By Jong-Shyong Wu
''This publication illustrates theories and linked mathematical expressions with numerical examples utilizing a number of equipment, resulting in targeted recommendations, extra actual effects, and extra computationally effective recommendations. It offers the derivations of the equations of movement for all constitution foundations utilizing both the continual version or the discrete version. It discusses functions for college kids taking classes together with vibration mechanics, dynamics of constructions, and finite aspect analyses of constructions, the move matrix strategy, and Jacobi method''
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Additional resources for Analytical and numerical methods for vibration analyses
1963) Machinery induced vibration. Transactions of the Institute of Marine Engineers, 75, 121–388. S. H. (1995) Computer method for torsion-and-flexure-coupled forced vibration of a shafting system with damping. Journal of Sound and Vibration, 180 (3), 417–435. 2 Analytical Solutions for Uniform Continuous Systems Derivation of the equations of motion of a vibrating system is essential for vibration analysis. Thus, methods to obtain the equations of motion of a vibrating system are introduced first in this chapter.
82f) will always be satisfied if one sets ! 78). 60) for the longitudinally vibrating F-F uniform rod, respectively, thus, br L ¼ rp or br ¼ rp=L ðr ¼ 0; 1; 2; 3; . . ; 1Þ sﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃ G G ðr ¼ 0; 1; 2; 3; . . ; 1Þ v r ¼ br ¼ rp r rL2 Qr ðxÞ ¼ Ar cosðrpx=LÞ ðr ¼ 0; 1; 2; 3; . . ; 1Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ~ 0 ðxÞ ¼ 1=ðrI p LÞ ðr ¼ 0Þ Q ~ r ðxÞ ¼ Q qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2=ðrI p LÞ cosðrpx=LÞ ðr ¼ 1; 2; 3; . . 88): br L ¼ rp br ¼ rp=L ðr ¼ 1; 2; 3; . . ; 1Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃ vr ¼ br G=r ¼ rp G=ðrL2 Þ ðr ¼ 1; 2; 3; .
Meirovitch, L. (1967) Analytical Methods in Vibrations, Macmillan, London. W. and Penzien, J. (1975) Dynamics of Structures, McGraw-Hill, New York. M. E. (eds) (1976) Shock and Vibration Handbook, 2nd edn, McGraw-Hill, New York. T. (1981) Theory of Vibration with Applications, 2nd edn, Prentice-Hall, Englewood Cliffs, NJ. , and Weaver, W. Jr. , New York. S. (1968) Theory of Matrix Structural Analysis, McGraw-Hill, New York. J. (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Analytical and numerical methods for vibration analyses by Jong-Shyong Wu