Fundamental frequency and testing mode of complicated elastic clamped-plate vibration

Abstract

Aimed at the modal analysis of complicated elastic clamped-plates, a trigonometric interpolation method of conformal mapping is applied to set up the mapping function between a complicated region and a unit dish region, and the fundamental frequency of the complicated vibrating region is analyzed with the help of the Galerkin method. Taking an elastic rectangle-plate with arc radius as an example, the testing mode frequency band of plates is determined by analyzing the fundamental frequency; meanwhile, according to hamming testing method of multi-point excitation to the single-point response, and by signal processing technology and its software programming, modal parameter recognition of the elastic clamped-plate is completed. Comparing the first order modal frequency with the theoretical fundament frequency, the validity of the testing mode method and theoretical analysis are verified.

References

1. Yu A . Rossikhin.Analysis of damped vibrations of linear viscoelastic plates with dampingmodeled with fractional derivatives. SignalProcessing, 2006, 86(10): 2703–2711. doi:10.1016/j.sigpro.2006.02.016
2. Yang Q J . Vibration reliability characterization of PBGA assemblies. Microelectronics Reliability, 2000, 40(7): 1097–1107
3. Pitarresi J M . Modeling of printed circuit cards subject to vibration. Circuits and Systems, 1990, 3: 2104–2107. doi:10.1109/ISCAS.1990.112213
4. Felix D H . Natural frequencies of a vibrating repaired panel in an ocean structure. Ocean Engineering, 2003, (30): 955–963. doi:10.1016/S0029-8018(02)00082-3
5. Pan Junqi, Liu Zhifeng . Recycling process assessmentof mechanical recycling of printed circuit board. J Cent South Univ Technol, 2005, 12(2): 157–161. doi:10.1007/s11771-005-0031-z
6. Ndambi J M . Comparison of techniques for modal analysis of concrete structures. Engineering Structures, 2000, 22(9): 1159–1166. doi:10.1016/S0141-0296(99)00054-1
7. Teppati. . Conformal-mappingdesign tools for coaxial couplers with complex cross section. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(10): 2339–2345. doi:10.1109/TMTT.2002.803424
8. Amatore. . Simulationof the double hemicylinder generator-collector assembly through conformalmapping technique. Journal of ElectroanalyticalChemistry, 2003, 553(Suppl) 49–61. doi:10.1016/S0022-0728(03)00269-9
9. Netku Y . ConformalField Theory. Cambridge Massachusetts USA: Perseus Pub,2000-1v. 35
10. Qi Hongyuan, Zhu Hengjun . Conformal mapping modelingof metal plastic deformation and die cavity in special-shaped extrusion. Trans Nonferr Metal Soc, 2002, 12(5): 858–861
11. Crandall S . EngineeringAnalysis. New York: McGraw-Hill Book Co. 1950, 218