A modified Gram-Schmidt procedure for determining the mode shapes of a special compensator for fluid flow pulsations

Abstract Filtering out fluid flow pulsations in hydraulic systems is a major task in mechanical engineering and hydraulic engineering. One possibility is the use of solid body compensators. An approach for tuning such a solid body compensator goes back to Mikota , who introduced the so-called Mikota’s vibration chain. As has been shown in previous investigations, this rather special multi-body system shows neat properties regarding its eigenfrequencies and mode shapes, respectively. Based on these findings, the current contribution adds another possibility of analytically determining the mode shapes. The suggested approach is based on a modified Gram-Schmidt procedure. Interestingly, the stiffness matrix is not used explicitly within this approach.