Investigation on dynamic characteristics of two pole discrete elements by matrix description approach and applications in analysis of anti-vibration mounting

Relationships between input state vectors and output state vectors of discrete elements(mass,spring,damper,rigid body) are deduced respectively in element coordinating system.Analytical formulae of forward transfer matrix,reverse transfer matrix and generalized impedance matrix are derived separately.The correlation respectively between driving point impedance and transfer matrix or generalized impedance matrix and between driving point mobility and transfer matrix or generalized impedance matrix are dis-cussed.Furthermore,the longitudinal vibration equations of the anti-vibration mounting are achieved both by transfer matrix method and mobility matrix method.The analytical formula of the longitudinal force transmissibility is given.Two approaches yield similar results,but the process of transfer matrix method is simpler.The transverse vibration equations of the anti-vibration mounting are also deduced using transfer matrix method.The analytical formula of the transverse force transmissibility is consequently given.Analyt-ical formulae in this paper can be applied in dynamic design of the anti-vibration mounting to achieve good precision with less computation.