Thesis (Ph.D.)--Boston University / This thesis presents methods for interpolating transfer functions of damped vibrating systems. Primary applications lie in the design and control of damped structures. The interpolations reduce the number of frequencies at which the transfer function must be computed or measured. The transfer functions are assumed to have impulse responses that are real-valued and causal, so a method is developed for constructing interpolations that implicitly satisfy these conditions. The method is applied to a particular choice of basis function that corresponds to a Fourier series in the time domain. Numerical results indicate that satisfaction of the causality condition increases the accuracy of the interpolation. A detailed investigation is made into interpolations for viscously damped systems, whose transfer functions are linear combinations of basis functions derived from the complex-valued eigenpairs of the system. Since the estimation of all eigenpairs is computationally expensive, a method is developed to estimate only those eigenpairs that significantly contribute to the transfer function in the specified frequency band. The method uses eigenvalues of the corresponding undamped system, which are much easier to compute, as starting guesses in an iterative algorithm. One advantage of the method is the assurance that it finds all eigenvalues in a specified region of the complex plane.

Yes / Earthquake response spectrum is the most popular tool in the seismic analysis and design of structures. In the case of combined primary-secondary (P-S) systems, the response of the supporting P substructure is generally evaluated without considering the S substructure, which in turn is only required to bear displacements and/or forces imposed by the P substructure (¿cascade¿ approach). In doing so, however, dynamic interaction between the P and S components is neglected, and the seismic-induced response of the S substructure may be heavily underestimated or overestimated. In this paper, a novel CQC (Complete Quadratic Combination) rule is proposed for the seismic response of linear light S substructures attached to linear P substructures. The proposed technique overcomes the drawbacks of the cascade approach by including the effects of dynamic interaction and different damping in the substructures directly in the cross-correlation coefficients. The computational effort is reduced by using the eigenproperties of the decoupled substructures and only one earthquake response spectrum for a reference value of the damping ratio.