Mistuning parameter identification and vibration localization analysis of the integration rotor

This paper deals with the coupling vibration characteristic of the disk-blade-shaft integration rotor. First, a reduced-order model (ROM) based on an improved hybrid interface component mode synthesis method (IHISCMSM) is carried out, which takes the prestress effect into account. The frequency of the disk-blade-shaft integration rotor at different rotating speeds are calculated and the influence of selecting different mode truncation numbers is investigated. In order to quantitatively evaluate the coupling degree of blade and disk, the coupling factor is defined from the perspective of strain energy, and the influence of prestress on system’s dynamic is discussed. Then, an experimental modal analysis is performed on blades to identify the mistuning parameters, and the mode localization of the disk-blade-shaft integration rotor is analyzed with and without blade mistuning. The results indicate that there are several types of coupling modes among blade, disk and shaft of the integration rotor. After considering the prestress, the frequency increases, and the axial coupling vibration degree and radial coupling vibration degree of the integration rotor change. The mode localization of mistuned rotor is more likely to occur in the modes dominated by mistuning stage blades. There also exists a subtle mode localization phenomenon for tuned integration rotor.

Investigating the influence of connecting constraint properties and modeling parameters on vehicle dynamic responses

This paper presents a detailed investigation about the effect of structural damping and modal truncation number on vehicle dynamic characteristics. Finite element method and experimental method are applied to research vehicle’s dynamic response. According to the real vehicle’s structure, the dynamic simulation model of vehicle is established by the substructure modeling method. In order to research the influence of different variables on vehicle’s dynamic responses, the control variable method is adopted. In other words, the parameters of structural damping and mode truncation number are changed respectively. Comparing the dynamic response results, the influence rules of structural damping and mode truncation number on dynamic responses are obtained. Results show that the dynamic responses of vehicle changes significantly with the change of structural damping and mode truncation number. The studying results provide important significance for the determination of parameters. As well as, the correctness and reliability of the analysis results are verified by the experimental method.

On (Non) Applicability of a Mode-Truncation of a Damped Traveling String

This study investigates a linear homogeneous initial-boundary value problem for a traveling string under linear viscous damping. The string is assumed to be traveling with constant speed, while it is fixed at both ends. Physically, this problem represents the vertical (lateral) vibrations of damped axially moving materials. The axial belt speed is taken to be positive, constant and small in comparison with a wave speed, and the damping is also considered relatively small. A two timescale perturbation method together with the characteristic coordinate’s method will be employed to establish the approximate analytic solutions. The damped amplitude-response of the system will be computed under specific initial conditions. The obtained results are compared with the finite difference numerical technique for justification. It turned out that the introduced damping has a significant effect on the amplitude-response. Additionally, it is proven that the mode-truncation is applicable for the damped axially traveling string system on a timescale of order ε -1

Dynamic Analysis of an Offshore Platform With Compressor Packages—Application of the Substructure Method

This paper presents the substructure-based dynamic analysis of an offshore platform with compressor packages. Three typical substructure methods, the Guyan condensation method, the fixed-interface component mode synthesis (CMS) method and the free-interface CMS method, were compared to identify the appropriate substructure method for this application. A mode truncation criterion was proposed to ensure the accuracy of the recommended substructure method. The results indicated that the free-interface CMS method could generate almost the same results as the fully coupled method and save more than 50% in calculation time and more than 60% in storage space. When the same amount of time was used, the free-interface CMS method obtained more accurate results than the fixed-interface CMS method and Guyan condensation method; thus, the use of this method for evaluating the dynamics of an offshore platform with compressor packages was recommended. The cutoff frequency of the substructure was suggested to be 1.25 times the highest frequency of interest when conducting a dynamic analysis of an offshore platform with compressor packages using the free-interface CMS method. In addition, the offshore platform is a flexible structure with low and dense mechanical natural frequencies (MNFs), with approximately 4500 orders vibration modes in the frequency range of 0–40 Hz, and the displacement response at the area around the compressor package exceeded the allowable value under the excitation of the compressor package.

Multi-Mode Pushover Procedure to Estimate Higher Modes Effects on Seismic Inelastic Response of Steel Moment-Resisting Frames

The paper deals with a multi-mode pushover procedure that considers higher mode effects, frequency content of response spectra as well as nonlinear interaction between modes. Pushover analyses are conducted with story-specific generalized force vectors. Each force vector is calculated through modal analysis and builds up the instantaneous distribution of forces acting on the structure when the interstory drift at each story attains its maximum value during the seismic motion. In order to improve the computational cost effectiveness, both mode truncation and limitation in the number of generalized pushovers are used by checking, however, the accuracy in the evaluation of the interstory drifts at all levels. The target interstory drift is calculated through three different modal combination procedures.

On non-local energy transfer via zonal flow in the Dimits shift

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

The coupled effect of bearing misalignment and friction on vibration characteristics of a propulsion shafting system

The propulsion shafting system of ships is usually supported, in part, by water-lubricated rubber bearings, which often work at mixed or boundary lubrication state under heavy-load and low-speed conditions, resulting in strong friction on the bearing–shaft interface and even abnormal vibration in the overall system. In addition, bearing misalignment can further affect the distribution of friction and consequently change the lateral and torsional vibration characteristics of the shafting system. In this work, the rubber bearing was simplified into parallel-distributed springs and the water film was neglected. The dynamic model of the propulsion shafting system was built with the finite element method and reduced by mode truncation. The coupled effect of bearing misalignment and friction was subsequently analyzed with this reduced model and the fourth-order Runge–Kutta method. Finally, lateral and torsional vibration characteristics of the overall system under different bearing misalignment were obtained, which can be used in the identification or diagnosis of abnormal vibration induced by friction.