Finite amplitude, free vibrations of an axisymmetric load supported by a highly elastic tubular shear spring
The authors study free vibrational characteristics of a simple nonlinear mechanical system consisting of an axisymmetric rigid body supported by a highly elastic rubber tubular shear spring and subjected to axial, rotational, and coupled shearing motions. These elastic springs bonded on their inner and outer cylindrical surfaces to a rigid support are widely used in engineering structures as vibration isolation, shock suppression, and noise statement devices. Two classes of elastic tube materials are considered: a compressible material whose shear response is constant, and the incompressible Mooney-Rivlin material whose shear response is a quadratic function of the total amount of shear. For each material, the quasi-static elasticity problems are solved to determine the telescopic and gyratory shearing deformations needed to calculate the restoring force and torque exerted on the body. The motion of the tube itself and internal material damping is ignored. For the quadratic material, the free coupled shearing motion for which either the axial or the azimuthal shear deformation may be small is governed by a pair of equations of the Duffing and Hill types. The finite amplitude pure axial and pure rotational motions of the load are described by the classical nonlinear Duffing equation alone.
scientific article; zbMATH DE number 753722
scientific article