Vibration of nonclassical shear beams with Winkler-Pasternak-type restraint

Abstract

Transverse vibration of the shear beams containing rotary inertia and with a two-parameter elastic foundation is studied. Using asymptotic analysis of Timoshenko beam theory, we derive explicit characteristic equations of the nonclassical shear beams with Winkler-Pasternak elastic restraint and with both ends linked to translational and rotational springs. The condition of the nonclassical shear beams reducing to the classical ones is found. Natural frequencies of the nonclassical modes are evaluated for free- and pinned-elastically restrained shear beams with or without bracing. The influences of elastic restraint stiffness and rotary inertia on the natural frequencies are discussed. Some extreme cases can be recovered from the present. The obtained results are helpful in the design of a tall frame building.