Frequency Tuning of Chain Structure Oscillators to Place the Natural Frequencies at Omega1 and N-1 Integer Multiples Omega2 ... OmegaN

Numerous activities in Engineering, e.g. the design of solid body compensators, involve the tuning of dynamic systems to place the natural frequencies omega_1 ... omega_N at a certain base harmonic Omega_1 and N-1 integer multiples of it Omega_2 ... Omega_N. In this paper a novel concept for the frequency tuning of multi-degree of freedom mass-spring oscillators will be presented which allows an exact placement of the natural frequencies in case of an un-damped system. Frequency tuning will be achieved by the selection of masses m_1 ... m_N and spring stiffnesses c_1 ... c_N of the system following an amazingly simple procedure.