Lower Bounds to Eigenvalues for Vibrations and Buckling of Structures by Analytical Applications of a-priori Known Qualitative Information |
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| Institution: | 1. Department of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000 Israel;1. School of Pharmaceutical Sciences (Shen Zhen), Shenzhen Campus of Sun Yat-sen University, No. 66, Gongchang Road, Guangming District, Shenzhen, Guangdong, 518107, PR China;2. Department of Chemistry, National University of Singapore, 3 Science Drive 3, 117543, Singapore;1. Health Services Research and Development (HSR&D), Center of Innovation for Veteran-Centered Value-Driven Care, Veteran Affairs (VA) Puget Sound Health Care System, 1660 S. Columbian Way, S-152, Seattle, WA, USA;2. Department of Health Services, University of Washington, 1959 NE Pacific St, Magnuson Health Sciences Center, Room H-680, Box 357660 Seattle, WA, USA;3. Veterans Aging Cohort Study Coordinating Center, VA Connecticut Healthcare System, 950 Campbell Avenue, Building 35A, 11-ACSLG, West Haven, CT, USA;4. Kaiser Permanente Washington Health Research Institute, 1730 Minor Ave, Seattle, WA, USA;5. Kidney Health Research Collaborative, University of California, San Francisco and San Francisco VA Medical Center, 4150 Clement St., Building 18, San Francisco, CA, USA;6. Betty Irene Moore School of Nursing, University of California at Davis, 2570 48th St., Sacramento, CA, USA;7. National Institute on Alcohol Abuse and Alcoholism, Bethesda, MD, USA;8. Yale University Schools of Medicine and Public Health, 333 Cedar Street, New Haven, CT, USA;9. Department of Psychiatry, Weill Institute for Neurosciences, University of California, 401 Parnassus Ave., San Francisco, CA, USA;10. Kaiser Permanente Northern California, Division of Research, 2000 Broadway, Oakland, CA, USA;11. Department of Epidemiology, Brown University School of Public Health, 121 South Main St., Second floor, Providence, RI, USA;12. Division of General Internal Medicine, University of Pittsburgh School of Medicine, UPMC Montefiore Hospital, Suite 933W, Pittsburgh, PA, USA;13. Center for Health Equity Research and Promotion, VA Pittsburgh Healthcare System, 3900 Woodland Avenue, Annex Suite 202, Pittsburgh, PA, USA;14. Health Services Research, Rutgers University, 61 Dudley Rd, New Brunswick, NJ, USA;15. Department of Internal Medicine, University of Utah School of Medicine, 30 N 1900 E, Salt Lake City, UT, USA;p. Informatics, Decision-Enhancement and Analytic Sciences Center (IDEAS 2.0), Salt Lake City VA Health Care System, 500 Foothill Drive, Salt Lake City, UT, USA;q. Center of Excellence in Substance Abuse Treatment and Education (CESATE) VA Puget Sound Healthcare System – Seattle Division, 1660 S Columbian Way, Seattle, WA, USA;r. Department of Medicine, University of Washington, 1959 NE Pacific Street, Box 356420, Seattle, WA, USA |
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| Abstract: | Two methods to obtain lower bounds to eigenvalues are presented for cases which have equivalent minimum variational formulations. One method is an extension and elaboration of a theorem presented by the author in 1972, which affected the transfer of a weight function from one location to another over the physical system considered. The extension relies on information known a-priori about the exact solution of the problem, although the exact solution is not obtained. The other method is akin to the Rayleigh–Ritz method but yields lower bounds. The two methods are applied to various physical examples of vibrations and of buckling with rather good results. The application to other examples is direct and may be performed in a way quite similar to those examples shown. |
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