Nonlinear dynamical modeling and response analysis of complex structures based on assumed mode weighting

Nonlinear dynamic modeling and model reduction strategy are studied in this paper for a rotating thin cylindrical shell. The nonlinear dynamic model is first established in terms of ordinary differential equations, in which the effects of Coriolis and centrifugal forces are considered, as well as the initial hoop tension due to rotation. This model describes both the in‐plane vibrations and the flexural vibration and reflects the coupling effects of those deformations. Based on this original model, a novel model reduction strategy is proposed to reduce the degrees of freedom by neglecting vibration modes predominated by in‐plane vibrations. Meanwhile, for the reduced‐order model, the in‐plane vibrations’ contributions to the rotating shell’s response are still preserved. To validate the dynamic model and the model reduction strategy, comparisons and simulations are carried out. Subsequently, nonlinear dynamic behaviors are investigated preliminarily by analyzing the rotating cylindrical shell’s amplitude‐frequency responses under different excitation levels.

In this paper, a dynamic subgrid scale (SGS) stress model is proposed by modifying the existing quadratic nonlinear model. Unlike the conventional eddy viscosity models, the nonlinear model suggests an anisotropic tensorial polynomial relation between the SGS stress and the resolved strain rate tensor. Examined in the rotating turbulent channel flow, the previous nonlinear model is found unable to successfully predict the turbulent kinetic energy and the Reynolds shear stress. In the previous nonlinear model, an excessive backward energy transfer from the SGS to the resolved scale is found, so it is removed in the new model to provide sufficient SGS dissipation. The dynamic method is reconsidered, based on the analysis of the transport equation of the resolved Reynolds shear stress. The new dynamic nonlinear model is examined in the rotating turbulent channel flow at Re = 7000 and various rotation numbers (Ro), ranging from 0.0 to 0.6. The new dynamic procedure determines a more proper model coefficient for the nonlinear term, so the modified nonlinear model predicts superior results to the previous nonlinear models. The Vreman's approach of the eddy viscosity is implemented into the nonlinear model, to compare with the conventional dynamic Smagorinsky type nonlinear model in the rotating turbulent channel flow.

In this article, we describe the use of a new dynamic cubic nonlinear model, a new nonlinear subgrid-scale model, for simulating the cavitating flow around an NACA66 series hydrofoil. For comparison, the dynamic Smagorinsky model is also used. It is found that the dynamic cubic nonlinear model can capture the turbulence spectrum, while the dynamic Smagorinsky model fails. Both models reproduce the cavity growth/destabilization cycle, but the results of the dynamic cubic nonlinear model are much smoother. The re-entrant jet is clearly captured by the models, and it is shown that the re-entrant jet cuts the cavity into two parts. In general, the dynamic cubic nonlinear model provides improvement over the dynamic Smagorinsky model for the calculation of cavitating flow.

Nonlinear dynamic model with multi-fields coupling effects for giant magnetostrictive actuators

To realize high precision servo control for the extension pneumatic muscle (E-PM), the nonlinear dynamic model of the E-PM is established and the effect parameters of the nonlinear dynamic model are analyzed, according to the phenomenological dynamic modeling theory. Firstly, an E-PM is designed based on the basic principle of PMs. Secondly, based on the dynamic characteristics of the E-PM, the nonlinear dynamic model of the E-PM is established. Thirdly, the parameters of the nonlinear dynamic model are identified by the elasticity test. Lastly, in the Matlab\Simscape environment, the nonlinear dynamic model of the E-PM is simulated and the effect parameters of the nonlinear dynamic model are analyzed. The result shows that the nonlinear dynamic model by phenomenological dynamic modeling theory can accurately reflect the dynamic characteristics of the E-PM. In addition, when the damping parameter changes in the range of 0.35-0.55, the biggest difference between the rise time is 1.5s and the biggest difference between the stable time is 3.1s. It indicates that the damping parameter has a great effect on the dynamic characteristics of the E-PM.

The existence of many different dynamic large eddy simulation (LES) methods leads to questions about the theoretical foundation of dynamic LES methods. It was shown recently that the use of stochastic analysis enables a theoretically well based systematic derivation of a realizable linear dynamic model (LDM) and a realizable nonlinear dynamic model (NDM). A priori and a posteriori analyses of turbulent channel flow are used here to study the characteristic properties of these dynamic models. The LDM and NDM are compared with other dynamic models: the non-stabilized and stabilized dynamic Smagorinsky model (DSM), which is used in many applications of LES, and Wang-Bergstrom's dynamic model (WBDM), which represents an extension of the DSM. The DSM and WBDM do not represent realizable models because they are not derived as consequences of a realizable stochastic process. The comparisons reported here show that the LDM and NDM are based on a dynamic model formulation that avoids shortcomings of existing concepts. The LDM and NDM account for backscatter, and they are computationally stable without any modification. The LDM and NDM represent the instantaneous small scale structure of turbulence very well. Compared to the DSM and WBDM, respectively, the LDM and NDM are computationally more efficient.

Distributed asynchronous multiple sensor fusion with nonlinear multiple models

Nonlinear modeling and identification of an autonomous tractor–trailer system

Nonlinear dynamic modeling and analysis of spur gears considering dynamic contact state under misalignment errors

Hybrid control of a satellite with membrane antenna considering nonlinear vibration

Accurate prediction of the vibration response of aircraft engine assemblies is of great importance when estimating both the performance and the lifetime of its individual components. In the case of underplatform dampers, for example, the motion at the frictional interfaces can lead to a highly nonlinear dynamic response and cause fretting wear at the contact. The latter will change the contact conditions of the interface and consequently impact the nonlinear dynamic response of the entire assembly. Accurate prediction of the nonlinear dynamic response over the lifetime of the assembly must include the impact of fretting wear. A multi-scale approach that incorporates wear into the nonlinear dynamic analysis is proposed, and its viability is demonstrated for an underplatform damper system. The nonlinear dynamic response is calculated with a multiharmonic balance approach, and a newly developed semi-analytical contact solver is used to obtain the contact conditions at the blade-damper interface with high accuracy and low computational cost. The calculated contact conditions are used in combination with the energy wear approach to compute the fretting wear at the contact interface. The nonlinear dynamic model of the blade-damper system is then updated with the worn profile and its dynamic response is recomputed. A significant impact of fretting wear on the nonlinear dynamic behaviour of the blade-damper system was observed, highlighting the sensitivity of the nonlinear dynamic response to changes at the contact interface. The computational speed and robustness of the adopted multi-scale approach are demonstrated.

Thanks to their advantages over rigid ones, interest for lightweight parallel manipulator was increased. Besides, structural flexibility effects at high operational speeds are more significant. Thus, developing an appropriate model for the assessment of the dynamic properties of flexible mechanisms and linkages to gain effective vibration control will raise high demand. Therefore, this paper represents the dynamic and kinematic modeling using the assumed mode method and first‐type Lagrange equations of the 2‐DOF planar parallel manipulator with two flexible links. To truly predict vibrations of the manipulator without any major simplifying assumptions, nonlinear dynamic modeling, which thoroughly attempts to represent the flexible behavior of the links, is considered. As a result, an active damping approach is being studied with PZT actuators. The results show that this approach is effective in damping the vibrations of the links that give accurate trajectory control.

Identification Method for Nonlinear Dynamic Models of Gas Turbine Engines on Acceleration Mode

Accurate prediction of the vibration response of aircraft engine assemblies is of great importance when estimating both the performance and the lifetime of their individual components. In the case of underplatform dampers, for example, the motion at the frictional interfaces can lead to a highly nonlinear dynamic response and cause fretting wear at the contact. The latter will change the contact conditions of the interface and consequently impact the nonlinear dynamic response of the entire assembly. Accurate prediction of the nonlinear dynamic response over the lifetime of the assembly must include the impact of fretting wear. A multiscale approach that incorporates wear into the nonlinear dynamic analysis is proposed, and its viability is demonstrated for an underplatform damper system. The nonlinear dynamic response is calculated with a multiharmonic balance approach, and a newly developed semi-analytical contact solver is used to obtain the contact conditions at the blade–damper interface with high accuracy and low computational cost. The calculated contact conditions are used in combination with the energy wear approach to compute the fretting wear at the contact interface. The nonlinear dynamic model of the blade–damper system is then updated with the worn profile and its dynamic response is recomputed. A significant impact of fretting wear on the nonlinear dynamic behavior of the blade–damper system was observed, highlighting the sensitivity of the nonlinear dynamic response to changes at the contact interface. The computational speed and robustness of the adopted multiscale approach are demonstrated.

Spiral bevel gears: Bifurcation and chaos analyses of pure torsional system