1. A method for analyzing vibrations and automatically optimizing design variable values describing at least one isolator to be used in a damped structure, the damped structure being comprised of at least one component, the method comprising: classifying each component as either rigid or flexible; if at least one component is classified as flexible, developing a finite element model representing flexible components of the structure; if at least one component is classified as rigid, entering parameters describing each rigid component; entering initial values for isolator design variables, a set of design constraints, and an optimization criterion, the isolator design variables forming a design vector; determining eigenvectors of flexible components using the finite element model; determining a total system model using the eigenvectors of flexible components and parameters of rigid components; performing vibration analysis on the total system model; determining an optimization function using the optimization criterion and the results of vibration analysis; determining optimized design variable values using the optimization function and the set of design constraints by determining a search direction, determining a step size along the search direction, determining a new design vector as the current design vector increased by the step size in the search direction, and repeating the steps of determining a search direction, determining a step size, and determining a new design vector until locally optimized design variable values are obtained; repeating the steps of determining a total system model, performing vibration analysis, determining an optimization function, and optimizing design variable values until the optimization function is minimized; and generating output data corresponding to the optimized design variable values.