An Analytical Scheme for Stochastic Dynamic Systems Containing Fractional Derivatives

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method proposed by Suarez and Shokooh is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duhamel integral type expressions. The general response contains two parts, namely zero state and zero input. For a stochastic analysis the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics of the system. Closed form stochastic response expressions are obtained for white noise. Numerical results are presented to show the stochastic response of a fractionally damped system subjected to white noise.

Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

A new solution technique is developed for solving the moving mass problem for nonconservalive, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of terms because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented in the method proposed here by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, 1997). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. A set of real differential ordinary equations in time are derived which require exactly as much work to solve as Galerkin’s method with a set of real, linearly independent trial functions. Results indicate that the proposed method is competitive with traditional Galerkin’s method in terms of speed, accuracy and convergence.

Multirate Integration for Real-Time Simulation of Wheel Loader Hydraulics

This paper details a real-time simulation of an articulating wheel loader, which is comprised of a multibody system modeling the chassis and the bucket assembly and a set of subsystems. The hydraulic subsystem is modeled by a set of ODE’s which represent the oil pressure fluctuations in the system. An Adams-Bashforth-Moulton integration algorithm has been implemented using the Nordsieck form to develop a constant step-size multirate integration scheme, modeling the interaction between the hydraulic subsystem and multibody dynamics models. An example illustrating the simulation of a wheel loader bucket operation is presented at the end of the paper.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

A New Strategy for Detecting Gear Faults Using Denoising With the Orthogonal Discrete Wavelet Transform (ODWT)

This paper investigates a new strategy for early detection of defects in a power transmission pair of spur gears. Sensitivity to local defects is enhanced by processing the signal as follows. The orthogonal discrete wavelet transform (ODWT) of the band-pass filtered averaged signal is first obtained. This is followed by thresholding in the wavelet domain, thereby removing the low amplitude noise contribution. The inverse wavelet transform then essentially reconstructs the component of the signal that is due to the defect. Experimental results demonstrate the efficiency of this procedure.

Separating the Contributions in Localization Methods: A Technique to Enhance Identification of Damping Related Parameters

Finite Element Model Updating has for objective to increase the correlation between the experimental dynamic responses of a structure and the predictions from a model. Among different initial choices, these procedures need to establish a set of representative parameters to be updated in which some are in real error and some are not. It is therefore important to select the correct properties that have to be updated to ensure that no marginal corrections are introduced. In this paper the standard localization criteria are presented and a technique to separate the global localization criteria in family-based criteria for damped structures is introduced. The methods are analyzed and applied to both numerical and experimental examples; a clear enhancement of the results is noticed using the family-based criteria. A simple way to qualify the stability of a localization method to noise is presented.

Use of Measured Mobility to Improve SEA Predictions in the Mid-Frequency Range

Statistical energy analysis provides a technique to predict acoustic and vibration levels in complex dynamic systems. The technique is most useful for broad-band excitation at high frequencies where many modes contribute to the response in any given frequency band. At mid and low frequencies, the number of modes contributing to the response may be quite small. In this case SEA predictions show large variability from measured data and may not be useful for vibroacoustic design. This paper focuses on the use of measured data to improve the accuracy of the predictions. Past work to measure the SEA coupling and damping loss factors has not been successful for a broad range of systems that do not have light coupling. This paper introduces a new hybrid SEA technique that combines measured mobility functions with analytical SEA predictions. The accuracy of the hybrid technique is shown to be greatly improved at mid and low frequencies.

Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

Multirate Integration for Multibody Dynamic Analysis With Decomposed Subsystems

This paper details a constant stepsize, multirate integration scheme which has been proposed for multibody dynamic analysis. An Adams-Bashforth Moulton integration algorithm has been implemented, using the Nordsieck form to store internal integrator information, for multirate integration. A multibody system has been decomposed into several subsystems, treating inertia coupling effects of subsystem equations of motion as the inertia forces. To each subsystem, different rate Nordsieck form of Adams integrator has been applied to solve subsystem equations of motion. Higher order derivative information from the integrator provides approximation of inertia force computation in the decomposed subsystem equations of motion. To show the effectiveness of the scheme, simulations of a vehicle multibody system that consists of high frequency suspension motion and low frequency chassis motion have been carried out with different tire excitation forces. Efficiency of the proposed scheme has been also investigated.

Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.