A finite element method in time is presented for the periodic solution of vibrating elastic mechanisms with clearances. The solution of motion is made possible by utilizing time finite elements which discretize the solution period into a number of time intervals. The periodic response is described in terms of a set of temporal nodes of all spatial degrees of freedom of the system, yielding a block-diagonal nonlinear algebraic system to be solved iteratively. The suggested method is applied to an example problem of cam-driven valve train, demonstrating the effectiveness of the method in dealing with multiple clearance nonlinearities.

1.
Borri
M.
,
Bottasso
C.
, and
Mantegazza
P.
,
1992
, “
Basic Features of the Time Finite Element Approach for Dynamics
,
Meccanica
, Vol.
27
, pp.
119
130
.
2.
Dubowsky
S.
, and
Deck
J. F.
,
1994
, “
On the Limitation of Predictions of the Dynamic Response of Machines With Clearance Connections
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, No.
3
, pp.
833
841
.
3.
Dubowsky
S.
,
Deck
J. F.
, and
Costello
H.
,
1987
, “
The Dynamic Modeling of Flexible Spatial Machine Systems With Clearance Connections
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
109
, pp.
87
94
.
4.
Haines
R. S.
,
1980
, “
Survey: 2-dimensional Motion and Impact at Revolute Joints
,”
Mechanism and Machine Theory
, Vol.
15
, pp.
361
370
.
5.
Turcic
D. A.
, and
Midha
A.
,
1984
, “
Dynamic Analysis of Elastic Mechanisms, Parts 1 and 2
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
106
, pp.
249
260
.
6.
Wang, Y., 1994, “Prediction of Periodic Response of Rotor Dynamic Systems With Nonlinear Supports,” ASME Journal of Vibration and Acoustics, in press.
7.
Winfery
R.
,
1973
, “
Analysis of Elastic Machinery With Clearances
,”
ASME Journal of Engineering for Industry
, Vol.
95
, No.
3
, pp.
695
703
.
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