ascending stages,designated by me in the following words-reason,mind,and wisdom,with the subsequent use of these concepts in philosophy and other fields of knowledge.

Stiffness-tunable biomaterials provide a good extracellular matrix environment for axon growth and regeneration

Neuronal growth, extension, branching, and formation of neural networks are markedly influenced by the extracellular matrix—a complex network composed of proteins and carbohydrates secreted by cells. In addition to providing physical support for cells, the extracellular matrix also conveys critical mechanical stiffness cues. During the development of the nervous system, extracellular matrix stiffness plays a central role in guiding neuronal growth, particularly in the context of axonal extension, which is crucial for the formation of neural networks. In neural tissue engineering, manipulation of biomaterial stiffness is a promising strategy to provide a permissive environment for the repair and regeneration of injured nervous tissue. Recent research has fine-tuned synthetic biomaterials to fabricate scaffolds that closely replicate the stiffness profiles observed in the nervous system. In this review, we highlight the molecular mechanisms by which extracellular matrix stiffness regulates axonal growth and regeneration. We highlight the progress made in the development of stiffness-tunable biomaterials to emulate in vivo extracellular matrix environments, with an emphasis on their application in neural repair and regeneration, along with a discussion of the current limitations and future prospects. The exploration and optimization of the stiffness-tunable biomaterials has the potential to markedly advance the development of neural tissue engineering.

Association between Gene Polymorphisms and SNP-SNP Interactions of the Matrix Metalloproteinase 2 Signaling Pathway and the Risk of Vascular Senescence

Objective This study aimed to explore the association of single nucleotide polymorphisms(SNP)in the matrix metalloproteinase 2(MMP-2)signaling pathway and the risk of vascular senescence(VS).Methods In this cross-sectional study,between May and November 2022,peripheral venous blood of151 VS patients(case group)and 233 volunteers(control group)were collected.Fourteen SNPs were identified in five genes encoding the components of the MMP-2 signaling pathway,assessed through carotid-femoral pulse wave velocity(cf PWV),and analyzed using multivariate logistic regression.The multigene influence on the risk of VS was assessed using multifactor dimensionality reduction(MDR)and generalized multifactor dimensionality regression(GMDR)modeling.Results Within the multivariate logistic regression models,four SNPs were screened to have significant associations with VS:chemokine(C-C motif)ligand 2(CCL2)rs4586,MMP2 rs14070,MMP2rs7201,and MMP2 rs1053605.Carriers of the T/C genotype of MMP2 rs14070 had a 2.17-fold increased risk of developing VS compared with those of the C/C genotype,and those of the T/T genotype had a19.375-fold increased risk.CCL2 rs4586 and MMP-2 rs14070 exhibited the most significant interactions.Conclusion CCL2 rs4586,MMP-2 rs14070,MMP-2 rs7201,and MMP-2 rs1053605 polymorphisms were significantly associated with the risk of VS.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.

Biofabrication of nanocomposite-based scaffolds containing human bone extracellularmatrix for the differentiation of skeletal stem and progenitor cells

Autograft or metal implants are routinely used in skeletal repair.However,they fail to provide long-term clinical resolution,necessitating a functional biomimetic tissue engineering alternative.The use of native human bone tissue for synthesizing a biomimeticmaterial inkfor three-dimensional(3D)bioprintingof skeletal tissueis anattractivestrategyfor tissueregeneration.Thus,human bone extracellular matrix(bone-ECM)offers an exciting potential for the development of an appropriate microenvironment for human bone marrow stromal cells(HBMSCs)to proliferate and differentiate along the osteogenic lineage.In this study,we engineered a novel material ink(LAB)by blending human bone-ECM(B)with nanoclay(L,Laponite®)and alginate(A)polymers using extrusion-based deposition.The inclusion of the nanofiller and polymeric material increased the rheology,printability,and drug retention properties and,critically,the preservation of HBMSCs viability upon printing.The composite of human bone-ECM-based 3D constructs containing vascular endothelial growth factor(VEGF)enhanced vascularization after implantation in an ex vivo chick chorioallantoic membrane(CAM)model.The inclusion of bone morphogenetic protein-2(BMP-2)with the HBMSCs further enhanced vascularization and mineralization after only seven days.This study demonstrates the synergistic combination of nanoclay with biomimetic materials(alginate and bone-ECM)to support the formation of osteogenic tissue both in vitro and ex vivo and offers a promising novel 3D bioprinting approach to personalized skeletal tissue repair.

Amino-functionalized UiO-66-doped mixed matrix membranes with high permeation performance and fouling resistance

For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then adding amino-functionalized UiO-66-NH_(2)(Am-UiO-66-NH_(2)).Aminofunctionalization of UiO-66 was accomplished by melamine,followed by an amidation reaction to immobilize Am-UiO-66-NH_(2),which was immobilized on the surface of the membrane as well as in the pore channels,which enhanced the hydrophilicity of the membrane surface while increasing the negative potential of the membrane surface.This nanoparticle-loaded ultrafiltration membrane has good permeation performance,with a pure water flux of up to 482.3 L·m^(-2)·h^(-1) for C-SPAEKS/AmUiO-66-NH_(2) and a retention rate of up to 98.7%for bovine serum albumin(BSA)-contaminated solutions.Meanwhile,after several hydrophilic modifications,the flux recovery of BSA contaminants by this series of membranes increased from 56.2%to 80.55%of pure membranes.The results of ultra-filtration flux time tests performed at room temperature showed that the series of ultrafiltration membranes remained relatively stable over a test time of 300 min.Thus,the newly developed mixed matrix membrane showed potential for high efficiency and stability in wastewater treatment containing bovine serum proteins.

先锋女性主义者的建筑实验--英国Matrix的女性主义建筑观念与实践研究

英国的Matrix是西方第一个明确以女性主义为主张的女性建筑事务所。在特定的时代背景下,她们试图挑战父权制下的建筑体系并发展一种女性主义的设计方法,是西方将女性主义理论运用到建筑空间实践中的先锋者。本文回溯了Matrix组建时的政治与社会背景,分析她们以建筑师的身份采取集体合作工作模式、以女性为主体的参与式机制、以技能培训为辅助的女性建筑教育介入的方法来促进女性解放并重构建筑的空间生产。基于女性主义社会建构论的观念,解读Matrix是如何以性别批判的视角来看待和认知城市空间与女性主义建筑,并结合具体建筑案例分析女性视角下的包容性建筑设计。最后本文探讨了以Matrix为代表的女性建筑师及其女性主义建筑观念与实践对于当下建筑学科研究的价值与意义。

Low-Complexity Reconstruction of Covariance Matrix in Hybrid Uniform Circular Array

Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.

Effect of Heat Treatment on Microstructure and Mechanical Properties of Multiscale SiC_p Hybrid Reinforced 6061 Aluminum Matrix Composites

The performance of solid solution aging treatment on aluminum matrix composites prepared by powder metallurgy and reinforced with 6061 aluminum alloy powder as matrix;meanwhile, nano silicon carbide particles(nm Si Cp), submicron silicon carbide particles(1 μm Si Cp) and Ti particles were studied. The Al/Si Cp composite powder was prepared by high-energy ball milling, and then cold-pressed, sintered, hotextruded, and then heat-treated with different solution temperatures and aging times for the extruded composites. Optical microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy(EDS), X-ray diffractometer(XRD) and extrusion testing were used to analyze and test the microstructure and mechanical properties of aluminum matrix composites. The results show that after the multi-stage solid solution at 530 ℃×2 h+535 ℃×2 h+540 ℃×2 h, the particles are mainly equiaxed grains and uniformly distributed. There is no reinforcement agglomeration, and the surface is dense and the insoluble phase is basically dissolved. In the matrix, the strengthening effect is good, and the hardness and compressive strength are 179.43 HV and 680.42 MPa, respectively. Under this solution process, when the aluminum matrix composites are aged at 170 ℃ for 10 h, the hardness and compressive strength can reach their peaks and increase to 195.82 HV and 721.48 MPa, respectively.

The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Automatic modulation recognition of radiation source signals based on two-dimensional data matrix and improved residual neural network

Automatic modulation recognition(AMR)of radiation source signals is a research focus in the field of cognitive radio.However,the AMR of radiation source signals at low SNRs still faces a great challenge.Therefore,the AMR method of radiation source signals based on two-dimensional data matrix and improved residual neural network is proposed in this paper.First,the time series of the radiation source signals are reconstructed into two-dimensional data matrix,which greatly simplifies the signal preprocessing process.Second,the depthwise convolution and large-size convolutional kernels based residual neural network(DLRNet)is proposed to improve the feature extraction capability of the AMR model.Finally,the model performs feature extraction and classification on the two-dimensional data matrix to obtain the recognition vector that represents the signal modulation type.Theoretical analysis and simulation results show that the AMR method based on two-dimensional data matrix and improved residual network can significantly improve the accuracy of the AMR method.The recognition accuracy of the proposed method maintains a high level greater than 90% even at -14 dB SNR.

Reinforced tissue matrix to strengthen the abdominal wall following reversal of temporary ostomies or to treat incisional hernias

BACKGROUND Abdominal wall deficiencies or weakness are a common complication of tem-porary ostomies,and incisional hernias frequently develop after colostomy or ileostomy takedown.The use of synthetic meshes to reinforce the abdominal wall has reduced hernia occurrence.Biologic meshes have also been used to enhance healing,particularly in contaminated conditions.Reinforced tissue matrices(R-TMs),which include a biologic scaffold of native extracellular matrix and a syn-thetic component for added strength/durability,are designed to take advantage of aspects of both synthetic and biologic materials.To date,RTMs have not been reported to reinforce the abdominal wall following stoma reversal.METHODS Twenty-eight patients were selected with a parastomal and/or incisional hernia who had received a temporary ileostomy or colostomy for fecal diversion after rectal cancer treatment or trauma.Following hernia repair and proximal stoma closure,RTM(OviTex®1S permanent or OviTex®LPR)was placed to reinforce the abdominal wall using a laparoscopic,robotic,or open surgical approach.Post-operative follow-up was performed at 1 month and 1 year.Hernia recurrence was determined by physical examination and,when necessary,via computed tomo-graphy scan.Secondary endpoints included length of hospital stay,time to return to work,and hospital readmissions.Evaluated complications of the wound/repair site included presence of surgical site infection,seroma,hematoma,wound dehiscence,or fistula formation.RESULTS The observational study cohort included 16 male and 12 female patients with average age of 58.5 years±16.3 years and average body mass index of 26.2 kg/m^(2)±4.1 kg/m^(2).Patients presented with a parastomal hernia(75.0%),in-cisional hernia(14.3%),or combined parastomal/incisional hernia(10.7%).Using a laparoscopic(53.6%),robotic(35.7%),or open(10.7%)technique,RTMs(OviTex®LPR:82.1%,OviTex®1S:17.9%)were placed using sublay(82.1%)or intraperitoneal onlay(IPOM;17.9%)mesh positioning.At 1-month and 1-year follow-ups,there were no hernia recurrences(0%).Average hospital stays were 2.1 d±1.2 d and return to work occurred at 8.3 post-operative days±3.0 post-operative days.Three patients(10.7%)were readmitted before the 1-month follow up due to mesh infection and/or gastrointestinal issues.Fistula and mesh infection were observed in two patients each(7.1%),leading to partial mesh removal in one patient(3.6%).There were no complications between 1 month and 1 year(0%).CONCLUSION RTMs were used successfully to treat parastomal and incisional hernias at ileostomy reversal,with no hernia recurrences and favorable outcomes after 1-month and 1-year.

Factors influencing Frey syndrome after parotidectomy with acellular dermal matrix

BACKGROUND Frey syndrome,also known as ototemporal nerve syndrome or gustatory sweating syndrome,is one of the most common complications of parotid gland surgery.This condition is characterized by abnormal sensations in the facial skin accompanied by episodes of flushing and sweating triggered by cognitive processes,visual stimuli,or eating.AIM To investigate the preventive effect of acellular dermal matrix(ADM)on Frey syndrome after parotid tumor resection and analyzed the effects of Frey syndrome across various surgical methods and other factors involved in parotid tumor resection.METHODS Retrospective data from 82 patients were analyzed to assess the correlation between sex,age,resection sample size,operation time,operation mode,ADM usage,and occurrence of postoperative Frey syndrome.RESULTS Among the 82 patients,the incidence of Frey syndrome was 56.1%.There were no significant differences in sex,age,or operation time between the two groups(P>0.05).However,there was a significant difference between ADM implantation and occurrence of Frey syndrome(P<0.05).ADM application could reduce the variation in the incidence of Frey syndrome across different operation modes.CONCLUSION ADM can effectively prevent Frey syndrome and delay its onset.

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.