Methods for comprehensive structural dynamic analysis generally employ input-output modal analysis with a mathematical model of structural vibration using excitation and response data. Recently operational modal analysis methods using only vibration response data have been developed. In this thesis, both input-output and operational modal analysis, in the presence of significant unmeasured excitations, is considered. This situation arises when a test structure cannot be effectively isolated from ambient excitations or where the operating environment imposes dynamically-important boundary conditions. The limitations of existing deterministic frequency-domain methods are assessed. A novel time-domain estimation algorithm, based on the estimation of a discrete-time autoregressive moving average with exogenous excitation (ARMAX) model, is proposed. It includes a stochastic component to explicitly account for unmeasured excitations and measurement noise. A criterion, based on the sign of modal damping, is incorporated to distinguish vibration modes from spurious modes due to unmeasured excitations and measurement noise, and to identify the most complete set of modal parameters from a group of estimated models. Numerical tests demonstrate that the proposed algorithm effectively identifies vibration modes even with significant unmeasured random and periodic excitations. Random noise is superimposed on response measurements in all tests. Simulated systems with low modal damping, closely spaced modes and high modal damping are considered independently. The accuracy of estimated modal parameters is good except for degreesof- freedom with a low response level but this could be overcome by appropriate placement of excitation and response measurement points. These observations are reflected in experimental tests that include unmeasured periodic excitations over 200% the level of measured excitations, unmeasured random excitations at 90% the level of measured excitations, and the superposition of periodic and random unmeasured excitations. Results indicate advantages of the proposed algorithm over a deterministic frequency domain algorithm. Piezoceramic plates are used for structural excitation in one experimental case and the limitations of distributed excitation for broadband analysis are observed and characterised in terms of actuator geometry and modal deformation. The ARMAX algorithm is extended for use with response measurements exclusively. Numerical and experimental tests demonstrate its performance using time series data and correlation functions calculated from response measurements.

We consider geometric and material nonlinearities when studying numerically, by the finite element method, transient three-dimensional electroelastic deformations of a graphite-epoxy square plate sandwiched between two piezoceramic (PZT) layers. Points on the four edges of the bottom surface of the plate are restrained from moving vertically. The two opposite edges of the plate are loaded by equal in-plane compressive loads that increase linearly with time and the other two edges are kept traction free. The plate material is modeled as orthotropic and neoHookean. For the transversely isotropic PZT the second Piola-Kirchhoff stress tensor and the electric displacement are expressed as second degree polynomials in the Green-St. Venant strain tensor and the electric field. Both direct and converse piezoelectric effects are accounted for in the PZT. The plate is taken to have buckled when its centroidal deflection equals three times the plate thickness. The dynamic buckling load for the plate is found to strongly depend upon the rate of rise of the applied tractions. With the maximum electric field limited to 1kV/mm, the buckling load is enhanced by 18.3% when the PZT elements are activated. For a peak electric field of 30kV/mm, the buckling load increased by 58.5%. When more than 60% of the surface area of the top and the bottom surfaces of the plate are covered by the PZT layers, then square PZT elements placed symmetrically about the plate centroid provide a larger enhancement in the buckling load than rectangular shaped or cross-shaped PZT elements. An increase in the plate thickness relative to that of the PZT actuators decreases the effectiveness of the PZT in enhancing the buckling load for the plate. The finite element code was modified to also analyze, in time domain, transient deformations of a viscoelastic material for which the second Piola-Kirchhoff stress tensor is expressed as a linear functional of the strain history of the Green-St. Venant strain tensor. It was used to analyze three-dimensional deformations of a thick laminated plate with layers made of aluminum, a viscoelastic material and a PZT. The following two arrangements of layers are considered. In one case a central PZT layer is surrounded on both sides by viscoelastic layers and aluminum layers are on the outside surfaces. The PZT is poled in the longitudinal direction and an electric field is applied in the thickness direction. Thus shearing deformations of the PZT layer are dominant. In the second arrangement, the aluminum layer is in the middle and the PZT layers are on the outside. The poling direction and the electric field are in the thickness direction; thus its extensional deformations are predominant. Three indices are used to gauge the damping of motion of plate particles, and the effectiveness of PZT actuators in enhancing this damping. It is found that the optimum thickness of the viscoelastic layers for maximum total energy dissipation is the same for each set-up. Also, the total thickness of the PZT layers which results in the maximum value of one of these indices of energy dissipation is the same for the two set-ups. Both arrangements give the largest value of this index for a plate of aspect ratio 10. Buckling behavior of a sandwich plate containing a soft core is also studied. The effects of the ratio of the elastic moduli of the outer layers to those of the core, and of the core thickness on the buckling load are analyzed. The top and the bottom layers are connected by very stiff blocks on two opposite edges where in-plane compressive time-dependent tractions are applied. / Ph. D.