3-D Analytical Treatment of Base Isolation for Mechanical Testing Systems

Abstract

A mathematical model for dynamic analysis of vibration isolation systems is presented. The model is based on small deformation mechanics of 3-D rigid body with 6-DOF and supported by flexible structural members. The mass, static stiffness and damping matrices for the system are derived. Eigen-analysis using the presented model and solution method are applied to a real spacecraft vibration test system with base isolation. A finite element model of the system is also developed. The results of the proposed math model, FE model and test results of a real vibration testing system are compared. The math model solution results agree well with the FEM model and actual test results. The model can be used in the design of the engineering structures with base isolation such as vibration and acoustic test systems, large static and dynamic testing systems, buildings etc.

Keywords

• Vibration isolation,rigid-body motion,eigen-analysis

References

1. [1] Abaqus FEA software, Computer software https://www.3ds.com/products-services/simulia/products/abaqus/ 2017. [2] J. Angeles, “On the Nature of the Cartesian Stiffness Matrix,” Ingeniería mecánica, tecnología y desarrollo, vol. 3, no. 5, pp. 163–170, 2010. [3] J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 3rd ed. Springer International Publishing, 2013. [4] B. Bachman, Vibration Problems in Structures; Practical Guidelines. Birkhauser Verlag Basel Boston Berlin, 1997. [5] M/L Technical Bulletins, “Elastomer or Spring Isolators: Which Type to Use and When.” retrieved http://www.vibrodynamics.com/usa/bulletin.html 2017. [6] J. Harry Himelblau and R. Sheldon, Vibration of a Resiliently Supported Rigid Body, 6th ed. McGraw-Hill, 2010, pp. 1–56. [7] R. A. Ibrahim, “Recent advances in nonlinear passive vibration isolators,” Journal of sound and vibration, vol. 314, no. 3, pp. 371–452, 2008. [8] W. D. Iwan, “The earthquake design and analysis of equipment isolation systems,” Earthquake Engineering & Structural Dynamics, vol. 6, no. 6, pp. 523–534, 1978. [9] E. S. Leonard, “Generalized Matrix Method for the Design and Analysis of Vibration-Isolation Systems,” The Journal of the Acoustical Society of America, vol. 40, pp. 195–204, 1966. [10] P. Madsen, “A Mathematical Approach to the Forced Vibrations of the Suspended Compressor Block,” in International Compressor Engineering Conference, 1972, no. Paper 52, pp. 326–329. [11] S. R. Singiresu, Mechanical Vibrations, 5th ed. Prentice Hall, 2011. [12] M. Stephen, “Analytical Modelling of Single and Two-Stage Vibration Isolation Systems,” in Proceedings of the Annual Conference of the Australian Acoustical Society Acoustics 2011: Breaking New Ground, 2011, p. 116. [13] Cfm-Schiller website, “Steel Spring Isolators - Type SSI.” http://www.cfm-schiller.de/index.php?zeige_rubrik=15&dbase=produktdetails, 2017. [14] J. Z. Yongjun Jin and X. Guan, “Theroretical Calculation and Experimental Analysis of the Rigid Body Modes of Powertrain Mounting System,” WSEAS Transactions on Applied and Theoretical Mechanics, vol. 8, no. 3, pp. 193–201, Jul. 2013.