Yongfeng Wang, Yanhong Ma, Jie Hong, G. Battiato, C. M. Firrone
{"title":"Influence of the Contact Interfaces on the Dynamics and Power Flow Behavior of the Bolted Structure","authors":"Yongfeng Wang, Yanhong Ma, Jie Hong, G. Battiato, C. M. Firrone","doi":"10.1115/gt2022-82840","DOIUrl":"https://doi.org/10.1115/gt2022-82840","url":null,"abstract":"\u0000 Bolted joints are widely used for the assembly of mechanical components to provide continuity of the structure and transfer internal actions (i.e. forces and moments) from one member to another. Contact and dry friction at the jointed interface have a great influence on the dynamical performance of the assembly, especially for light-weight and heavy-loaded structures, such as the aero-engine.\u0000 In this paper, the nonlinear dynamic response of a turbo-engine casing in the presence of bolted flanges is studied, using one reduced order model of an elementary casing sector with means of node-to-node contact elements. while the vibration power flow method for the structural system with frictional interfaces is proposed, to reveal effects of energy dissipation at contact interfaces. It concluded that, the resonance frequencies and vibration responses of the bolted structures are influenced by the interfacial contact state, and the damping induced at the slipping contact area surrounding the bolt decreased the vibration response. Power flow through the bolted structure are visualized, which clarified the energy dissipation at the bolted interfaces.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134286115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Digital Replicas of Low Pressure Steam Turbine Moving Blades - Assessment of Geometrical and Mechanical Quality Requirements Using Roboter-Assisted Optical Scanning","authors":"F. Popig","doi":"10.1115/gt2022-80464","DOIUrl":"https://doi.org/10.1115/gt2022-80464","url":null,"abstract":"\u0000 Steam turbines are primarily used as direct drives for generator applications to produce electrical power for regional grids. To ensure the safe operation of the steam turbine during the entire lifetime it is important to minimize the unbalance of the rotor and to avoid blade vibrations at operational speed. One measure to minimize the unbalance is the specification of an assembling order of the last stage moving blade row. The required mass and center of gravity of each blade are experimentally determined during the final inspection process. The avoidance of last stage blade vibrations at fixed rotational operating speeds is achieved by designing the freestanding last stages moving blades to be free of resonances in a specific speed range. Nevertheless, the disadvantages of freestanding blades are the increased sensitivity to both the occurrence of flutter and forced response limitation in terms of mode localization and amplitude magnification of single blades due to mistuning effects. Those disadvantages as well as the requirement that no resonances shall occur in a specific speed range lead to quality requirements that define the blades’ eigenfrequencies and the blade row’s mistuning pattern at standstill. The blade eigenfrequencies are experimentally determined during the final inspection process via modal testing with an impact hammer in a test bench facility.\u0000 Besides the mechanical requirements the manufactured blades have to fulfill geometrical requirements. For this purpose, geometrical features and parameters of the blades as manufactured are inspected and have to be within the defined geometrical tolerances. Commonly geometrical features are inspected at local inspection sections regarding the blade’s root and airfoil using a coordinate measurement machine. An alternative approach is an optical measurement that enables the digitalization of manufactured 3D parts and the inspection of geometrical features based on digital replicas. Furthermore, the digital replicas can be used to calculate the blades’ eigenfrequencies as well as mass and center of gravity.\u0000 The presented paper addresses the final inspection of geometrical features and parameters as well as mechanical properties of last stage moving blades based on roboter-assisted optical scanning. The measurements are performed using an automated roboter-assisted scanning approach with a newly developed modular reference frame and a high-speed optical scanning system. On the one hand the blade airfoil geometrical inspection based on the obtained geometrical replica is compared to the corresponding CMM-measurements. On the other hand, the optical measurements are used to determine the blades’ eigen-frequencies, mass and center of gravity numerically via Finite Element Analyses. Therefore, an approach is presented that uses a mesh-morphing algorithm to adapt the FE-mesh of the dis-cretized nominal CAD geometry by means of deviations between the optical scan data and nominal designed CA","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127188875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Study on the Vibration Characteristics of Bladed Disks With Damping Mistuning","authors":"Y. Kaneko, Toshio Watanabe, T. Furukawa","doi":"10.1115/gt2022-79644","DOIUrl":"https://doi.org/10.1115/gt2022-79644","url":null,"abstract":"\u0000 Bladed disks with slight blade variations are referred to as a mistuned system. Many researchers have suggested that while mistuning induces an undesirable effect on the forced response, it provides a beneficial (stabilizing) effect on the blade flutter (self-excited vibration). However, almost all studies have focused on the deviation in the blade frequency, and few studies have investigated damping mistuning. In a blisk (integrally manufactured bladed disk), damping mistuning appears to be negligible because material damping is dominant and its deviation is small. However, in a bladed disk where the blade root is inserted into the disk groove, damping mistuning caused by partial contact between the root and groove during rotation cannot be neglected in predicting the resonant response of a bladed disk. Some works suggest that the structural damping of a root-type bladed disk measured using the half-power method during rotation tests largely fluctuates in each individual blade. Damping mistuning may also affect the stability of the blade flutter. Therefore, in predicting the stability of a blade flutter, the effect of damping and frequency mistuning should be considered. From these backgrounds, in the current study, by incorporating the damping mistuning into a reduced-order model, namely, fundamental mistuning model, frequency response and stability analyses of bladed disks are systematically performed. From the calculated results, the effect of damping mistuning on the forced and self-excited vibrations of bladed disks is clarified. In addition, although the authors proposed a simultaneous optimization method for mistuned bladed disks for forced vibration and amount of unbalance in a previous work, damping mistuning was not considered. In the present study, the robustness of an optimal mistuned system for damping mistuning is also evaluated.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126804173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhiqiang Meng, S. Krishnababu, S. Jackson, B. Sjödin
{"title":"Probabilistic Assessment of Gas Turbine Compressor Blade HCF Life","authors":"Zhiqiang Meng, S. Krishnababu, S. Jackson, B. Sjödin","doi":"10.1115/gt2022-82323","DOIUrl":"https://doi.org/10.1115/gt2022-82323","url":null,"abstract":"\u0000 This paper uses a novel and practical probabilistic approach to assess the risk of a compressor blade HCF failure in the gas turbine. For a specific design case, the tip timing tests for a newly designed gas turbine compressor blade successfully passed HCF design criteria during engine operation when operated over a wide speed range. However, on a later test high amplitude responses were seen under a VGV configuration which was different from that used during normal operation.\u0000 Firstly, the gas turbine operational data and blade bench test data are used by the probabilistic assessment to identify the characteristics of the HCF problem. The resonance counting is carried out by the Monte Carlo simulations. The simulation indicates that the HCF endurance limit for the alternating stress is required to be satisfied for this blade.\u0000 Secondly, the material test data, blade tip timing data and finite element (FE) results are used to build a HCF endurance stress probabilistic model, following which the probability of blade HCF failure was estimated. The Monte Carlo simulations are used for the probabilistic model. The simulation results show that the probability of HCF failure per blade and the risk of HCF failure for any blade of the stage are very small and acceptable.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132061458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anindya Bhaduri, Jing Li, Sayan Ghosh, Liping Wang
{"title":"Efficient Surrogate Modeling for Turbine Blade Row Cyclic Symmetric Mode Shapes","authors":"Anindya Bhaduri, Jing Li, Sayan Ghosh, Liping Wang","doi":"10.1115/gt2022-83414","DOIUrl":"https://doi.org/10.1115/gt2022-83414","url":null,"abstract":"\u0000 In this study, we consider the Modal Cyclic Symmetric (MCS) analysis to generate the modal frequencies and mode shapes of a tip-shrouded turbine blade row. In total 87 input parameters are considered here that define the geometry of the turbine blades. The objective here is to build an efficient surrogate model which maps these input parameters to the mode shapes. The main challenge is the high dimensionality of a complex mode shape at a mesh resolution of industrial standard which is almost of the order of O(107). Thus, the idea here is to efficiently reduce the high dimensional output into a lower dimensional representation using the unsupervised deep learning architecture called the Convolutional Variational AutoEncoder (CVAE). The CVAE model helps in performing efficient surrogate model building using GE’s Bayesian Hybrid Model (BHM) in a lower dimensional output space as well as produce feasible mode shapes for new geometries after training.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122404651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Active Rotor Controller Design for Vibration and Bend Mitigation Utilizing Active Magnetic Bearings and Internal Shaft Actuation","authors":"Gauthier A. Fieux, N. Bailey, P. Keogh","doi":"10.1115/gt2022-82528","DOIUrl":"https://doi.org/10.1115/gt2022-82528","url":null,"abstract":"\u0000 Strategies are required to reduce vibrations in machines that use rotor systems, as these disturbances reduce the life and quality of the machine. A novel low-frequency on-board counter-bend actuator topology has been designed in order to control high frequency vibrations by taking advantage of synchronous forces from the rotating frame of a rotor supported by Active Magnetic Bearings (AMBs). The AMBs ensure in return stable contact-free levitation of the rotor. A complete model of the rotor system is established, based on a finite element representation of the rotor. The feedback control forces of the AMBs are described to account for the non-collocation of the sensor and actuation, and the PD controller gains are chosen using the sensitivity function. The lowest frequency mode of the operating range is located at 2,700 RPM, and time domain analysis shows that the application of symmetric 80 N.m counter-bend moments on the rotor coupling flanges can reduce the vibration amplitude by 88% at this rotation speed.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122673471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mistuning and Damping of a Radial Turbine Wheel. Part 2: Implementation and Validation of Intentional Mistuning","authors":"Alexander Nakos, B. Beirow, Arthur Zobel","doi":"10.1115/gt2022-80643","DOIUrl":"https://doi.org/10.1115/gt2022-80643","url":null,"abstract":"\u0000 A radial turbine impeller of an exhaust turbocharger is analyzed in view of both free vibration and forced response. Due to random blade mistuning resulting from unavoidable inaccuracies in manufacture or material inhomogeneities, localized modes of vibration may arise, which involve the risk of severely magnified blade displacements and inadmissibly high stress levels compared to the tuned counterpart. Contrary, the use of intentional mistuning (IM) has proved to be an efficient measure to mitigate the forced response.\u0000 In part 1 of this three-part paper fundamental analyses have been carried out to find a suitable intentional mistuning pattern featuring only two different blade designs [1]. This part is focused on the implementation and validation of the intentional mistuning pattern and discusses the detailed geometric adaption of the turbine wheel hardware. The final design of the geometric adaption is developed in terms of manufacturability and efficiency so that a reliable and robust solution is presented. Its machined adaption is validated by both vibration testing at rest and optical measurements so that manufacturing deviations are detected and their impacts discussed and evaluated. Reduced order models are built up for checking the effect of the implemented intentional mistuning pattern on the forced response by using the subset of nominal system modes (SNM) approach introduced by Yang and Griffin [2], which conveniently allows for accounting both the design intention of the mistuning pattern and the actually machined implementation due to manufacturing deviations.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122217525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fengguang Xiang, Xi Chen, Bo Zhang, G. Ren, Xiaohua Gan
{"title":"Simulation Method of Rotor Dynamic Characteristics Considering Temperature Distribution and Aerodynamic Load","authors":"Fengguang Xiang, Xi Chen, Bo Zhang, G. Ren, Xiaohua Gan","doi":"10.1115/gt2022-82417","DOIUrl":"https://doi.org/10.1115/gt2022-82417","url":null,"abstract":"\u0000 When operating in a high-temperature and high-pressure environment, the high-speed rotor systems of aero-engines are inevitably subjected to thermal and aerodynamic loads. However, conventional simulations and experiments of rotor dynamics did not consider temperature distribution and aerodynamic load. Therefore, it’s necessary to investigate the influence mechanism of temperature distribution and aerodynamic loads on rotor dynamics.\u0000 Using polynomial function fitting for the continuously various parameters in elements, combined with the temperature distribution, the axial distribution of physical parameters in shaft elements was established. The stiffness coefficient matrix considering temperature load was derived based on Timoshenko beam theory. By introducing the tension (compression) potential energy, the additional stiffness coefficient matrix was derived from Lagrange equation. Using state-space vector method, the differential equations of motion for rotor-support system were solved, and dynamic characteristics of rotor system subjected to temperature distribution and aerodynamic force were analyzed. The simulation method was verified with a typical fan rotor under the maximum operating condition.\u0000 The results indicate that the rotor dynamic behavior is more sensitive to temperature distribution than aerodynamic load when operating in the temperature range of 40∼190°C. And the decrease of first two critical speeds is mainly caused by thermal load. Due to the relatively low temperature, the first-order critical speed of fan rotor considering the additional load is reduced slightly, while the second-order one is decreased by 3.42%. When a mass unbalance of 500 g·mm is located at the first disk, the resonant amplitude of unbalance response rises slightly (0.25%) with additional load. If such amount of unbalance is located at the third disk, the peak amplitude is increased by 1.28%. In addition, such a simulation method could be extended to core engines or even dual- or triple-rotor engines with higher temperature and aerodynamic load, where the dynamic characteristics and unbalance responses are expected to be significantly affected.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132094916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rotordynamic Design and Experimental Validation of a sCO2 Centrifugal Compressor Equipped With a Pocket Damper Seal","authors":"G. Vannini, Matteo Dozzini, Filippo Cangioli","doi":"10.1115/gt2022-79563","DOIUrl":"https://doi.org/10.1115/gt2022-79563","url":null,"abstract":"\u0000 Supercritical carbon dioxide (sCO2) is the fluid medium for those novel thermodynamic cycles aiming to produce electric power at a reduced environmental impact. CO2 at supercritical conditions is still in the gas phase but very close to the liquid-gas transition, it is a dense fluid allowing to design more compact size turbomachinery delivering same power. The centrifugal compressor which shall be employed into this thermodynamic cycle is supposed managing sCO2 at suction (79.8bar, 33°C). The Authors’ Company has been working in a EU project called sCO2Flex (H2020 founded program, grant agreement #764690) with the aim to design and test a 5MW prototype which has been finally tested at full density and full load in a dedicated test loop at the Authors’ premises.\u0000 Main subject of this paper is the prototype rotordynamic design with a special focus on the balance piston seal design. Since the compressor is operating at very high density (600kg/m3 at suction and 800kg/m3 at delivery) the stability aspect is the main concern and seal design is very critical. During the design phase a trade-off between alternative damper seals was performed and a Pocket Damper Seal (PDS) was selected. PDS showed more stability with respect to honeycomb seal, together with a lower stiffness level. PDS predictions are considered reliable enough since they are based on a proprietary numerical code which has been calibrated on high pressure experimental data, nevertheless, the very high-density level of the current application requires an experimental validation. PDS was also selected due to the good performance shown in managing liquid phase (as experienced previously by authors) which might be present in the balance piston seal during transient operation close to the supercritical conditions.\u0000 From rotordynamic viewpoint the test was conducted through steps: at the beginning a mechanical running test with nitrogen at 10bara was performed to assess the vibration behaviour of rotor running on journal bearings. After that the CO2 test started, the pressure level was increased by steps and the main compressor operating parameters were continuously monitored. The vibration behaviour during machine startup/shutdown showed a very damped response with no indications of any critical speed. When compressor was running at steady speed the vibration spectrum showed only the synchronous component and relevant minor harmonics. The whole compressor operating curve was explored, from choke to near surge conditions, and no major subsynchronous vibrations was detected. At the same time high frequency vibration data were recorded and postprocessed through OMA approach: no mode was identified due to the very high damping level.\u0000 The test campaign finally confirmed all the positive design indications for the PDS technology application in sCO2 service.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133307589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Experimental Investigation of Three-Dimensional Shroud Contact Forces in Forced-Vibration Testing of a Shrouded Blade","authors":"Rizwan Ahmed, C. M. Firrone, S. Zucca","doi":"10.1115/gt2022-84205","DOIUrl":"https://doi.org/10.1115/gt2022-84205","url":null,"abstract":"\u0000 Low Pressure Turbine (LPT) blades encounter highly stressed forced vibrations driven by centrifugal force and steady/unsteady aerodynamic loads. To prevent the blades from failure due to high cycle fatigue (HCF), the amplitude of these vibrations must be estimated and reduced. Friction damping devices like under-platform dampers, shrouds and snubbers are usually implemented to lessen these blade vibration amplitudes. For adjacent shrouded blades coupled to each other at the blade tips, the blade vibration levels are strongly affected by the three-dimensional periodic contact forces at shrouds resulting in energy dissipation due to friction. Therefore, to experimentally validate the numerical contact models that predict nonlinear forced response of shrouded blades, it is equally important to measure the contact forces acting at the shrouds.\u0000 This study outlines the development and commissioning of an experimental test rig that allows the measurement of three-dimensional shroud contact forces and the forced response of the shrouded blade simultaneously. Firstly, the design requirements of the experimental setup that were considered while deciding the test rig components, are highlighted. The test rig comprises of a pair of tri-directional contact force transducers in contact with the two shroud ends of a dummy blade and includes a blade twisting mechanism for the application of the normal preload. The employed tri-directional contact force transducers consist of three uniaxial strain gauge-based force sensors, arranged in a tripod configuration, and attached to a reference block that accommodates the shroud. The calibration and the decoupling procedure of the tri-directional contact force measurement system is then briefly described. This is followed by the details of the experimental process to acquire the forced response and three-dimensional shroud contact forces simultaneously for a specified frequency range determined by a prior experimental modal analysis of the blade and test rig. Subsequently, the effects of the variation in shroud normal preload and excitation force on measured response and shroud contact forces are also discussed. Finally, the results demonstrate how the proposed experimental test rig provides a thorough understanding of the dynamic response of the shrouded blade and shroud contact forces which will lead to a more reliable experimental validation of simulation tools and its effect on system dynamics.","PeriodicalId":171593,"journal":{"name":"Volume 8B: Structures and Dynamics — Probabilistic Methods; Rotordynamics; Structural Mechanics and Vibration","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129186509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}