Direct time integration methods are usually applied to determine the dynamic response of systems with local nonlinearities. Nevertheless, these methods are computationally expensive to predict the steady state response. To significantly reduce the computational effort, a new approach is proposed for the multiharmonic response analysis of dynamical systems with local nonlinearities. The approach is based on the describing function (DF) method and linear receptance data. With the DF method, the kinetic equations are converted into a set of complex algebraic equations. By using the linear receptance data, the dimension of the complex algebraic equations, which should be solved iteratively, are only related to nonlinear degrees of freedom (DOFs). A cantilever beam with a local nonlinear element is presented to show the procedure and performance of the proposed approach. The approach can greatly reduce the size and computational cost of the problem. Thus, it can be applicable to large-scale systems with local nonlinearities.

An optimal method is developed to estimate the dynamic loads for systems subjected to multiple inputs. The method focuses on minimizing the ensemble mean square error of the estimation. First, the inverse system analysis technique is employed to establish the error estimation equation. Then, by applying the noncausal Wiener filtering theory, the optimal estimator of dynamic loads is derived out. Numerical simulation work demonstrates that the method is of a good ability in suppressing the influence of measurement noises on estimation accuracy. Meanwhile, the simulating calculation of load estimation by a conventional method is also performed and the comparison of both results shows that the method proposed in this paper is rather effective and practicable for dynamic load estimation.

This paper presents some important characteristics of enhanced active constrained layer damping (EACL) treatments for vibration controls. Specific interests are on understanding how the edge elements will influence the active action authority, the passive damping ability, and their combined effects in EACL. Analysis results indicate that the edge elements can significantly improve the active action transmissibility of the current active constrained layer damping (ACL) treatment. Although the edge elements will slightly reduce the viscoelastic material (VEM) passive damping, the EACL will still have significant damping from the VEM. Combining the overall active and passive actions, the new EACL with sufficiently stiff edge elements not only could achieve better performance with less control effort compared to the current ACL system, but also could outperform the purely active system. With careful analysis, we can map out the required critical edge element stiffness for successful designs. In addition, analysis also shows that the EACL treatment is a more robust design. That is, it could outperform both the purely active and passive systems throughout a much broader design space than the current ACL configuration. With these desirable characteristics, the EACL could be used to realize an overall optimal active-passive hybrid system.

Details are presented of an analysis and computer code for the calculation of complex multi-span rotor-bearing-pedestal-foundation systems. This multi-level system analysis is based on the Prohl-Myklestad transfer matrix method. The rotor model used is similar to that given by Lund and Orcutt [ 1 ] . Eight-coefficient bearings are also used, to permit elliptical orbit rotor motions. The bearings are mounted in massive, damped flexible pedestals, which are themselves mounted upon a foundation structure with distributed mass and stiffness properties. The foundation in turn, is supported on a number of flexible-damped supports. Different foundation properties in the horizontal and vertical directions are included. The analysis is described in detail, along with the computer code, and the results obtained with it are compared with data published previously by other investigators. It is shown that transfer matrix methods can be successfully used for multi-level systems, and that the additional computational ejfort involved is moderate. Three applications of the code are described which validate various aspects of the analysis and the computer program.

The analysis of systems subjected to periodic excitations can be highly complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-periodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates the periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solutions and locates system parameter ranges where aperiodic and chaotic responses bifurcate from the periodic response. Once the system response for a parameter is known, the solution for near range of the parameter is calculated efficiently using a pseudo-arc length continuation procedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor supported on squeeze-film dampers and journal bearings, which have nonlinear stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi-periodic and chaotic motions are calculated for a set of system parameters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.

A residual flexibility approach for the analysis of systems involving multiple components subjected to dynamic loading is presented. The reactive forces at the junctions of the components are computed directly without synthesis of component modes or determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirements of displacement compatibility and force equilibrium at the junction coordinates are enforced. This leads to a set of junction-sized simultaneous algebraic equations for the unknown forces, similar in form to that of the flexibility formulation in statics; this is done by invoking the Newmark integration algorithm. The computed reactive forces at a given time point are used to integrate the equations of motion of the individual components separately for that time point, hence the terminology decoupled analysis. The new method compares well with traditional Component-Mode Synthesis approach for a nonclassically damped fixed-fixed beam consisting of two classically damped cantilevered beam components.

In many systems, the normal force at friction contacts is not constant, but is instead a function of the system’s state variables. Examples include machine tools, friction dampers, brake systems and robotic contact with the environment. Friction at these contacts has been shown to possess dynamics associated with changes in normal force. In an earlier paper, the authors derived a critical value of system stiffness for stability based on a linearized analysis of constant velocity sliding (Dupont and Bapna, 1994). In this paper, the domain of attraction for the steady sliding equilibrium point is characterized for a system in which normal force is coupled to tangential displacement. Perturbations consisting of sudden changes in the displacement and velocity of the loading point are considered. These perturbations can be viewed as either actuator disturbances or changes in control input. The effect and interaction of the frictional and geometric parameters are elucidated. The results are applicable to the design and analysis of systems in which steady motion without friction-induced limit cycles is desired.

The power transmission system is a critical component of any machine. Accordingly, the detailed analysis of this system is essential for both design purposes and the detailed assessment of machine performance. Due to the large number of possible power transmission system components and the nature of these systems, general power transmission system analysis methods have been difficult to develop. However, such analysis methods could meet a wide variety of needs for system design. This paper discusses the general power transmission system analysis approach developed by the authors over the last several years based on their study of vehicle powertrains. The formulation and solution of the governing equations are discussed, and the ability of the approach in addressing critical design related issues is demonstrated through an example system simulation.

This note outlines an extension of the Data Dependent Systems (DDS) methodology to the modal analysis of vibratory systems with eigenvalues of arbitrary multiplicity. DDS [1, 2] is a time-series approach to system analysis that combines a rational modeling strategy with elements of linear system theory. The use of an appropriate state-space setting makes it a powerful tool for system identification, and the approach has been successfully applied to the modal characterization of mechanical systems in references [2–4], which provide many examples with real life data.