models, EXperiments and high PERformance computing for Turbine mechanical Integrity and Structural dynamics in Europe (EXPERTISE)

Energy and Mobility are two primary driving forces in the 21st century. Development of incremental and disruptive technologies will have key impacts on the world’s societies, and on safety, security and competitiveness of Europe. Amongst those technologies, gas turbines will play a major role. Recovery of shale gas depends decisively on compressors. Modern gas supplied power plants are bridging towards the age of renewable energies. Aeroengines are to undergo the most massive changes in their history with the advent of composite materials, gear boxes, and turbine-electric concepts separating generation of power and thrust. A technological commonalities of the upcoming challenges is the need for full model based development and computer system simulation. There is agreement on this in the computational fluid dynamics (CFD) community. The structural dynamics and vibration questions are at present far from being addressed adequately. While US agencies and Asian powers have already started to prepare themselves, European research organisations and companies still seem to be too fragmented to reach critical research ressources and start corresponding initiatives. There are two main reasons for this. First, the physics of mechanical joining technologies that dominate the damping behavior of the large-scale structures under debate, are still poorly understood. Second, there is a lack of high performance computing (HPC) capabilities in structural dynamics, which goes back to the lack of knowledge of effective HPC technologies for structural dynamics. Since the US, China and India have started efforts in the field, we propose a European contribution through a Marie Curie ETN to allow a first generation of early stage researchers to catch up on the topics, ideally open up new fields of insight and approaches, and finally form a seed group for the upcoming challenges of the European turbine industry with respect to nonlinear structural dynamics and HPCMSCA-ITN-ETN - European Training Networks (H2020-MSCA-ITN-2016

Twenty years of computational methods for harmonic response analysis of non-proportionally damped systems

Twenty years ago, accurate harmonic response analysis of non-proportionally damped systems required the solution of a complex eigenvalue problem and modal superposition of complex modes. In order to avoid the computational effort of complex modal superposition, several approximate methods were proposed and accuracy of each such technique was studied extensively. In the past twenty years, while the search for appropriate approximate techniques for each different application continued, more rigorous methods were also developed. In this paper, the progress in computational methods for harmonic response analysis of nonproportionally damped systems is reviewed, emphasis being placed on a powerful technique which was first extended to structural modification analysis and then to harmonic response analysis of systems with non-linearities

On the critical speed of continuous shaft-disk systems

The critical speed of a shaft-disk system can be approximately determined from a single degree-of-freedom model. The errors in the critical speed predictions obtained from such a model are investigated. The percentage errors are plotted against disk to shaft mass ratio for different bearings and various disk locations

STRUCTURAL MODIFICATIONS USING FREQUENCY-RESPONSE FUNCTIONS

A general method using frequency response functional (FRFs) is developed for reanalysing a structure subjected to structural modification. In this method, theoretically calculated or experimentally measured FRFs can be used in determining the FRFs of the modified structure. Structural modifications may be in the form of additional structural components which may be expressed in terms of additional mass, stiffness and damping matrices. The formulation is given for two possible cases where there are and are not additional degrees of freedom due to structural modification. The application of the method is demonstrated with numerical examples in which theoretically calculated receptances of the original system are used

A NEW METHOD FOR HARMONIC RESPONSE OF NONPROPORTIONALLY DAMPED STRUCTURES USING UNDAMPED MODAL DATA

A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. Advantages of the method over classical methods are discussed, and it is concluded that the method is most advantageous when used for a structure with frequency and/or temperature dependent damping properties, or when the non-proportional part of the damping is local. The technique suggested can easily be applied to structural modification problems if there is no additional degree-of-freedom due to the modifying structure

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

A six-degree-of-freedom non-linear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the non-linear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the “static transmission error method” developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics

Receptances of non proportionally and continuously damped plates Reduced dampers method

This paper presents a method for the dynamic analysis of continuously and non-proportionally damped plates in bending modes. The damping can be in the form of constrained or unconstrained layers. The method is an extension of the equivalent dampers method discussed in a previous paper, in which the damping matrix of a discretized plate is replaced by a diagonal equivalent damping matrix. Each diagonal element represents an equivalent damper inserted between the structure and ground. In this method the number of equivalent dampers is reduced so that the receptance matrix of the damped structure can be obtained economically by a direct matrix method. The receptances of two different partially coated plates in transverse directions are computed by the method suggested. The verification of the results is demonstrated by comparison with the experimental values and also with the theoretical values obtained by the equivalent dampers method. The method presented can also be applied to the transverse vibration analysis of plates with discrete damping inserts

Dynamic Decoupling of Nonlinear Systems

Structural decoupling problem has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time and a method is proposed for calculating the frequency response functions of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modelled as a single nonlinear element. The method proposed is validated through simulated case studies

Harmonic Response of Large Engineering Structures with Nonlinear Modifications

In a structural design, the structure may need to be modified and for each modification its dynamic characteristics may need to be determined by reanalyzing the structure dynamically. Since computational time and cost are very critical in design processes, structural modification methods become decisive, particularly for large systems, in predicting the dynamic behavior of modified structures from those of the original and modifying structures. Due to nonlinearity in most engineering structures, linearity assumption may not be applicable to all cases. Then, well known structural modification methods can not be directly used, and it is required to employ a nonlinear structural modification method. In this paper, a structural modification/coupling method proposed in an earlier study is extended for nonlinear modification/coupling. The nonlinearities are quasilinearised using describing function method, and thus nonlinear internal force vector is expressed in terms of a response-dependent matrix which can be regarded as a response level dependent "equivalent stiffness matrix", called "nonlinearity matrix". Then the method developed for linear structural modification/coupling is employed by using an iterative solution procedure. Three case studies are presented in this paper. In the first case study, a nonlinear test structure used in an earlier study is employed and the frequency responses of the system at different forcing levels are calculated by using the approach suggested. Then they are compared with experimental results. Secondly, a simple discrete system is analyzed to demonstrate the accuracy of the approach proposed. Lastly, a large scale model is considered to illustrate the applicability of the approach proposed to large order systems