A six degrees of freedom dynamic model of a planetary geared rotor system with equally spaced planets is developed by considering gyroscopic effects. The dynamic model is created using a lumped parameter model of the planetary gearbox and a finite element model of the rotating shafts using Timoshenko beams. The gears and carrier in the planetary gearbox are assumed to be rigid, and the gear teeth contacts and bearing elements are assumed to be flexible. The modal analysis results show that torsional and axial vibrations on the shafts are coupled in the helical gearing configuration due to the gear helix angle whereas these vibrations become uncoupled for spur gearing. Mainly, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur gear configuration. Modal energy analysis is used to quantify the coupling level between the shafts and the planetary gearbox, highlighting the impact of the gearbox on certain mode families. Gyroscopic effects of the planetary gearbox are found to be of great importance in the gearbox dominated modes.

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a phase-locked loop controller is implemented to acquire periodic oscillations near resonance and construct a nonlinear-mode model. This model is based on amplitude-dependent modal properties, i.e. does not require nonlinear basis functions. The second methodology exploits uncontrolled experiments with broadband random inputs to build polynomial nonlinear state-space models using advanced system identification tools. The methods are applied to two experimental test rigs, a magnetic cantilever beam and a free-free beam with a lap joint. The respective models of both methods and both specimens are then challenged to predict dynamic, near-resonant behavior observed under different sine and sine-sweep excitations. The vibration prediction of the nonlinear-mode and state-space models clearly highlight the capabilities and limitations of the models. The nonlinear-mode model, by design, yields a perfect match at resonance peaks and high accuracy in close vicinity. However, it is limited to well-spaced modes and sinusoidal excitation. The state-space model covers a wider dynamic range, including transient excitations. However, the reallife nonlinearities considered in this study can only be approximated by polynomial basis functions. Consequently, the identified state-space models are found to be highly input-dependent, in particular for sinusoidal excitations where they are found to lead to a low predictive capability.

Two approaches for experimental identification of the nonlinear dynamical characteristics of jointed structures are investigated, (a) Nonlinear Modal Testing, (b) State-Space Model Identification. Both require only minimal a priori knowledge of the specimen. For method (a), the definition of nonlinear modes as periodic motions is used, in its generalized formulation recently proposed for nonconservative systems. The theoretically required negative damping compensating the frictional dissipation is experimentally realized by properly controlled excitation. This permits the extraction of modal frequencies, damping ratios and vibrational deflection shapes as a function of the vibration level. For method (b), a state-space model with multivariate polynomial nonlinear terms is identified from the vibration response to a properly designed excitation signal. Both methods are applied to a structure with bolted joints. The quality of the extracted modal and state-space models, respectively, is assessed by comparing model-based predictions of the forced vibration response to reference measurements.

This study focuses on the dynamic modelling and analysis of the wind turbine blades made of multiple layers of fibre reinforced composites and core materials. For this purpose, a novel three-dimensional analytical straight beam model for blades is formulated. This model assumes that the beam is made of functionally graded material (FGM) and has a variable and asymmetrical cross section. In this model, the blades are assumed to be thin, slender and long with a relatively straight axis. They have two main parts, namely the core and the shell. The so-called core consists of a lightweight isotropic foam material, which also adds significant damping to the system. The core material is covered by the shell, which is modelled using homogenous and orthotropic material assumptions as the structure is reinforced with continuous fibres. Therefore, the blades are modelled under a straight beam with varying cross-section assumptions, in which the effective elastic properties are acquired by homogenizing the cross section. The beam formulation for modelling the system is performed both analytically and numerically with the finite element method. The results of both methods are in well agreement. The maximum deviation between the results is found below 4%.