An analytical formulation for the vectors of contact forces and the stiffness matrix of the nonlinear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed disks. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

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A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of' nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using .standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced re.'iponse analysis of bladed disks with contact interfaces: (i) at biade roots, (ii) between interlock shrouds, and (iii) at underpiatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases

An analytical formulation for the vectors of contact forces and the stiffness matrix of the non-linear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed discs. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

An approach is developed to analyze the multiharmonic forced response of large-scale finite element models of bladed disks taking account of the nonlinear forces acting at the contact interfaces of blade roots. Area contact interaction is modeled by area friction contact elements which allow for friction stresses under variable normal load, unilateral contacts, clearances, and interferences. Examples of application of the new approach to the analysis of root damping and forced response levels are given and numerical investigations of effects of contact conditions at root joints and excitation levels are explored for practical bladed disks.

Advanced structural dynamic models for both wedge and split underplatform dampers have been developed. The new damper models take into account inertia forces and the effects of normal load variation on stick-slip transitions at the contact interfaces. The damper models are formulated for the general case of multiharmonic forced response analysis. An approach for using the new damper models in the dynamic analysis of large-scale finite element models of bladed disks is proposed and realized. Numerical investigations of bladed disks are performed to demonstrate the capabilities of the new models and an analysis of the influence of the damper parameters on the forced response of bladed disks is made.

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

A new method for the dynamic analysis of mistuned bladed disks is presented. The method is based on exact calculation of the response of a mistuned system using response levels for the tuned assembly together with a modification matrix constructed from the frequency response function (FRF) matrix of the tuned system and a matrix describing the mistuning. The main advantages of the method are its efficiency and accuracy, which allow the use of large finite element models of practical bladed disk assemblies in parametric studies of mistuning effects on vibration amplitudes. A new method of calculating the FRF matrix of the tuned system using a sector model is also developed so as to improve the efficiency of the method even further, making the proposed method a very attractive tool for mistuning studies. Various numerical aspects of the proposed method are addressed and its accuracy and efficiency are demonstrated using representative test cases.