The use of higher-order difference methods in beam vibration analysis /

"Simple and higher-order difference methods for the solution for the natural frequencies of vibration of a uniform beam are compared. The same basic higher-order method is used throughout for the interior cells, but three different methods of boundary-condition representation are given. Tables and graphs of the error in mode frequencies, as compared with a continuous beam, are given for the various methods as a function of the number of cells. It is concluded that higher-order methods improve accuracy for a given number of cells, with essentially no change in the quantity of computing equipment required."--P. 1.Document ID: 19980227794."NASA TN D-964.""December 1961."Cover title.Includes bibliographical references (p. 73).Introduction -- Symbols -- Continuous beams -- Differences of order h² -- Differences of order h⁴ -- The use of symmetry in representing boundary conditions -- The passive circuit method -- Sources of error -- Conclusions -- Appendix A. Alternate matrix formulation -- Appendix B. Tapered cantilever beam -- References -- Tables -- Figures."Simple and higher-order difference methods for the solution for the natural frequencies of vibration of a uniform beam are compared. The same basic higher-order method is used throughout for the interior cells, but three different methods of boundary-condition representation are given. Tables and graphs of the error in mode frequencies, as compared with a continuous beam, are given for the various methods as a function of the number of cells. It is concluded that higher-order methods improve accuracy for a given number of cells, with essentially no change in the quantity of computing equipment required."--P. 1.Performed by Michigan Universiy, Ann Arbor, Dept. of Aeronautical and Astronautical Engineering under NASAMode of access: Internet