Experimental spatial dynamics modeling is a new approach to dynamics modeling using high-spatial-density experimental data from a scanning laser Doppler vibrometer (LDV). This instrument measures the surface velocity of vibrated structures. Time-signal data from the LDV is statistically modeled with multiple linear regression for harmonically excited structures. A weighted least-squares discrete finite element formulation is developed to solve for the complex-valued continuous 3-D velocity response field from sampled velocity data. The formulation is derived from the steady-state solution of the differential equation with spatial and temporal components of harmonic structural dynamic response. Linear, quadratic, cubic, and cubic B-spline basis functions are used to form isoparametric finite elements in the dynamic response model. Velocity measurements acquired from multiple positions are transformed into a single model that minimizes the least-squares error between the experimental data and the field equations in the 3-D shell element model. A multiple point nonlinear registration algorithm is developed to determine position and orientation of the LDV relative to the test structure. Polygonal shape models are successfully integrated with the experimental spatial dynamic response models via polygon ray intersection. Finite element shape models are generated from simple flat surfaces or extracted from existing finite element models of 3-D structures. By postprocessing the model solution, many dynamic properties including rotations, full-field strains and stresses, and acoustic prediction are derived from the dynamic response representation. Visualization software was developed for animation of the 3-D spatial dynamic response models with superimposed color to represent the postprocessed results. The interactive graphics allow presentation and investigation of the experimental spatial dynamics. To examine the method, an analytical test model is defined to simulate the surface velocity response of a structure with both in-plane and out-of-plane harmonic vibration. Random and uniformly spaced measurements of the simulated dynamic system are acquired from multiple locations. Applications of experimental spatial dynamics modeling, postprocessing, and visualization are also demonstrated with five different test structures. Through mesh refinement, increase in order of the basis functions, and additional sampling, the finite element models are converged to statistically qualified solutions. / Ph. D.

This dissertation is concerned with the evaluation of a new statistically sound reconstruction methodology for continuous 3-D dynamic response fields of harmonically excited structures in steady-state vibration. This results in an experimental process which reconstructs the response field from a set of 3-D projections based on Laser-Doppler-Vibrometer (LDV) localized instantaneous velocity measurements. Included along with an estimate of the 3-D velocity field, are its statistical characteristics and the inferential tools required to test the quality of the estimation. This dissertation documents in detail the development and evaluation of the proposed reconstruction methodology and its relevant subprocesses which inc1ude the formulation of a deterministic laser-structure kinematic model, and regression models that afford statistical inference for the time-domain and spatial-domain structural dynamics, as well as for the projection recombination process. / Ph. D.

A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ_s + λ_t <u>~</u>2Ï _q, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w_r<u>~</u>3w_q on the resonance λ_s + λ_t <u>~</u>2Ï _q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ_s + λ_t. / Master of Science

Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam. / Master of Science

Under static of dynamic loadings, the junction (interface) between a structure-foundation system can experience contact, slip, separation and rebonding modes of deformations. Two interface models are proposed for simulation of interface behavior in finite element analysis of dynamic soil-structure interaction problems. The first element called the thin-layer element has (small) finite thickness. Geometrically, this element is similar to the continuum (soil or structural) element; however, its constitutive relations are defined differently. The normal behavior is defined as a function of the material properties and stress-strain characteristics of the neighboring continuum element. The shear behavior is defined in terms of observed shear stress-relative displacement behavior expressed as function of factors such as normal stress, number of cycles of loading and amplitude of load (or displacements). Mohr-Coulomb criterion is used to define activated sliding strength of interface. Modes of deformations are simulated by using appropriate stress redistribution iterative schemes. The second model called the mixed interface element has zero thickness. Both displacements and tractions are treated as primary unknowns. Constraints associated with modes of deformations are included using a variational approach. An incremental solution scheme is proposed. Material parameters related to the proposed models are evaluated from the results of sand-concrete interface tests in a Cyclic Multi-Degree-of-Freedom shear device. Accuracy of the proposed models are verified with respect to a number of example problems. In general, consistent and satisfactory results are obtained. For further verification and evaluation of these models, several soil-structure interaction problems are solved and detailed results are presented. It is observed that behavior of structure-foundation systems can be significantly influenced by interface conditions. An analysis based on bonded interface condition appears to underestimate actual response. Hence, it will be appropriate to include interface behavior in the analysis and design of structures subjected to dynamic and earthquake loadings.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Bibliography: leaves 363-373. / Ph.D.

Thesis. 1977. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography : leaves 130-132. / M.S.

The vibration control of composite beams and plates subjected to a travelling load is studied in this dissertation. By comparing the controlled as well as uncontrolled responses of classical and refined structural models, the influence of several important composite structure properties which are not included in the classical structural model is revealed. The modal control approach is employed to suppress the structural vibration. In modal control, the control is effected by controlling the modes of the system. The control law is obtained by using the optimal control theory. Comparison of two variants of the modal control approach, the coupled modal control (CMC) and independent modal-space control (IMSC), is made. The results are found to be in agreement with those obtained by previous investigators. The differences between the controlled responses as well as actuator outputs that are predicted by the classical and the refined structural models are outlined in this work. In conclusion, it is found that, when performing the structural analysis and control system design for a composite structure, the classical structural models (such as the Euler-Bernoulli beam and Kirchhoff plate) yield erroneous conclusions concerning the performance of the actual structural system. Furthermore, transverse shear deformation, anisotropy, damping, and the parameters associated with the travelling load are shown to have great influence on the controlled as well as uncontrolled responses of the composite structure. / Ph. D.

A new method is developed for experimentally determining the system parameters of a structure that is suitable for implementation in microprocessor-based systems. It uses single degree-of-freedom models to describe a multi-degree-of-freedom system. The system is assumed to be describable by a linear, proportionally and lightly damped, lumped parameter model. Two types of damping models, viscous and structural damping, are provided. The effective mass, stiffness, and damping are obtained by fitting the experimental data in the inverse Nyquist plane. The effective mass, stiffness, and damping are convertible to global modal mass, stiffness, and damping through normal mode corrections. Then a physical space mathematical model may be assembled from the modal properties for complete and truncated modal vector system descriptions. Therefore, this method will deal with the general case where the number of degree-of-freedom exceeds the number of identified modes. After a mathematical model is developed, different ways of modifying the structure analytically are investigated. This modified model is used to predict the new dynamic characteristics of the modified structure due to changes in its mass, stiffness, or damping properties. There are three ways that modifications can be made. They are: l) modifications made in the physical coordinates model; 2) modifications made in both the physical and modal coordinates models; and 3) modifications made in the modal coordinates model. The last way is found to be the most efficient way; therefore, model modifications should be done totally in modal spaces, modal space I and II. The derivation of mass, stiffness, and damping modification matrices for general structure is also presented. The resonance specification and frequency response function synthesis are two useful techniques that aid in system modification and are, therefore, included. A resonant peak can be shifted to another frequency by making certain modifications to the structure, thus avoiding undesired vibration. The resonance specification will determine the amount of physical change needed. It is not practical to store all the frequency response function measurements of a structure during testing. Therefore, a frequency response function synthesis is needed, such that any one can be synthesized from the model developed. A theoretical three degree-of-freedom system and two experimental systems--a square plate and a C-clamp--were used to verify the techniques developed. / Ph. D.

In order to perform structural optimization and/or modification on a structure, an analytical model which sufficiently describes the behavior of the structure must be developed. Analytical models can be generated for almost any structure, but such a model will generally not effectively predict the behavior of the structure unless the model is somehow reconciled with experimental data taken from the structure. Additionally, the model must also be complete, i.e., it must not only model the structure but also model any suspension system used to support the structure. If the suspension is not included in the model, any attempt to reconcile the model with experimental data will result in a incorrect model. Using this incorrect model to perform structural modification cannot be expected to give correct results. In this thesis, an approach for estimating the effects of a suspension system on the flexural vibration of a structure is developed. These effects are treated mathematically as variations in boundary conditions. Topics discussed include formulation of an analytical model that includes suspension effects, experimental methods for acquiring mode shapes which exhibit these effects, and reconciliation techniques for matching analytical mode shapes to experimental mode shapes to determine the effective boundary conditions. / Master of Science