The Matrix Analysis of Vibration [Paperback]

This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations.This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.Vibration problems arise in the design of almost all engineering machinery and structures. Many of these problems are extremely complex but their solution is essential if a safe and satisfactory design is to be achieved. The equations of motion are often insoluble by the classical methods of the calculus and so it is necessary to approximate on order to reduce them to a set of linear equations. The use of matrices simplifies the solution of sets of linear equations. This book describes the matrix formulation of the equations of motion and techniques for the solution of matrix equations. The book describes some typical computer methods and also includes a large number of problems (with solutions) which may conveniently be solved by using a desk calculating machine.Preface; 1. Notation and elementary properties of matrices; 2. The vibration of conservative systems having finite number of degrees of freedom; 3. Linear equations; 4. Further development of the theory of conservative systems; 5. Damped forced vibration; 6. Continuous systems; 7. The solution of linear equations and the inversion of matrices; 8. Iterative methods for characteristic value problems; 9. Direct methods for characteristic value problems; Appendix; Answers to examples; Index.