Small-amplitude flexural vibration of a slightly deformable binary link in a planar linkage is governed by a fourth-order parabolic partial differential equation. Specifically, for a slider- crank mechanism with an elastic connecting rod, stability charts are obtained via analog simulation on the basis of the principal modal equation of vibration. It is found that stability of the mechanism depends on three nondimensional parameters - length ratio, mass ratio, and rigidity-speed ratio. The procedure of dynamic stability analysis via analog simulation for the slider-crank may be applied to other planar linkages with elastic binary links.
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References
1.
Bolotin V.V.The dynamic stability of elastic systems (English translation)Holden-Day, Inc., San Francisco1964
2.
Brewer J.W.Analysis, simulation and control of dynamic systemsD. Van Nostrand Company Inc.New York (preliminary edition) 1969
3.
EVAN-IWANOWSKI R M On the parametric response of structures Applied Mechanics Reviews vol 18 no 9 pp 699-702 September 1965
4.
Evenson H.A. and Evan-Iwanowski R.M.Effects of longitudinal inertia upon the parametric response of elastic columnsJournal of Applied Mechanics Transactions of ASME vol 88 Series E pp 141-1481966
5.
Faraday M.On a peculiar class of acoustical figures and on certain forms assumed by particlesPhilosophical Transactions of the Royal SocietyLondon England pp 299-318 May 1831
6.
Gayfer J.R. and Mills B.Small-amplitude vibrations of the four-bar linkage chainJournal of Mechanical Engineering Science vol 7 no 3 pp 252-2581965
7.
Hsu C.S.On a restricted class of coupled Hill's equations and some applicationsJournal of Applied Mechanics Transactions of ASME vol 83 Series E pp 551-5561961
8.
Hsu C.S.On the parametric excitation of a dynamic system having multiple degrees of freedomJournal of Applied Mechanics Transactions of ASME vol 85 Series E pp 367-3721963
9.
Hsu C.S.The effects of various parameters on the dynamic stability of a shallow archJournal of Applied Mechanics Transactions of ASME vol 89 Series E pp 349-3581967
10.
Ince E.L.Researches into the characteristic numbers of the Mathieu equationProceedings of the Royal Society of Edinburgh vol 451924-25
11.
Kotowski G.Lösungen der inhomogenen Mathieuschen differentialgleichung mit periodischer storfunktion beliebiger frequenzZeitschrift für angewandte Mathematic und Mechanik vol 23 pp 213-2291943
12.
Kotter K. and Kotowski G.Über die stabilität der Lösungen Hillscher differential gleichungen mit drei unabhangigen parameternZeitschrift für angewandte Mathematik und Mechanik vol 23 pp 144-1551943
13.
Mahalingam S.Small amplitude vibrations of a four-bar mechanismJournal of Mechanical Engineering Science vol 8 no 4 pp 456-4581966
14.
McLachlan N.W.Theory and application of Mathieu's equationOxford University PressLondon England 1947
15.
Neubauer A.H. JRCohen R. and Hall A.S. JRAn analytical study of the dynamics of an elastic linkageJournal of Engineering for Industry Transactions of ASME vol 88 Series B pp 311-3171966
16.
Pauling J.R. and Rosenberg R.M.On unstable ship motions resulting from nonlinear couplingJournal of Ship Research vol 3 pp 36-461959
17.
Seevers J.A.Dynamic stability of linkages with elastic members M S thesis Department of Mechanical Engineering University of California Davis California March 1969
18.
19.
Somerset J.H. and Evan-Iwanowski R.M.Experiments on parametric instability of columnsProceedings, Second Southeastern Conference on Theoretical and Applied MechanicsAtlanta Georgia pp 503-529 March 1964
20.
Van Der Pol B. and Strutt M.J.0 On the stability of the solutions of Mathieu's equationPhilosophical Magazine vol 5 p 181928
