Wave Analysis and Control of Non-Uniform Double Cascade-Connected Damped Mass-Spring Systems

Abstract

This paper considers wave analysis and control of double cascade-connected damped mass-spring systems whose mass is connected to two adjacent masses on both sides. As an extension of our previous research on the uniform case, physical parameters of the system are assumed to vary along the layers. For the wave analysis, we require for the propagation constants to be independent of the layer position, and show that the physical parameters should vary uniformly along the layer. For the system satisfying the condition, properties of the secondary constants (propagation constants, characteristic admittances) and the transformation matrix as analytic functions are examined in detail. Under a weak condition (inequality) on two springs and dampers in the same layer, we show that the secondary constants and the transformation matrix satisfy the required properties for the wave analysis (analyticity on the open right half-plane, positive real property of the characteristic admittances, etc.). Validity of the derived results and efficiency of the impedance matching controller for vibration control are illustrated in the numerical example.