A study of vibration-control design parameters using models with two degrees of freedom - Andalecio, Melinda N. (2001)
This thesis studies the optimum condition of design parameters in vibration control problems analyzed as two-mass model. The conclusions from this model will serve as guide for initial selection of design parameters for the vibration control system. The three problems considered are tuned mass damper (TMD) system, machine isolation (MI) system, and base isolation (BI) system. The thesis presents: the selection of examples of 2DOF (two-degree-of-freedom) problems with their corresponding practical range of parameters; the design criteria; and procedures implemented in Mathcad2000 software. Three design criteria for each problem are formulated and adapted based on relevance and usefulness in civil engineering. Parametric studies have been conducted to investigate the effect design variables. Results are presented trough tables and figures for many combinations of design parameters. Most cases consider harmonic excitation; but the study also extends to such simple periodic excitations as rectangular wave, or triangular or sawtooth. To calculate the dynamic response of two-degree-of-freedom problems with varying parameters, a technical tool has been developed through implementation of algorithms in Mathcad2000; the program is called "2DOF".
The 2DOF program has been verified by comparing results with graphical or numerical results or empirical formulas that can be found in literatures. It is illustrated that existing empirical formulas for optimum parameters and corresponding response have limitations compared to the exact results of the 2DOF program. Hence the 2DOF software is proven to be a convenient alternative to the simplified empirical formulas that have been the tool of designers until now. From a wide realistic range of parameters, it is concluded, for example, that the usual approach in the design of the TMD by neglecting the damping of the primary sub-system has at least 10% underestimate of response value for C1<0.005. In general, for any of the three systems, optimum design parameters in frequency, damping, or mass may or may not exist, depending on the optimization criterion being chosen. The dynamic response calculation of the two-mass model subjected to harmonic excitation is extended to periodic excitation using superposition technique offered by Fourier series. Tables are derived from the 2DOF program with periodic excitations. A parametric study shows that in most criteria, the response calculation for the three periodic excitations can be simplified by multiplying constant factor into the corresponding response for harmonic excitation.
Thesis (M.S. Civil Engineering)--University of the Philippines Diliman.
Keywords: Vibration; Degree of freedom -- Mathematical models; Structural dynamics