A study of the dispersion of transient stress waves in the first layer of a weakly coupled semi-infinite bilayered system is performed. The analysis employs asymptotic Fourier transform inversions, and makes use of the fact that the weakly coupled system possesses small propagation zones (PZs) in frequency. The derived analytic expressions contain nonoscillating terms and convolution integrals with decaying oscillatory kernels. Depending on the frequency and amplitude of the convolution kernels, the dispersed waves overshoot or undershoot the applied impulsive excitation. This result is of significant practical importance in the design of layered systems as stress attenuators.

System identification and diagnostic methodologies for detecting defective bearings in rotating machinery are developed. This is of direct relevance to the utility industry, where vibrational-related failure in rotating machinery is a leading cause of forced outages in power plants. Modal analysis techniques and nonlinear system identification methodologies (higher-dimensional frequency response functions and Volterra series) are considered. A second problem studied is the computational investigation of transient heat conduction in laminated thermal barriers used for thermal protection of gas turbine components. A double integral transform methodology is used and numerical inversions are performed by efficient computational algorithms.

An analytical/numerical study of nonlinear confinement of transient motions in a flexible truss structure is carried out. We investigate nonlinear motion confinement due to clearance or geometric nonlinearities. We then develop passive or active techniques to enhance the motion confinement phenomenon.

A new approach for studying traveling or stationary waves with spatially localized envelopes in nonlinear periodic particle chains is studied. The technique used is an extension of previously used nonlinear normal mode (NNM) methodologies for analyzing NNMs of discrete and (bounded, one-dimensional) continuous nonlinear oscillators. In the context of these methods, stationary wave solutions in the chains are regarded as localized NNMs of unbounded, continuous, one-dimensional systems. Propagating, weakly modulated waves are then computed by imposing Lorentz coordinate transformations to the stationary wave solutions.

The distortions in the receptance plots of forced nonlinear mechanical systems are examined. Weak nonlinearities of stiffness and damping are considered, and approximate harmonic steady-state responses are evaluated. The Nyquist plots of weakly nonlinear systems are then constructed and the nonlinear distortions are identified and analytically investigated. Based on the results of the analysis, a method for identifying and quantifying weak nonlinearities in the frequency responses of practical systems is suggested. The applicability of the proposed technique is then tested with theoretical and experimental data.

We experimentally investigate transient and steady-state localized modes in periodic flexible systems with stiffness nonlinearities. The goal is to show that for sufficiently small coupling between substructures these systems possess passive nonlinear motion confinement properties, which can be used in new vibrations and shock isolation designs.

The aim of this research is to develop new methodologies for suppressing noise disturbances in spacecrafts. The fundamental issue is the maintenance of small levels of vibration on a spacecraft whose mission involves precision pointing. A new vibration isolation technique to effectively suppress high-frequency noise in the range 30-300Hz is studied. The technique relies on passively or actively inducing localized nonlinear normal modes (NNMs) in the spacecraft system using actively or passively induced stiffness nonlinearities. This design is new and innovative, and relies on the efficient use of nonlinear forces to spatially confine the unwanted motion from sensitive parts of the spacecraft.