The problem of free vibration of a complex system with a natural frequency identical to that of one of its subsystems is further discussed. Such eigenvibrations need special consideration in many modal synthesis methods, as the Green’s operator of the resonating subsystem does not exist at subsystem natural frequencies. A general treatment of this problem has been given by the authors in a companion paper. In this supplement, the previous work is extended to include the case of interaction forces applied to the resonating subsystem at points where the corresponding eigenfunction of the subsystem has maxima. Examples of such eigenvibrations are presented for two simple systems. The differences between these examples and those of the previous paper are noted and discussed.

1.
McFarland, D. M., and Bergman, L. A., 1990, “Analysis of Passive and Active Discrete-Distributed Linear Dynamical Systems Using Green’s Function Methods,” Technical Report UILU ENG 90-0504, University of Illinois, Urbana, pp. 38 and 95–97.
2.
Pesterev, A. V., and Bergman, L. A., 1994, “On Vibrations of a System with an Eigenfrequency Identical to That of One of its Subsystems,” ASME JOURNAL OF VIBRATION AND ACOUSTICS, in press.
3.
Pesterev, A. V., and Tavrizov, G. A., 1994, “On Inversion of Some Meromorphic Matrices,” Linear Algebra and Its Applications, Vol. 212/213, in press.
4.
Yee
E. K. L.
, and
Tsuei
Y. G.
,
1989
, “
Direct Component Modal Synthesis Technique for System Dynamic Analysis
,”
AIAA Journal
, Vol.
27
, pp.
1083
1088
.
This content is only available via PDF.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8143876791000366, "perplexity": 1617.6127636375927}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675409.61/warc/CC-MAIN-20191017145741-20191017173241-00413.warc.gz"}