Support Stiffness Research Articles

Numerical modeling of floating geosynthetic-encased stone column–supported embankments with basal reinforcement

The performance of the floating geosynthetic-encased stone column–(GESC)-supported embankments with basal reinforcement was examined using a 3-dimensional (3D) hydro-mechanical coupling finite element model. Comprehensive parametric analyses were performed on the governing factors such as consistency of substratum soil, tensile stiffness of basal reinforcement and encasement, and embankment height. The results indicated that a higher embankment load is transferred to the surrounding soil when a GESC was constructed on a weaker substratum. This causes larger increases in the settlement and lateral displacement of the GESC on the weaker substratum. The tensile strain of the basal reinforcement and hoop strain in the encasement also increases. In addition, high tensile stiffness in basal reinforcement and encasement is necessary to ensure feasible settlement reduction in a floating GESC-supported embankment with basal reinforcement.

A New Hypersonic Wind Tunnel Force Measurement System to Reduce Additional Bending Moment and Avoid Time-Varying Stiffness.

In order to improve traditional hypersonic wind tunnel airframe/propulsion integrated aerodynamic testing technology for hypersonic vehicles, a new force measurement system called the aerodynamic force measuring support (AFMS) was designed. The AFMS effectively overcomes the defect that the traditional internal box-balance occupies a large amount of internal space in the aircraft test model, which makes the airframe/propulsion integrated aerodynamic test more difficult. The AFMS also alleviates the interference of the additional bending moment caused by the non-coincidence between the calibration center of traditional external box-balance and the gravity center of the aircraft test model, innovatively designing a convex structure in the joint part of the force measuring system. Furthermore, the AFMS effectively overcomes the time-varying stiffness of joints caused by test model vibration in hypersonic wind tunnel testing, which eventually leads to test errors. Compared with the traditional box-balance, the AFMS proposed in this study has sufficient design space. This ensures more thorough aerodynamic decomposition of the AFMS and less interference between channels, whilst also having the advantages of the large support stiffness of traditional box-balance. Thus, the AFMS provides a new technical path for airframe/propulsion integrated aerodynamic testing of air-breathing hypersonic vehicles in a hypersonic wind tunnel.

“Geosynthetic reinforcement stiffness for analytical and numerical modeling of reinforced soil structures” by Richard J. Bathurst and Fahimeh M. Naftchali, geotextiles and geomembranes, 49 (2021) 921–940

• The maximum reinforcement loads, T max , calculated using the finite difference method in the paper under discussion are significantly different with those presented by Huang et al. (2010). • The summations of T max calculated in these analyses are different by a factor of ∼3. • The corresponding active state condition is theoretically considered as a lower bound in the calculation of T max for the reinforcement layers, in which the load is not influenced by the combination of the facing stiffness and toe restriction.

Vibrations of complex composite double-column system by extended Laplace transform method

PurposeDouble-beam/column systems have drawn much attention in many engineering fields. This work aims to present the free and forced vibrations of a novel and complex double-column system with concentrated masses, axial loads and discrete viscoelastic supports subjected to the excitation of ground acceleration are solved by the extended Laplace transform method (ELTM).Design/methodology/approachIn this work, the authors proposed an extended Laplace transform method (ELTM), which is an exact and explicit analytical method. Firstly, the mathematical model simulating the vibrations of the double-column system is reformulated with Dirac's delta function. Secondly, the exact and explicit mode shape solutions are obtained, based on which the natural frequencies and dynamic responses are obtained. An illustrating example is presented to show the validity of the proposed method. A parametric study is carried out to investigate the influences of the non-dimensional column stiffness ratio and the support stiffness ratio on the peak dynamic displacement and velocity.FindingsIt is shown that the proposed method can give exact and explicit solutions of the mode shapes and natural frequencies. It is found that the asynchronous vibrations of the proposed double-column systems can be implemented to efficiently dissipate seismic energy, as shown in the time-histories of displacement and velocity.Practical implicationsThis research systematically studied the free and forced vibrations of the complex double-column system. The proposed extended ELTM is a general method. Its application to studying the energy dissipation capability implicates that the double-column system can be utilized to reduce responses in structures under earthquake attacks.Originality/valueThe proposed extended ELTM is original and powerful. Its application to study the complex double-columns system with discrete supports, concentrated masses and axial loads is novel.

Response to discussion by S. H. Mirmoradi and M. Ehrlich on “Geosynthetic reinforcement stiffness for analytical and numerical modelling of reinforced soil structures” by Richard J. Bathurst1 and Fahimeh M. Naftchali2, Geotextiles and Geomembranes, 49 (2021) 921–940

• The model was made purposely simple to focus attention on the qualitative influence of stiffness on reinforcement loads. • Using numerical models to infer quantitative performance of actual MSE walls must be undertaken with caution and skill. • Small changes in numerical model details can give widely different estimates of reinforcement loads. • The veracity of any numerical model should be based on comparisons with more than one physical wall of realistic height. • The accuracy of design methods must be assessed using measured loads from full-scale walls, not numerical models.

Modeling and Parameter Identification for a Flexible Rotor With Impacts

Abstract The accuracy of a multibody model to predict the behavior of a real physical system depends heavily on the correct choice of model parameters. Identifying unknown system parameters that cannot be computed or measured directly is usually time-consuming and costly. If measurement data is available for the physical system, the parameters in the corresponding mathematical model can be determined by minimizing the error between the model response and the measurement data using optimization methods. While there is a wide range of optimization methods available, genetic optimization is a more generic approach for finding optimal solutions to complex engineering problems. So far, however, there is no general approach on how to use genetic optimization to determine unknown system parameters automatically—which is, however, of great importance when dealing with real flexible multibody systems. In this paper, we present a methodology to automatically determine several unknown system parameters of a complex flexible multibody system using genetic optimization. The proposed methodology is demonstrated using a small-scale test problem and a real flexible rotor excited with impacts. Experiments were performed on the physical rotor to obtain measurement data which is used to identify bearing and support stiffness and damping parameters as well as the impact force.

Evolution of trackbed performance and ballast degradation due to passages of million train wheel axle loads

The increases in train speeds and wheel axle loads produce significantly higher dynamic responses and ballast breakage in ballasted tracks, which could cause reduced trackbed performance and the deterioration of the ballast particles under long-term train traffic loads. To evaluate trackbed performance under long-term moving train loads, a full-scale ballasted track experiment with eight sleepers was designed and tested on a validated physical model test platform (ZJU-iHSRT).Sleeper support stiffness is a qualitative index of the ballasted track in the evaluation of trackbed performance, which was studied based on the sleeper displacement measured by a laser displacement sensor during the test.Then, ballast breakage analysis was conducted to quantify the ballast degradation of ballast particles after every 400,000 passes of train wheel axle loads through the sieving test of particle size distribution.Vibration velocity sensors and “SmartRock” wireless sensors were installed at specific locations in the ballast layer to compare the ballast dynamic responses before and after the implementation of long-term train traffic loads. The test results showed that both the static and dynamic sleeper support stiffness increased tremendously with the densification of trackbed caused by long-term train loads; especially, heavy train loads increased the BBI by 60% and doubled the static sleeper support stiffness. The evolution of static sleeper support stiffness and ballast breakage showed a similar trend, which significantly intensified with the increase in train speed, then stabilized with the number of train wheel axle loads, and increased sharply again due to the increase in axle load. Ballast breakage and particle rearrangement made the small particles fill the ballast voids, which enhanced the densification of ballast particles, thereby reducing the trackbed elasticity.

Different Design Feature Combinations of Flatfoot Orthosis on Plantar Fascia Strain and Plantar Pressure: A Muscle-Driven Finite Element Analysis With Taguchi Method.

Customized foot orthosis is commonly used to modify foot posture and relieve foot pain for adult acquired flexible flatfoot. However, systematic investigation of the influence of foot orthotic design parameter combination on the internal foot mechanics remains scarce. This study aimed to investigate the biomechanical effects of different combinations of foot orthoses design features through a muscle-driven flatfoot finite element model. A flatfoot-orthosis finite element model was constructed by considering the three-dimensional geometry of plantar fascia. The plantar fascia model accounted for the interaction with the bulk soft tissue. The Taguchi approach was adopted to analyze the significance of four design factors combination (arch support height, medial posting inclination, heel cup height, and material stiffness). Predicted plantar pressure and plantar fascia strains in different design combinations at the midstance instant were reported. The results indicated that the foot orthosis with higher arch support (45.7%) and medial inclination angle (25.5%) effectively reduced peak plantar pressure. For the proximal plantar fascia strain, arch support (41.8%) and material stiffness (37%) were strong influencing factors. Specifically, higher arch support and softer material decreased the peak plantar fascia strain. The plantar pressure and plantar fascia loading were sensitive to the arch support feature. The proposed statistics-based finite element flatfoot model could assist the insole optimization and evaluation for individuals with flatfoot.

A biomechanical comparison between cement packing combined with extra fixation and three-dimensional printed strut-type prosthetic reconstruction for giant cell tumor of bone in distal femur

BackgroundThe most common reconstruction method for bone defects caused by giant cell tumor of bone (GCTB) is cement packing combined with subchondral bone grafting and extra fixation. However, this method has several limitations involving bone cement and bone graft, which may lead to poor prognosis and joint function. A titanium-based 3D-printed strut-type prosthesis, featured with excellent biocompatibility and osseointegration ability, was developed for this bone defect in our institution. The goal of this study is to comparatively analyze the biomechanical performance of reconstruction methods aimed at the identification of better operative strategy.MethodsFour different 3D finite element models were created. Model #1: Normal femur; Model #2: Femur with tumorous cavity bone defects in the distal femur; Model #3: Cavity bone defects reconstructed by cement packing combined with subchondral bone grafting and extra fixation; Model #4: Cavity bone defects reconstructed by 3D-printed strut-type prosthesis combined with subchondral bone grafting. The femoral muscle multiple forces were applied to analyze the mechanical difference among these models by finite element analysis.ResultsOptimal stress and displacement distribution were observed in the normal femur. Both reconstruction methods could provide good initial stability and mechanical support. Stress distributed unevenly on the femur repaired by cement packing combined with subchondral bone grafting and extra fixation, and obvious stress concentration was found around the articular surface of this femur. However, the femur repaired by 3D-printed strut-type prosthetic reconstruction showed better performance both in displacement and stress distribution, particularly in terms of the protection of articular surface and subchondral bone.Conclusions3D-printed strut-type prosthesis is outstanding in precise shape matching and better osseointegration. Compared to cement packing and extra fixation, it can provide the almost same support and fixation stiffness, but better biomechanical performance and protection of subchondral bone and articular cartilage. Therefore, 3D-printed strut-type prosthetic reconstruction combined with subchondral bone grafting may be evaluated as an alternative for the treatment of GCTBs in distal femur.

Performance of two-tiered reinforced-soil retaining walls under strip footing load

In the current study, an attempt was made to investigate the performance of two-tiered mechanically stabilized earth walls (T-TMSEWs) under static footing loading using reduced-scale model tests. For this purpose, twenty-four T-TMSEW models were constructed with three different types of reinforcement (metal strips, geogrid and geostraps) and were loaded using the rotatable and non-rotatable strip footings in different distances to the wall crest. Findings indicated that, although decreasing the reinforcement stiffness and the soil-reinforcement interaction reduces the ultimate bearing capacity of footings, the use of extensible reinforcements with low pull-out capacity and allowing the footing to tilt can be two effective solutions in T-TMSEWs to minimize deformations of backfill surface and connection loads as well as lateral pressures. It was observed that the use of a two-tiered configuration in MSE walls and also reducing tensile stiffness and soil-reinforcement interaction simultaneously, not only lead to change in the slip surface geometry but also prevent the development of deep slip surfaces in the lower tier. On the other hand, increasing the footing distance to the wall crest in the range of reinforced zone was found to be another influential solution to improve the bearing capacity, reduce wall deformations and also minimize lateral pressures.

A New Numerical Finite Strain Procedure for a Circular Tunnel Excavated in Strain-Softening Rock Masses and Its Engineering Application

The small strain theory underestimates the self-bearing capacity of rock masses, especially for a soft rock tunnel under high geostress. To perform an efficient and accurate calculation and provide a reference for the stiffness design of a tunnel, the finite strain solution for a circular tunnel in Mohr–Coulomb strain-softening rock masses with a non-associated flow rule was derived as three sets of differential equations under the Lagrangian coordinate, which are in the residue region, the softening region, and the elastic region, respectively. Based on the bisection method, an iteration procedure for solving the finite strain solution was proposed to approximate the boundary condition at infinity, the values of two adjacent boundaries, and the initial values on the excavation boundary. This numerical procedure was verified by comparing with self-similar solutions, recursive solutions, and FLAC simulation results. In the calculation example, the relative error on boundaries can be decreased to less than 10−8 after only 10 times iteration and the time for each calculation is less than 15 s. Applying this procedure on the sensibility analysis and stiffness reliability design for the Zhongyi tunnel, a support stiffness of 4.3 MPa/m is recommended to guarantee a tunnel displacement lower than 0.5 m.

Effect of reinforcement stiffness on response of back-to-back MSE wall upon infiltration

Back-to-back mechanically stabilized earth (MSE) walls are being widely utilized as bridge abutments and highway ramps, considering their cost effectiveness and ease of construction. Though high quality well-graded granular fill is the most appropriate backfill material, owing to its scarcity, locally available low-quality soils are often used as backfill. Nevertheless, numerous failure cases of such walls with low-quality soil are reported, especially subsequent to rainwater infiltration. The stiffness of reinforcement is a key parameter affecting the overall behaviour of MSE walls. The present study investigates the influence of reinforcement stiffness on the response of select fill, marginal fill, and hybrid-fill back-to-back MSE walls using a finite element (FE) based approach. Results show that stiffness of reinforcement has a significant effect on the overall performance of marginal fill wall upon rainfall infiltration. Specifically, with the increase of reinforcement stiffness, the infiltration-induced facing displacement decreases and reinforcement tension increases. However, the performance of select fill and hybrid-fill walls following rainfall infiltration was found to be satisfactory even with low stiffness reinforcements, and further improvement with increase of reinforcement stiffness was insignificant. The reduction of safety factors during infiltration was shown to be independent of reinforcement stiffness for all wall types.

Nonlinear vibration characteristics of gear-rotor-bearing system

Based on the Timoshenko beam element model in the finite element theory and the lumped mass method, the meshing dynamics equation of helical gears was established considering the time-varying meshing stiffness of helical gears, tooth side clearance, bearing support stiffness and other factors, and the nonlinear dynamics model of the gear-rotor-bearing system was established. Through the analysis of the dynamics model, meshing stiffness, backlash and the influence of bearing stiffness for the system vibration characteristics, studies have shown that the bearing stiffness for the purpose of this article studies the effect to the stability of the main reducer system transmission, vibration noise of the gear-rotor-bearing system parameter selection, and provides theory basis for diagnosis.

An improved least square similitude method based on Lagrange energy for estimating scaling laws and eliminating coupling effects

Scaling laws refer to the relationships of the input and output parameters between prototype and scaled models. They are usually used to predict the vibration characteristics of a large-scale structure with scaled-down models. In general, scaling laws are estimated from the dimensional analysis of concerned variables or the dimensionless governing equation of vibrating structures. However, there are still some limitations that existed in the partial similitude of complex systems. The present work is concerned with determining scaling laws to predict the vibration characteristics of a thin rectangular plate containing elastic boundary conditions and even complicated geometrical features. The Lagrange energy-least squares similitude method (LE-LSSM) is proposed in this paper, the Lagrange energy approach eliminates the coupling effect of support stiffness on powers, and the LSSM can then be used to deduce output scaling laws. In numerical verifications, a perfect rectangular thin plate is simulated by finite element analysis (FEA) to verify the scaling laws, and a perforated thin rectangular plate is further applied for standing out the highlight of the LE-LSSM. Moreover, the coupling effects on scaling laws are analyzed among geometric dimensions, support stiffness, and material parameters. The coupling effects exist if powers change over the geometric dimensions of scaled models, but the inverse is not. Powers are stable and do not change over the geometric dimensions of scaled models under the free boundary condition, illustrating no coupling effect of geometric dimensions on powers. However, the support stiffness exhibits a significant coupling effect on powers of geometric scaling factors, which leads to inaccurate scaling laws. It can be effectively eliminated no matter how large the support stiffness values when LSSM is combined with the Lagrange energy approach. It is found that the results under the uncoupled powers are more accurate than those under the coupled powers. Moreover, material parameters produce a coupling effect on powers in non-zero support stiffness. Unlike support stiffness, only the power values change, but their stability not. Finally, the simulated results and proposed method are experimentally validated using the Brüel & Kjær test system, which derives consistent results.

A Gray Wolf Optimization-Based Improved Probabilistic Neural Network Algorithm for Surrounding Rock Squeezing Classification in Tunnel Engineering

Surrounding rock squeezing deformation is a common and prominent hazard in tunnel engineering projects, which often induces the shield jamming disaster during the TBM tunneling process. Based on the 139 groups of historical squeezing deformation cases, this study developed a hybrid PCA-IWGO-PNN model for squeezing classification. According to the influencing factors and characteristics of squeezing deformation, the strength-stress ratio, tunnel burial depth, tunnel equivalent diameter, rock mass quality index, and support stiffness were selected to establish the prediction index system of squeezing level. Because the probabilistic neural network (PNN) requires that the input variables are independent, principal component analysis (PCA) was used to preprocess the original data to eliminate the correlation between prediction indexes and achieve dimensionality reduction. The spread coefficient was the critical hyper-parameter in the PNN, and the improved gray wolf optimization (IGWO) algorithm was used to realize its efficient automatic optimization. Then, the PNN model was applied to engineering practice. Only 1 of 20 test samples was misjudged, achieving the 95% prediction accuracy. Finally, the comparison analysis with the artificial neural network (ANN) model, support vector machine (SVM) model, and random forest (RF) model was conducted. Among them, the PNN model achieved the highest prediction accuracy, followed by the artificial neural network (85%), RF (85%), and SVM (80%). In addition, the PNN model had the fastest running speed, which only consumed 5.6350 s, while the running time of ANN, SVM, and RF was 8.8340, 6.2290, and 6.9260 s, respectively. The hybrid PCA-IWGO-PNN model developed in this research provides an effective method for surrounding rock squeezing classification, and it has superiorities in both prediction accuracy and running speed.

Triple Crossed Flexure Pivot Based on a Zero Parasitic Center Shift Kinematic Design

Abstract Thanks to their absence of play, absence of contact friction and possible monolithic fabrication, flexure pivots offer advantages over traditional bearings in small-scale, high accuracy applications and environments where lubrication and wear debris are proscribed. However, they typically present a parasitic center shift that deteriorates their rotational guidance accuracy. Existing solutions addressing this issue have the drawbacks of reducing angular stroke, prohibiting planar design, or introducing overconstraints or underconstraints. This article presents a new triple crossed flexure pivot we have named TRIVOT whose kinematics theoretically nullify its parasitic center shift without overconstraints nor internal mobility. In the physical implementation, the center shift is non-zero but we show using the finite element method (FEM) that it is reduced by one order of magnitude in comparison to the widely used crossed flexure pivot (CFP). This allows to choose a crossing ratio of the flexures that either maximizes the angular stroke limit for given flexures or results in a compact planar design with the possibility of a remote center of compliance (RCC). Based on a pseudo-rigid-body model (PRBM), formulas for the rotational stiffness and angular stroke limit of the TRIVOT are derived, which are then validated by FEM. Finally, we show that a high support stiffness can be achieved based on a preliminary study for a mechanical watch time base application. We expect this new pivot to become a competitive alternative to the standard CFP for applications where high accuracy and compactness are required.

Preliminary analysis of vibration characteristics of human body on high-speed train

To study the ride comfort of high-speed train passengers, a detailed human body–seat–vehicle–track coupled model is developed. This model adopts a dual-axis human-body dynamic model and considers the nonlinearity of the primary and secondary suspensions and the wheel–rail contact condition. Additionally, the input wheel/rail irregularity excitation data are measured for a high-speed railway line in China. According to the model, the root-mean-square (RMS) values of the acceleration for the passenger head at different positions of the car body are determined, and the effects of the car-body loading conditions, speed, and seat support parameters on the head vibration characteristics are studied. The results indicate that the RMS value is the highest for the passengers sitting in the front row near the window seat, followed by those sitting in the middle row of the car body. There are small differences in the RMS value between the passengers sitting on the left and right sides of the same row in the car body. At a certain speed, the track irregularity stimulates the rolling and pitching motions of the train. Therefore, effective methods should be implemented to avoid the inherent characteristics of the car body. Although an increase in the seat support stiffness intensifies the high-frequency vibration, it reduces the low-frequency vibration in the range of 0–15 Hz, reducing the RMS value of the head acceleration. When the train is loaded, the effect of passengers on the car body is similar to that of a damper or mass element, which can reduce the car-body vibration and enhance the ride comfort.

Study on theoretical modeling and mechanical performance of a spinning porous graphene nanoplatelet reinforced beam attached with double blades

In this article, theoretical modeling and vibration characteristics of a spinning double-blade beam assembly restricted by elastic supports are studied. Graphene nanoplatelet (GPL) reinforcement and porous foamed metal matrix are adopted to make up the assembly structure. Due to the nonuniformity of the porosity and graphene nanofillers, the material properties of the attached blades and beam are considered to change along the blade thickness and beam radius, respectively. They are obtained via the rule of mixture, the open-cell scheme and the Halpin-Tsai micromechanics model. These attached blades and beam are modeled in accordance with the Euler-Bernoulli beam theory and the Rayleigh beam theory, respectively. Via employing the Lagrange’s equation, the equations of motion of the double-blade beam are derived. Then, the natural frequencies of the spinning nanocomposite double-blade beam are calculated by the substructure modal synthesis method and the assumed modes method. A detailed parameter analysis is performed to study the influences of dimension, distribution pattern and weight fraction of GPLs, distribution and coefficient of porosity, length and location of the blades, stiffness and location of supports, and spinning speed on the mechanical behaviors of the double-blade beam assembly.

Experiments and a reverse-curved compressive arch model for the progressive collapse resistance of reinforced concrete frames

The compressive arch action (CAA) is a critical force-transfer mechanism to mitigate the vulnerability of progressive collapse for reinforced concrete frames. To deeply analyze the mechanical behavior of concrete beam-column sub-assemblages under a middle-column-removal scenario, the progressive collapse tests and numerical simulations were accomplished, in which the stress distribution and the force-flow characteristic under CAA were revealed. To accurately evaluate the peak capacity of CAA, a mechanical model of a reverse-curved compressive arch (RCCA) is put forward. The theoretical formulas are derived on the basis of the model, considering both the bending deformation and the axial deformation of the arch. The theoretical calculation results (including the peak capacities and the corresponding displacements) agree well with the experimental results of 20 specimens. Moreover, a parametric analysis on CAA peak capacity is investigated considering the following factors: the axial and rotational restraint stiffness of end supports, the initial connection gap of test setups, the depth-to-span ratio of beams, the concrete strength and the reinforcement ratio of beams. The research results demonstrate that the relative axial (rotational) restraint stiffness should not be less than 1 and the initial connection gap should be less than 1.0 mm to ensure sufficient boundary constraints. According to the parametric analysis results, a simplified formula for CAA peak capacity is established, in which multiple influence coefficients are proposed for the formula. The proposed formula is practical and simple to apply because no iteration or derivation is required, and good calculation accuracy is also verified by 20 specimens. Based on the formulas, the CAA capacities of different column-spacing concrete frames designed with various depth-to-span ratios of beams are compared with the necessary gravity loads. The research results show that the larger the depth-to-span ratio, the greater the bearing capacity margin.

Research on Time Delay Feedback Control of Lateral Vibration Axially Moving Viscoelastic Beam

The nonlinear dynamic behavior of a viscoelastic beam in axially variable motion under time delay is studied. Considering that the axial velocity pulsation and radial tension change periodically with time under the action of time delay, the viscous damping and finite support stiffness are taken into account, and the viscoelastic constitutive relationship adopts Kelvin model. A mathematical model of lateral vibration of an axially moving viscoelastic beam with changes in axial velocity and tension under time delay is established, and a partial differential-integral control equation describing the lateral nonlinear vibration of an axially moving beam is given. Based on the Galerkin truncation method, the control equations established based on the mechanical model are discretized, so that the direct multi-scale method obtains the numerical solution of the lateral nonlinear vibration of the axially moving beam under the action of time delay, and determines the nonlinear dynamic behavior of the system under the action of time delay. By analyzing the numerical solution of the vibration displacement and velocity at the midpoint of the beam, the whole process of the average velocity of the axially moving structure along the axis, the amplitude of the disturbance tension and the change of the viscoelastic coefficient is simulated. It provides a numerical theoretical basis for the study of the nonlinear dynamic behavior of axially moving beams under time delay.Through the research in this article, the introduction of time delay is studied, and the time delay is used to analyze the axial force that changes along the radial direction of the beam caused by the speed pulsation, and the theoretical framework for nonlinear vibration analysis of the axially moving viscoelastic beam is constructed to expand the time delay. The application scope of the nonlinear vibration theory and nonlinear dynamics theory, the development and improvement of the approximate analysis and numerical solution of the nonlinear continuum (especially the gyro body) under the action of time delay, to provide a theoretical basis for the analysis and design of the corresponding engineering system and technical reserves.