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Elastic beams with identical buckling and vibration mode shapes. (English) Zbl 0963.74535

Summary: We discuss the determining the shape of simply supported beams with added masses to achieve identical buckling and vibration mode shapes. Motivation for this work stems from the design of a new type of hydraulic switching valve utilizing a parametrically excited beam as actuation element. An analytical expression for the necessary thickness of the beam is developed, and the shape of buckling mode and eigenvalues (i.e. buckling force and vibration frequency) are determined by solving a Sturm-Liouville eigenvalue problem numerically.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G60 Bifurcation and buckling
74H45 Vibrations in dynamical problems in solid mechanics
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