Displacement Coordinates Research Articles

Approximation method for yielding support analysis in high ground stress soft surrounding rock tunnels.

In solving the whole process of interaction between soft rock and yielding support in high-stress environments in tunnels using mechanical analysis methods, it is challenging to simultaneously satisfy both displacement coordination and static equilibrium at the contact surface between the rock and the support structure. This paper, based on the mechanical analysis of rock and rigid support, considers the impact of the circumferential installation of yielding elements on radial displacement, and proposes displacement approximation and support force approximation methods using displacement coordination and static equilibrium as approximation conditions. The study fits curves of numerical simulation results and laboratory test results of yielding elements, and attempts to directly use the laboratory test data set of yielding elements as computational data. By calculating two circular tunnel examples and comparing the effects of the trisection method, bisection method, and substitution method on the convergence of the displacement approximation method, the effectiveness of the methods proposed in this paper is verified. The research results show that the two approximation algorithms proposed in this paper have good accuracy and reliability in calculating the relative displacement of rock and yielding support structure contact surfaces, and the support force of yielding support. The bisection method outperforms the trisection and substitution methods in terms of stability and convergence. However, there are certain limitations in this study, such as the effectiveness of the algorithm may be influenced by geological conditions; the complexity of actual geological conditions may exceed the assumptions of the current rock-support mechanical analysis model.

A formally exact theory to construct nonreactive forcefields using linear regression to optimize bonded parameters.

This article derives theoretical foundations of force field functional theory (FFFT). FFFT studies topics related to the functional representation of nonreactive forcefields to achieve various desirable properties such as: (a) formal exactness of the forcefield's energy functional under certain conditions, (b) a formally exact ansatz separating the bonded potential energy from the nonbonded potential energy within a bonded cluster in a way that enables bonded parameters to be optimized using linear regression instead of requiring nonlinear regression, (c) the potential energy's continuous differentiability to various orders with respect to energetically accessible internal coordinate displacements within a subdomain defined by one electronic ground state, (d) forcefield design that guarantees the reference ground-state geometry is exactly reproduced as an equilibrium structure on the forcefield's potential energy landscape, (e) reasonably accurate and broadly applicable frugal model potentials, (f) computationally efficient embedded feature selection that identifies and removes unimportant forcefield terms, (g) well-designed methods to parameterize the forcefield from quantum-mechanically-computed and (optionally) experimental reference data, and (h) forcefields that approximately reproduce experimentally-measured properties. This article also introduces: (1) an angle-bending model potential that more accurately describes physical dynamics and is continuously differentiable to all orders with respect to internal coordinate displacements even when the bond angle is linear (i.e., θ = π (180°)) and (2) a first-principles-derived stretch potential that accurately describes short-range Pauli repulsion and the long-range bond dissociation energy. This new angle-bending potential gave good agreement to CCSD quantum-chemistry calculations for CaH2, CO2, H2O, HNO, Li2O, NO2, NS2, SF2, SiH2, and SO2 molecules. This new bond-stretch potential reproduced the first 12+ and 30+ vibrational energy levels of H2 and O2 molecules, respectively, within a few percent of experimental values. Studying the C-F bond stretch in C6F6 as an example, the new ansatz (item (b) above) reduced sensitivity of the optimized force constant's value to choice of nonbonded interaction parameters by an order of magnitude compared to the old ansatz. Normal mode analysis of optimized flexibility models for CO2, H2O, HNO, and SO2 molecules yielded vibrational transition frequencies within a few percent of experimental values. These results demonstrate advantages of this new approach.

Dynamic modeling and analysis of the rotor–stator coupling system of a coaxial contra-rotating gearbox

In this paper, a main gearbox using an encased differential gear train to achieve coaxial contra-rotating is considered, and a dynamic modeling method of the rotor–stator coupling system of the gearbox based on box model updating is introduced. The transverse torsional dynamic model of the gear transmission subsystem is established based on the lumped parameter method. The finite element model of the box is updated according to the modal test data, and the reduced dynamic parameters of the box are obtained. According to the displacement coordination condition, the dynamic model of the rotor–stator system of the gearbox is established. The vibration response of the transmission components with or without the coupling box is calculated by numerical integration, and the response of the box caused by the dynamic support reaction force is analyzed by the finite element method. The results show that the vibration peak and fluctuation range of the transmission parts with coupling box are smaller than those without coupling box. The box response at the support of the input bevel gear pair is large, while that at the support of the output shaft is small.

Failure mode discrimination and theoretical prediction method for unequal span bonded prestressed concrete substructures against progressive collapse

Unequal-span prestressed concrete (USPC) structures have unequal spans on the left and right sides and are configured with prestressed steel strands on both spans. However, research on the progressive collapse resistance of these structures is lacking. The strength of the asymmetry of the USPC structure varies depending on the span ratio and reinforcement configuration, resulting in two distinct failure modes in progressive collapse. A parametric analysis was conducted using finite element software to determine how the resistance to progressive collapse and failure modes of USPC structures under middle column failure are affected by variables such as the span ratio, reinforcement configuration, and proportion of prestressing. Accordingly, a discrimination criterion for determining the failure modes of USPC structures was proposed. A theoretical approach for predicting the ultimate displacement and resistance of the progressive collapse of USPC structures was presented for different failure modes. This theoretical approach proposes an innovative stiffness combination and tension path method to establish displacement coordination and force equilibrium conditions, respectively. The theoretical prediction method was deemed valid after comparing it with finite element simulation results.

Dynamic Response Analysis of Long-Span Bridges under Random Traffic Flow Based on Sieving Method

To overcome the limitations of using time interval division to calculate the bridge impact coefficient (IM), a sieving method has been proposed. This method employs multiple sieves on bridge time–history curve samples to ultimately obtain the bridge impact coefficients. Firstly, CA cellular automata are used to establish different levels of traffic flow fleet models. The random traffic flow–bridge coupling dynamic model is established through wheel–bridge displacement coordination and mechanical coupling relationships based on the theory of modal synthesis. Then, the variation of bridge dynamic time–history curves for different classes of random traffic flow, speed and pavement unevenness parameters are analyzed. The sieving method is applied to screen the extreme points of the dynamic time–history curve of the bridge, enabling the distribution law of the bridge IM to be obtained using the Kolmogorov–Smirnov test (K–S test) and statistical analysis. Finally, the calculated value is then compared with the IM specifications of multiple countries. The results show that the proposed method has high identification accuracy and produces a good inspection effect. The value obtained using the sieving method is slightly larger than the value specified in the US code, 0.33, which is considerably larger than the values specified in other national codes. As pavement conditions deteriorate, the IM of the bridge increases rapidly, especially under Class C and Class D pavement unevenness, which exceed the values specified in various national bridge specifications.

Natural frequency prediction of the 3-RPS parallel manipulator using the substructure synthesis technology

AbstractThis paper proposed an elastodynamic modeling method combined with independent displacement coordinates and substructure synthesis technology. Firstly, the connecting rod was discretized, and the elastodynamic control equation for each element was established. The multipoint constraint element theory, linear algebra, and singularity analysis were used to identify the globally independent displacement coordinates of the manipulator. On this basis, the elastodynamic model using the substructure synthesis for the 3-PRS parallel manipulator (PM) was developed, with its natural frequencies distribution in the regular workspace discussed. The comparison with the finite-element results showed that the maximum error of the first three-order natural frequencies was within 1.03%, which verified the correctness of the analytical model. The proposed elastodynamic model included all the kinematic constraints of the manipulator without increasing the Lagrangian multiplier. The method is computationally efficient and assesses the dynamic behaviors of the mechanism at the predesign phase.

Numerical analysis for isolation of vibrations by pile rows in transversely isotropic saturated media due to moving loads

An analytical layer-element–boundary-element coupling approach is presented to explore the isolation effect of pile rows in stratified transverse isotropic saturated media for moving-load induced vibration. The analytical layer-element basic solution for the soils is derived. The soil flexibility matrices are obtained using boundary integral equations for pile-soil. Then, the pile is modeled as a Bernoulli–Euler beam utilizing the finite difference approach. The dynamic equations for the piles are achieved by considering the pile-soil displacement coordination condition. Finally, to obtain the amplitude reduction ratio, the displacement of an observation point is calculated with and without pile isolation, respectively. The results are in good consistency with the existing solutions. The impacts of the soils’ transverse isotropy, the pile’s size and physical properties on the isolation effect are evaluated using numerical examples. It is observed that when the pile length exceeds a certain value, the increment in the pile length shows no obvious improvement in the vibration isolation effect. A stiffer pile has a greater impact on vibration reduction. The material anisotropy is also an important parameter for the pile isolation problem.

Vibration isolation of row of piles due to moving harmonic loads embedded in the layered isotropic saturated medium

AbstractThis paper develops an analytical layer element‐boundary element coupling method to study the vibration isolation effect of pile rows in multi‐layered isotropic saturated soils subjected to a moving harmonic load. The isotropic saturated soil is represented using an analytical layer‐element solution as a kernel function, and the pile‐soil boundary integral equation is applied to obtain the soil flexibility matrices. The finite difference method is used for the piles modeled as a Bernoulli–Euler beam. The dynamic response equations of the pile rows under a harmonic moving load are achieved by considering pile‐soil displacement coordination condition. Then, the displacements of the observation point with and without the pile effect are calculated, respectively. Several numerical examples are presented to examine the influences of the soils’ stratification characteristics, the pile length, pile spacing, pile‐soil Young's modulus ratio, and the load moving speed on the isolation effect of the pile rows.

INVESTIGATING THE EFFECT OF LABORATORY-INDUCED DISC INJURIES ON THE BIOMECHANICAL BEHAVIOUR OF ISOLATED SPINAL DISC SPECIMENS SUBJECT TO CYCLIC LOADING

Injury of the intervertebral disc (IVD) can occur for many reasons including structural weakness due to disc degeneration. A common disc injury is herniation. A herniated nucleus can compress spinal nerves, causing pain, and nucleus depressurisation changes mechanical behaviour. Many studies have investigated in vitro IVD injuries including endplate fracture, incisions, and nucleotomy. There is, however, a lack of consensus on how the biomechanical behaviour of spinal motion segments is affected. The aim of this study was to induce defined changes to IVDs of spine specimens in vitro and apply 6 degree of freedom testing to evaluate the effect of these changes.Six porcine lumbar spinal motion segments were harvested from organically farmed pigs. Posterior structures were removed to produce isolated spinal disc specimens. Specimens were potted in Wood's metal, ensuring the midplane of the IVD remained horizontal. After potting, specimens were sprayed with 0.9% saline, wrapped in saline-soaked tissue and plastic wrap to prevent dehydration. A 400N axial preload was equilibrated for 30 minutes before testing. Specimens were tested intact and after a partial nucleotomy removing ~0.34g of nuclear material with a curette through an annular incision.Stiffness tests were performed using the University of Bath's custom 6-axis spine simulator with coordinate axes and displacement amplitudes. Tests comprised five cycles with data acquired at 100Hz. Stiffness matrices were evaluated from the last three motion cycles using the linear least squares method.Stiffness matrices for intact and nucleotomy tests were compared. No significant differences in shear, axial or torsional stiffnesses were noted. Nucleotomy caused significantly higher stiffness in lateral bending and flexion-extension with increased linearity and the load-displacement behaviour in these axes displayed no neutral zone (NZ).Induced changes were designed to replicate posterolaterally herniated discs. Unaffected shear, axial and torsional stiffnesses suggest the annulus is crucial in these axes. However, reduced ROM and NZ after nucleotomy suggests bending is most affected by herniation. Increased linearity and lack of defined NZ in these axes demonstrates herniation causes major changes to the viscoelastic behaviour of spine specimens in response to loading.

Dynamic Vibration Absorbing Performance of 5-DoF Magnetically Suspended Momentum Wheel Based on Damping Regulation

The vibration performance is critical to the suspension control and the torque precision of the magnetically suspended momentum flywheel (MSMW). The translational and torsional vibration of the MSMW are investigated in this article, and the damping regulation method is proposed to improve the anti-vibration performance of the MSMW. Firstly, the modellings of the MSMW, including the dynamic models and the displacement coordinate, are developed, and the comprehensive damping characteristics of the MSMW are investigated. Moreover, the transfer functions of the translational and the torsional vibrations are established using the dimensionless model, and the relationship between the dynamic response and the stiffness/damping coefficient is studied. Furthermore, the numerical simulations of the dynamic response of the translational and torsional vibration are conducted. Finally, the experiments are designed to verify the vibration characteristics of the MSMW, and the dynamic displacements are measured to analyze the anti-vibration performance of the proposed damping regulation method. The results indicate that the displacement deflection of the translational vibration is reduced by 68.8%, and the angle deflection of the torsional vibration is mitigated by 71.2% by regulating the damping coefficient.

Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples

AbstractWe study traveling waves in mass and spring dimer Fermi–Pasta–Ulam–Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in relative displacement coordinates. These nanopteron profiles consist of the superposition of an exponentially localized “core,” which is close to a Korteweg–de Vries solitary wave, and a periodic “ripple,” whose amplitude is small beyond all algebraic orders of the long wave parameter, although a zero amplitude is not precluded. Here we deploy techniques of spatial dynamics, inspired by results of Iooss and Kirchgässner, Iooss and James, and Venney and Zimmer, to construct mass and spring dimer nanopterons whose ripples are both exponentially small and also nonvanishing. We first obtain “growing front” traveling waves in the original position coordinates and then pass to relative displacement. To study position, we recast its traveling wave problem as a first‐order equation on an infinite‐dimensional Banach space; then we develop hypotheses that, when met, allow us to reduce such a first‐order problem to one solved by Lombardi. A key part of our analysis is then the passage back from the reduced problem to the original one. Our hypotheses free us from working strictly with lattices but are easily checked for FPUT mass and spring dimers. We also give a detailed exposition and reinterpretation of Lombardi's methods, to illustrate how our hypotheses work in concert with his techniques, and we provide a dialog with prior methods of constructing FPUT nanopterons, to expose similarities and differences with the present approach.

Design of Tunnel Initial Support in Silty Clay Stratum Based on the Convergence-Confinement Method

The stress release ratio of the surrounding rock in tunnel excavation is one of the most important indicators that affect the stress distribution and displacement of the surrounding rock. To determine the variation law of the stress release ratio of the surrounding rock during excavation in silty clay stratum, the stress release law is determined based on the convergence–confinement method (CCM) and field test data. The stress release law of the surrounding rock under support is determined based on the displacement back analysis method. The permitted displacement safety factor of silty clay under different subgrade conditions and the optimal supporting time of the initial supporting structure are determined by comparing the stress release ratio with surrounding rock displacement. The results indicated that the stress release ratio of surrounding rock in the silty clay stratum is approximately 78–90% when the coordinate displacement of the supporting structure and surrounding rock is stable under the current excavation and support conditions. For the surrounding rock of subgrade V in the silty clay stratum, the safety factor of the permitted displacement in the tunnel vault is approximately 2.91, and the initial support should be carried out within 1 m behind the face advancing. For the surrounding rock of subgrade VI1, the safety factor of the permitted displacement is 1.40, and the initial support must be carried out 1 m ahead of the tunnel face. For the surrounding rock of grade VI2, the initial support must be carried out 4 m ahead of the tunnel face.

An Integrated 5-DoF Displacement Sensor System of Magnetically Suspended Flywheel

The displacement measurement of the magnetically suspended flywheel (MSFW) on five degrees of freedom (DoFs) is critical to the accurate position control of the flywheel rotor. Therefore, an integrated 5-DoF displacement sensor is designed to measure the dynamic displacements of the MSFW. Firstly, the detection surfaces of the MSFW on five DoFs are introduced, and the displacement coordinates are established. Moreover, the detection principle and the dynamic responses of the integrated 5-DoF displacement sensor are analyzed. The single-winding probe is used as the radial displacement sensor, and the series-connection dual-winding probe is applied in the axial displacement sensor to measure the large displacement variation. Furthermore, the magnetic intensity and the quality factor of the integrated 5-DoF displacement sensor are simulated and tested. Finally, the measurements of the translational displacements and the deflection angles are conducted. The results show that the linear ranges of the radial single-winding probe and the axial series-connection dual-winding probe are 1.3 mm and 2.4 mm, respectively. The frequency bandwidth could be 10 kHz, and the maximum temperature drift is only 3.87%.

Effect of abutment tooth location on the accuracy of digital impressions obtained using an intraoral scanner for removable partial dentures.

To verify the effect of abutment tooth location on the accuracy of digital impressions obtained using an intraoral scanner (IOS) for removable partial dentures (RPDs). The target abutment teeth included the left first premolar (#34), second molar (#37), and right second premolar (#45) in a mandibular Kennedy class II model and the left and right second molars (#37, #47) in a class III model. Only #37 was isolated from the remaining teeth by the mucosal area in both models. Digital impressions were obtained using a desktop scanner (reference data) and an IOS (IOS data; scanning origin #37; n=10). The general trueness based on the entire model superimposition (TG), local trueness (TL) of an individual tooth, and dimensional accuracy (coordinate and linear accuracy) of the IOS data of the target abutment teeth were compared (α=0.05). In both models, #37 showed significantly inferior TG (P<0.01), superior TL (P<0.01), and mesial coordinate displacement (P<0.01 and P<0.05 in class II and III models, respectively). Intra-model comparisons showed that #45 in the class II model and #47 in the class III model had significantly inferior linear accuracy (P<0.05 and P<0.01, respectively) and buccal coordinate displacement (P<0.05 and P<0.01, respectively) compared with the other target teeth. In digital impressions of RPDs, isolation of abutment teeth by mucosal areas can reduce general trueness based on the entire dental arch and mesial tooth displacement, whereas increased distance from the scanning origin can adversely affect local trueness and dimensional accuracy.

Analysis of Inherent Characteristics of Two‐Speed Planetary Gear Transmission System

In the helicopter transmission system, because the two‐speed gear planetary transmission system without power interruption adopts the design of a double planetary gear system, the complexity of the structure leads to the time‐varying meshing stiffness, tooth surface friction and the interaction between components and other nonlinear factors are uncontrollable, and causes the helicopter transmission system vibration noise, unstable operation, and other problems. To solve the above problems, the inherent characteristics of the two‐speed planetary gear transmission system without power interruption were studied and analyzed to find out the influence law of its inherent characteristics. The inherent characteristics of a planetary gear drive system are mainly related to the integrated stiffness such as component mass, support stiffness, and meshing stiffness in the system. Based on the centralized mass method, the translation‐torsional coupling dynamics model of the double planetary gear drive system was established. According to the displacement coordination relationship between the components of the system, the dynamics equation of the double planetary gear drive system was constructed. The mass matrix and stiffness matrix were obtained using MATLAB, and the system’s natural frequency was obtained by solving the dynamics equation. The results show that the low‐order natural frequency is mainly the torsional vibration mode of the center component and the torsional vibration mode of the center component. The influence of the mass of the component on the natural frequency is more complex and has a certain influence on both the high‐ and low‐order natural frequency. The support stiffness in the system mainly affects the low‐order natural frequency and the meshing stiffness in the system mainly affects the high‐order natural frequency.

Магнитная система одноосного инерционного магнитожидкостного акселерометра

Today, a physical problem of engineering design of inertial magnetic fluid accelerometers to measure dynamic processes is relevant. The main drawback of modern sensors is the nonlinear characteristic of the forced response, which limits the application area of the sensors to the case of quasi-static action (tilt angle sensor). The reason of nonlinearity is the design of the magneto-mechanical system of the elastic suspension of the inertial mass made in the form of a pair of permanent ring magnets. This drawback can be eliminated by designing an axisymmetric electromagnetic system that generates a magnetic field with a linear intensity gradient along the symmetry axis. Thus, the paper is devoted to this problem and experimental approvement of the results on a laboratory sensor prototype. The Monte Carlo algorithm is used to calculate electromagnetic system containing permanent magnets and magnetizing coils. The algorithm is implemented using the C++ programming language. Measurements of the most important parameters of the magnetic field from the point of view of the purpose of the study are carried out on the assembled model of the electromagnetic system of the accelerometer. The calculation of electromagnetic system that generate permanent magnetic field with linear intensity gradient along the symmetry axis is carried out. The applicability of the Monte Carlo method to solve similar engineering problems is shown. The measurements of the magnetic field strength of a given configuration have been made. The force of the magnetic field acting on the test sensitive element with a constant magnetic moment is measured. A comparison of the calculated magnetic field with the field of a real system is carried out. It shows satisfactory agreement between the calculated data and the real ones. A linear dependence of the restoring force on the displacement coordinate of a body with a constant magnetic moment from the equilibrium position is shown. The linearization of the response of the mechanical part of the magnetic fluid accelerometer is achieved by choosing the desired configuration of its electromagnetic system, which allows making reliable measurements of both static and dynamic quantities.

An improved stacking filtering for extracting the common-mode errors on GNSS coordinate time series in Shanxi

The presence of common mode error (CME) in the coordinate displacement time series of the Global Navigation Satellite System (GNSS) affects geophysical studies using GNSS observations. In order to investigate the effect of CME on the time series in GNSS networks in Shanxi, this paper proposes an improved superposition filtering method by introducing single-day solution accuracy, correlation coefficient, and spherical distance between stations as weights. The filtering effect is evaluated using the GNSS data in Shanxi. By using the improved stacking filtering method, the root mean square (RMS) values for N, E, U are reduced by approximately 27.8%, 29.0%, and 46.0%, respectively. And compared to the traditional stacking filter, our improved method can achieve better results with CME extraction. We investigate the CME spatial-temporal characteristics and its relationship with environmental loading. The results show that the CME between stations decreases as the distance between stations increases. In addition, we analyze the effect of CME on the noise component and velocity estimates. Results show that removing the CME refines the velocity and leads to a significant reduction in the magnitude of noise, indicating that the CME is dominated by the flicker noise in Shanxi Province.

Dynamic performance-based assessment for tied-arch bridges subjected to heavy multi-axial tractor-trailers

With rapid industrial development, the overloading of bridges caused by heavy multi-axle vehicles has become a critical problem worldwide. This work conducts a performance-based evaluation for tied-arch bridges subjected to heavy multi-axle vehicles, and a prediction function of the dynamic impact factor (DIF) for tied-arch bridges is proposed considering the bridge frequency, vehicle speeds, and road quality level. Specifically, the main parameters affecting the bridge response were first identified theoretically using a simplified multi-axle vehicle-bridge model. A tractor-trailer mechanical model and a tied-arch bridge model were subsequently constructed and coupled using displacement coordination conditions to explore the characteristics of the bridge response under heavy multi-axle tractor-trailers. Additionally, based on the identified factors, a detailed investigation of DIF was performed using the developed special vehicle-bridge interaction model. Finally, a suggested computational method for predicting DIF of tied-arch bridges was proposed. The results obtained indicate the impact effect of special tractor-trailers on bridges should not be ignored, even at low operating speeds and in good road conditions. Moreover, additional monitoring measures should be placed on the structural components that are sensitive to dynamic responses to regulate responses within an acceptable range.

Discrete element method investigation of shear behaviour of 3D geogrid–sand interface

Interface shear characteristics have an important impact on the stability of geosynthetically reinforced soil structures. The shear characteristics of three-dimensional (3D) geogrid–sand interfaces were investigated using large-scale direct shear tests and the discrete element method (DEM). Geogrids were manufactured by 3D printing. The effect of mesh pattern and transverse-rib thickness on the stress–displacement relationship, strength parameters, coordination number and porosity distribution were evaluated. The results showed that the mesh pattern and transverse-rib thickness have an impact on the interface shear characteristics. The peak and residual interface shear strength of the modified geogrid mesh pattern exceeded that of biaxial geogrids. The average coordination numbers of the modified geogrid mesh pattern were greater than those of biaxial geogrids. The variability of particle compactness, as characterised by the porosity distribution, shows how the modified mesh pattern increases the interface shear strength. The interface shear strength of the geogrid–sand interface was improved by thickening the transverse ribs of the modified geogrid mesh pattern.

A dynamic stiffness formulation for the vibration analysis of rotating cross-ply laminated coupled conical–cylindrical–conical shells

In this paper, a dynamic stiffness formulation is reported to analyze the free vibration characteristics of a rotating cross-ply laminated coupled conical–cylindrical–conical shell. In order to ensure the stability of the numerical results, the whole system is firstly divided into substructures, and each substructure is divided into several segments. The theoretical formulation of the rotating shell segment is derived by the first-order shear deformation theory and Hamilton’s principle. The effects of centrifugal force and Coriolis acceleration on the initial hoop tension are considered in the formulation. The dynamic stiffness matrix of the shell segment is derived from the relationship between the state vector and its derivative, where the state vector consists of the resultant force and displacement components of the shell segment. The dynamic stiffness matrix of the whole system is assembled by the displacement coordination relationship. After the number of segments is determined by the convergence analysis, it is compared with the results of the existing literature and finite element software to ensure the accuracy of the dynamic stiffness formulation. Based on this, the effects of rotational speed, geometry and boundary conditions on the structure are studied.