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Transient vibrations of cross-ply plates subject to uncertain excitations. (English) Zbl 0824.73026

Summary: Transient vibrations of cross-ply plates are studied under loads with uncertain components using a nonprobabilistic model. The dynamic loads involve the forcing function and the initial conditions with deterministic and uncertain components. Uncertainty in these functions is required to be bounded in the \(L_ 2\)-norm and expressed by a finite number of eigenmodes. The specific forms of the uncertain functions are determined so as to yield the least favorable dynamic response. The theory is illustrated with two numerical examples, and the effect of various problem parameters, in particular, the level of uncertainty, on the response is studied.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74H50 Random vibrations in dynamical problems in solid mechanics
74K20 Plates
74E30 Composite and mixture properties
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