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Your conditions: Applied Mechanics
  • 基于AnyBody仿真的八段锦动作下肢生物力学特征研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: To reveal the different movement characteristics of Baduanjin before and after 14 weeks’trainingbetween beginners and professionals , the infrared capture test system , three-dimensional dynamometry , andsurface electromyography test system were used to collect Baduanjin movement data.AnyBody 7.0 Model-ing System was used to calculate the knee joint dynamics and muscle activation parameters of Baduanjinmovement. The results show that Baduanjin intervention can enhance the strength of knees and stability oflower limb joints , muscle fibers of different movements participate in different contractions ,and the muscleactivation degree is different. The muscle activation degree of tibialis anterior , rectus femoris , gastrocnemiusand biceps femoris is the highest in the second , third , fifth and seventh movements ,respectively. Beginnerscan adopt different actions to affect the stimulation of the muscles , and improve the scientificity of Baduan-jin exercise. The research results of this paper have verified the dynamic differences of knee joints of dif-ferent movements in Baduanjin , and calculated the characteristics of different muscle activation , which is of great significance in guiding beginners to practice Baduanjin.

  • 靶向性调控胫骨前肌对静态平衡的影响——基于经颅直流电刺激的干预

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: The aim of this study was to explore the effect of targeted modulation of the tibialis anterior muscle by transcranial direct current stimulation ( tDCS) on static balance performance.Totally 24 collegestudents received 20 min of tDCS and sham on tibialis anterior muscle at 2 mA in a randomized order.Transcranial magnetic stimulation (TMS) and balance tests were completed to assess the neurophysiologi-cal and balance performance before and after each stimulation.Results show that tDCS significantly in-creased the mean displacements in the Y-direction ( MDY) on both double with eyes-opening and singlewith eyes-closing.Compared to the baseline , tDCS significantly reduced MDY on double with eyes-openingand the mean velocity in the Y-direction on single with eyes-closing. tDCS significantly increased the meandisplacements X-direction ( MDX) on double with eyes-opening and single with eyes-closing and the maxi-mum sway diameter in the X-direction on doublet with eyes-opening.Compared to the baseline , tDCS sig-nificantly increased MDX on double with eyes-opening , single with eyes-opening, and double with eyes-closing; furthermore , the mean velocity in the X-direction on double with eyes-closing was increased.Com-pared with baseline ,tDCS significantly reduced resting motor threshold.'Targeted stimulation on the tibialisanterior muscle by tDCS is effective in improving the single balance with eyes-closing.

  • 基于DPM模型的水平井水平段沥青质颗粒运移规律数值模拟研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: To study the problem of asphaltic particles deposition in horizontal wellbore , the DPM module inFluent was used to track the particle movement in tubing.And the realizable l-e model was adopted to in-vestigate the asphaltene aggregates with a size of 10 ~ 100 um on the inner wall of tubing.The effects ofparticle size and velocity on the asphaltene particle deposition rate are analyzed when the gravity , saffmanlift , and drag forces are exerted on the particles.CFD simulation results show :① 'The deposition rate de-creases with the increase of viscosity in the laminar flow stage. This is mainly because in the laminar flow stage , the fluid flow is relatively stable and Saffiman lift decreases. The asphaltene deposition rate increasesslowly in the range from 0.001 2 Pa· s to 0.012 Pa · s; the deposition rate and percentage decrease whenthe viscosity increases from 0.012 Pa·s to 0.053 Pa·s in the turbulent stage.2The deposition percent-age and deposition rate of asphaltene particles decrease with the increase of flow rate when the particle di-ameter is 10-100 um.3When the velocity is 0.3-2 m/s ,the percentage and deposition rate of asphalteneparticles increase with the increase of particle diameter.The analysis shows that reasonable control of well-bore fluid velocity and particle diameter can be an effective means to reduce asphaltic deposition in well-bore.

  • 微型矩形凹槽的长方体通道的减阻和传热特性

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Miniature cuboid dimples are arranged on the bottom surface of rectangular channel along span-wise direction. The depth of the dimples is of the same order of magnitude as the boundary layer thickness.The flow and heat transfer characteristics in rectangular channel are studied by large eddy simulation.Thenumerical results show that the“protrusion effect”and secondary vortexes can be induced by the minia-ture cuboid dimples.'The role of the secondary vortexes is similar to that of miniature air rolling bearings,thus reducing flow resistance and improving heat transfer performance slightly. 'The results show that theminiature cuboid dimples lead to velocity slip , which effectively reduce the velocity gradient near the chan-nel bottom. The low speed streaky widens and the mixing of high and low speed fluids is inhibited. 'Thesecondary vortexes in the miniature cuboid dimples increase the thickness of the viscous sub-layer.Moreo-ver , the rolling friction between the secondary vortexes and the upper fluid replaces the sliding friction be-tween the wall and the fluid.Compared with the rectangular channel without miniature cuboid dimples , therectangular channel with miniature cuboid dimples can achieve more than 6% drag reduction without af-fecting the heat transfer effect.

  • 基于FPM方法的入水问题数值模拟研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Water entry of structures ,a highly nonlinear impact dynamic process , is widely used in maritimeand military fields. Ilt is very necessary to simulate this problem accurately and effectively. The finite parti-cle method (FPM) combined with the non-reflection boundary was adopted to simulate the problem of wa-ter entry. 'The vertical force , the velocity and the pressure of two-dimensional wedge were analyzed andcompared with the results of the literature to verify the effectivity of this method.'The factors for the prob-lem of water entry were also studied in this paper.The effects of size , shape , initial velocity and mass onvertical force , velocity and pressure at different time were analyzed. It is shown that the mechanical proper-ties of the structure are affected by the bottom angle of the wedge , the shape of the structure , the initial ve-locity and the mass , which has a reference for the design of the water-entry structure.

  • 开孔纸蜂窝芯层的面外静态压缩特性

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In view of the out-of-plane static compression characteristics of paper honeycomb core layer withhole on double-layer cell walls , the compression deformation processes of paper honeycomb core layer with-out and with hole when the compression amount is 85% are investigated by experiments , and the effects ofrelative humidity and pore diameter on its strength performance are studied. Based on the symmetry of hon-eycomb structure and using two element models , the honeycomb cell walls loaded along the out-of-plane di-rection are regarded as simply-supported elastic plate without and with hole.'The prediction formulas of thecritical stress of elastic buckling and plastic plateau stress are derived.The results show that analytical cal-culations are in good agreement with the experimental results.Combining the orthotropic properties of thepaper sheet and the out-of-plane compressive feature of paper honeycomb core layer , the finite elementmodels of paper honeycomb without and with hole are established.The simulation of the bending and fold-ing deformation evolution processes for honeycomb cell walls during the elastic-plastic buckling stages is consistent with the deformation processes observed in the static compression experiment.

  • 含主次波纹换热器板结构的等效力学性能表征

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In this paper, the effective material properties and mechanical behavior of heat exchanger plateswith primary and secondary trapezoidal cormugated structure were theoretically modeled and numericallystudied.First , we derived the two predicted formulae for effective material properties of heat exchangerplates with only primary corrugated structures combining the two existing equivalent approaches and thegeometric dimensions of real heat exchanger cornugated plates.Then we investigated the accuracy and ap-plication range of the two predicted formulae by comparing the cornugated plate's deformation using differ-ent predicted formulae and the simulation results given by a solid mimic model using the commercial AN-SYS software.And then we derived a prediction formula for the heat exchanger plate structure with primaryand secondary corrugations using the series model of composite structures. The influence of the secondary cornugations and off-axis characteristics on the effective properties of the heat exchanger cormugated platestructure are also discussed and displayed.

  • 采用数字图像体相关方法的核级石墨断裂特性研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In order to study the fracture performance of candidate graphite ( SNG742 fine-grained graph-ite)for nuclear engineering and clarify 3D fracture mechanics of the material , in-situ compressive testswere performed on double cleavage drilled compression ( DCDC) specimens. X-ray computed tomography(XCT) technique was used to scan the specimen and digital volume correlation ( DVC) method was fur-ther applied to analyze the scanned images to obtain 3D displacement and strain fields of the specimen.E-lastic modulus was determined inversely by minimizing the strain discrepancy between the DVC results andfinite element results. When the elastic modulus of the model was 10.6 GPa , the discrepancy was the minimum and the minimum error was 0.09 x10-3. In addition , based on the gray difference between the crackand the surrounding area in XCT images , the internal defects comparable to the main crack in scale wereevaluated quantitatively.Generally , the defect density in the tension area was higher than that in the com-pression area and its average was about 2.7 times of that in the compression area.From the 3D character-istics of the crack obtained from the displacement field ,it was found that along the thickness direction , thelocal crack length was higher near the middle and lower near the surface, the crack opening displacementwas directly proportional to the local crack length , and the crack tip opening angle remains basically un-changed , about 1.5�.Finally , the strains at the crack front were analyzed. It was found that the strains didnot change with the local crack length and kept around 5.8 x 10-3.The study method can provide some i-deas for obtaining the fracture parameters of materials through small-sized specimens and the results canprovide direct experimental evidence for understanding the 31 fracture characteristics of nuclear graphite.

  • 鞍形膜结构在冲击载荷作用下的振动特性

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Taking the saddle membrane structure as the research object , the vibration of the saddle mem-brane structure under the impact load is studied.First , the nonlinear differential equation of structural vi-bration under impact load is derived, in which the orthotropic of membrane material ,air damping , and geo-metric nonlinearity of membrane deformation are considered.'Then , it is assumed that a small ball impactsthe membrane surface with a certain impact velocity difference to simulate the impact load. Finally , the sto-chastic perturbation method is used to solve the equation , and the displacement function of the vibration re-sponse of the saddle membrane structure is obtained.At the same time, the vibration of the saddle mem-brane structure is numerically simulated and compared with the analytical theory.The results show that thevibration displacement of saddle membrane structure decreases with the increase of membrane pretension or arch span ratio, and increases with the increase of velocity difference. It can be seen that the theoreticalmodel is feasible in studying the vibration characteristics of saddle membrane structure under impact load,and the results can accurately predict the response law of membrane structure.

  • 双层薄膜与弹性梯度基底三层结构表面失稳分析

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Surface instability of hard films adhered on soft substrate has always been a difficult problem forflexible electronic devices. Considering the shear stress between the bi-layer film and the elastic gradedsubstrate , an analytical model of bi-layer film/ elastic graded substrate is established.By using the dis-placement continuity of the interface , the analytical expressions of the critical strain and wavelength of thebi-layer film/elastic graded substrate are obtained. Then , through several examples , the validities of theproposed expressions are verified which are compared with those results obtained by the finite element analysis.At the same time, the influences of the geometric parameters of the bi-layer film and physical pa-rameters of the elastic graded substrate on the buckling behavior are analyzed. 'The results in this papershow that decreasing the thickness of device layer or increasing the thickness of encapsulation layer canimprove the stability of bilayer film/elastic graded substrate structure; if the substrate is relatively“soft”orthe device layer is “hard”,the shear force of the interface between the device layer and the substrate willbe taken into account , which can prevent the resistance of the three-layer film/ substrate structure from un-dergoing interface failure.Above all, the research will provide theoretical support for the fabrication of flex-ible electronic devices with hard film/elastic graded substrate structure.

  • 拉索预应力巨型网格结构参激振动及动力稳定性研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: T'he parametric vibration and dynamic stability of prestressed reticulated mega-structures was in-vestigated.Firstly , a bowstring-arch model was derived to analyze the mechanism and characteristics of theparametric vibration of the cables on cable-strut , and the influencing factors were further discussed by utili-zing ANSYS.Then the dynamic stability of the cable-strut and the prestressed reticulated mega-structureswas researched under harmonic loads.'The analytical and numerical results indicate that the cable will havea larger scale vibration stimulated by low excitation amplitudes when the structural vibration frequencies isclose to twice of natural frequency of cables. The dynamic instability failure usually occurs on cable-strutunder the horizontal harmonic load while the dynamic strength failure happens under the vertical harmonicload, and generally , the dynamic instability failure takes place in the prestressed reticulated mega-structures under the harmonic loads.

  • 基于集对分析模型的岩溶区浅埋穿河隧道突涌水危险性评价

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Tunnel construction in karst area often faces geological disasters such as water inrush , especiallyfor the construction of shallow tunnel under river , which is a very challenging work. Due to the in situ faultfracture zone , high weathering degree of rock mass , and the development of joints and fissures in the tunnelsite , the possibility of river water intrusion into the tunnel is greatly increased. In order to effectively evaluate the risk of water inrush in karst shallow tunnel under river, according to the geological conditions andtunnel characteristics of the tunnel site,11 factors affecting the water inrush , such as formation lithology,modified strata inclination, soluble and insoluble rock contact zones , surrounding rock grade , fault zonewidth ,fault property , fissure development degree , surface water flow , surface catchment area, buried depthof tunnel , construction disturbance degree , are selected as the evaluation indexes , and the risk evaluationsystem of karst shallow tunnel under river is established.The analytic hierarchy process (AHP) was usedto construct judgment matrix to determine the weight of evaluation indexes , the set pair analysis methodwas used to calculate the connection degree of each evaluation index , and then the comprehensive connec-tion degree of evaluation samples was determined.Secondly , the maximum membership degree principlewas used to identify the risk level of water inrush.Finally , according to the corresponding relationship be-tween the risk level and the water inflow, the scope of water inrush inflow can be preliminarily predicted.ln view of the risk of water innush in shallow buried section of Yuelongmen Tunnel under-crossing Gao-chuan River , the set pair analysis model was used to analyze the risk. 'The calculation results show that therange of water inrush volume predicted by the risk assessment is 3 000 ~ 10000 m'/d,and the actual waterinflow from site excavation is 7 000 m'/ d. That is to say , the results of risk assessment are basically con-sistent with the actual situation , which verifies the rationality and feasibility of the evaluation system andmethod and provides effective support for risk assessment of water inrush of karst shallow tunnel underriver.

  • 全沙漠砂纤维水泥基复合材料单轴受压尺寸效应试验研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In order to explore the feasibility of using desert sand entirely to prepare engineered cementi-tious composites (ECCs) in Xinjiang region , and study the uniaxial compression size effect of ECCs whichare prepared entirely from desert sand , on the basis of analyzing and comparing the macroscopic mechani-cal properties and microstructure of ECCs prepared by three aggregates ( i. e. , desert sand, quartz sand,and river sand) , the uniaxial compression tests of five groups of desert sand ECC specimens with differentsizes were carried out. The results show that at the same ratio of materials , the ECCs prepared entirely byusing desert sand have compressive , tensile , and flexural strength similar to that of the ECC prepared by the other two kinds of sand , in desert sand ECCs , fewer attachments and relatively complete morphology offiber surface are beneficial to its bridging effect;the uniaxial compression properties of ECC prepared en-tirely by using desert sand have size effect ; the expression of the relation between height-thickness ratioand compressive strength , and the stress-strain full curve model with dfferent height-thickness ratio are ingood agreement with the test results.

  • 深埋地下洞室局部让压效应及能量演化规律

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In order to reduce the dynamic disaster caused by rockburst , by using the energy principle ofrockburst , the concept of non-uniform thin-wall stress concentration is put forward. The analysis shows thatthe location of rockburst is stress concentration and high stress gradient.On basis of the construction ofpractical engineering ,and FLAC3 numerical simulation software was developed by FISH programming;theenergy evolution rules of deep underground cavern with dynamic load and the failure forms and dynamiceresponse of yield space of steel frame are systematically studied from the local yield of surrounding rock. The researches show that due to the local yield effect of the surrounding rock , the disturbance to the sur-rounding rock is reduced , and the shockwaves energy is absorbed and reflected in the working face , resul-ting in weak dynamic response and reduced dynamic load.After the excavation of the cave ,the rock massis firstly tension and then shear failure , and the residual elastic strain energy is released.The location ofrock burst is directly connection to the orientation of the maximum principal stress of the rock mass.

  • 土压平衡盾构螺旋输送机渣土运移及参数影响

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In order to more realistically study the role of screw conveyor in stable excavation surface andslag discharge in the earth pressure balance shield , on the basis of the existing screw conveyor slag trans-port theoretical model , the actual inclination angle of the screw conveyor and the gravity of the soil , as wellas the actual working conditions of the screw conveying soil in the screw conveyor,are considered , and thetheoretical mechanical model is established.Based on the principle of eath pressure balance , the formulasof earth flow and earth pressure gradient of the screw conveyor are derived, and the variation nules betweenthem and various parameters are analyzed. In addition to considering basic mechanical parameters and slagproperty parameters , the effect of dfferent types of soil on slag efficiency and the effect of soil flow angleon soil flow and soil pressure gradient are also analyzed; the increase rate of soil flow increases with soilflow angle. The increase shows a non-linear trend that decreases first and then increases; the gradient ofthe earth pressure increases with the increase of the soil flow angle in a trigonometric function. It provides a certain theoretical basis and engineering reference for reasonable design , type selection ,and evaluation ofearth pressure balance shield screw conveyor in practical engineering.

  • 混凝土面板砂砾石坝漫顶溃坝数值模拟

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Based on the field investigation of dam break cases and flume model test , the numerical model ofovertopping break of concrete-face sand-gravel dam (CFSGD) is established to simulate the interaction a-mong water flow characteristics , sand-gravel materials , and concrete face slab. The model is mainly com-posed of three parts : ① Considering the erosion characteristics between the vortex water flow and sand-gravel materials , the RNG k-e turbulence model is introduced to simulate the reverse erosion of the vortexwater flow.2 Through the sediment transport formula and fluid volume method (VOF) traces the inter-face between sand and water erosion , and considers the pore characteristics of sand-gravel materials.3Based on the moment equilibrium method, the failure process of the concrete face slab under its self-weightand water loads is calculated.The numerical model is verified by the flume model test. 'The results showthat the numerical model established in this paper can accurately simulate the reverse erosion of the vortexwater flow on the dam during the failure process and the detailed evolution process of the face slab breach.The relative error between the measured data and the calculated peak breach flow , the development of thebreach of the rockfill body , the duration of the break and the length of the face slabs are all less than15% , which verifies the rationality of the numerical model.Compared with the parametric model , the nu-merical model of dam breach proposed in this paper provides more detailed results.

  • 砂岩蠕变破裂多尺度演化试验研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: Rock deformation and failure occur with the increase of extemal load. When the external loadremains unchanged, the deformation does not stop, and it will continue to increase , resulting in creep de-formation.'The fundamental cause is the heterogeneity of rock.Rock creep fracture is a process of micro-scale fracture , meso-scale crack propagation and penctration , macro-scale deformation increase and failureprocess caused by the original heterogeneity of rock.'Therefore , it is necessary to study the multi-scale evo-lution mechanism of rock creep fracture.'Taking sandstone as the research object , this paper analyzes thedeformation and fracture mechanism of sandstone samples at different scales from the macro-evolution ex-periment of creep fracture and the micro-scanning experiment of fracture.Through the macroscopic evolution experiment of sandstone creep fracture ,it can be seen that there are no cracks on the surface of rockin the initial creep and constant velocity creep stages , but mainly the initiation and propagation of micro-and micro-cracks.When the macro-fracture surface is formed , it enters the accelerated creep stage. In theaccelerated creep stage , friction sliding occurs along the fracture surface ,and finally failure occurs. The mi-croscopic analysis of the micro-composition and fracture characteristics of the sandstone can be obtained byanalyzing the micro-composition and micro-fracture characteristics of the sandstone.The results of multi-scale analysis directly reflect the spatial position and direction of crack propagation in rock. This is of greatsignificance for further study of the evolution mechanism of rock creep rupture.

  • 振动主动控制系统降级工作模式研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: The active vibration control system is an electromechanical integrated system which can reducethe vibration level of the platform by obtaining the vibration sensor signal and driving the actuator outputforce.The stability of the active vibration control system directly affects the experience of using the plat-form which obtains harsh vibrations.'The system is highly sensitive to component reliability when the sys-tem contains lots of hardware. In order to improve the functional reliability of the system without changingthe hardware , this paper proposes two system degradation modes of system control strategies and analyzestheir reliability.Based on the system degradation modes and switch methods , different levels of degradationmodes are designed accordig to the different number of hardware faults.According to the system controlparameters under different degradation modes, the optimal combination design of the actuator is proposed.And the optimal high-dimensional matrix of system model under different degradation modes is obtained.Finally , in the laboratory , the degradation mode of the actuator is experimentally verified in the active vi-bration control system test platform. By disconnecting the power supply of the actuator , the system workscorrectly for the vibration reduce function.

  • 全动平尾颤振关键设计因素研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: All-movable horizontal tail flutter design is an important part in the overall design of fighters.The flutter envelope of all-movable horizontal tail directly determines the flight envelope of the aircraft.Afinite element model of all-movable horizontal tail for structural dynamics and flutter is established.Ac-cording to aerodynamic layouts and structural layouts , the key flutter design factors have been extracted, in-cluding the leading edge sweep angle , aerodynamic area distribution , empennage support stiffiness, spindlestiffness , location of spindle , control stiffness ,and mass distribution. By means of numerical simulation , therelationship between different design factors and flutter speed is obtained.The design trend of improvingflutter velocity of all-movable horizontal tail and the advantages and disadvantages of these factors on struc-ture weight are pointed out. The wind tunnel tests on a scaled model verify the correctness of the effects ofvarious parameters on all-movable horizontal tail flutter.'The numerical calculations of flutter and wind tun-nel tests are analyzed.'The results show that the flutter design parameters are effective and can be used asthe key factors in flutter design of all-movable horizontal tail.

  • 自旋挠性航天器非约束模态动力学特性研究

    Subjects: Mechanics >> Applied Mechanics submitted time 2023-03-20 Cooperative journals: 《应用力学学报》

    Abstract: In the study of dynamic problems of flexible spacecraft , the problem of rigid and flexible cou-pling of flexible spacecraft system is concerned , that is , the vibration of flexible appendage of spacecraftmay cause instability of spacecraft motion.A beam simplified model of the spacecraft panel structure isproposed for a spinning flexible spacecraft with a central rigid body and bilateral large flexible structureand an unconstrained modal dynamics model is established. In this paper , the unconstrained modal dynam-ics modeling and characteristics of a spinning flexible spacecraft are discussed considering the action of u-niversal gravitation.Firstly , the dynamic equation of the spinning flexible spacecraft is established by usingEuler equation and Hamiltonian principle , which explains the coupling between rigid and elastic modes.Then the modal discretization is carried out ,the eigenvalue problems of the constrained mode and uncon-strained mode are discussed respectively , and the frequency and relevant modes of vibration are quantita-tively compared.Finally , numerical simulation is carried out to solve the unconstrained mode eigenvalue problem of the spinning flexible spacecraft.The differences between the constrained mode and the uncon-strained mode are compared and verified with the finite element method.The conclusion is that with the in-crease of the length of the beam , that is , with the decrease of the ratio of inertia and mass , the uncon-strained mode is more accurate than the constrained mode.