Flexural vibrations of nonlinearly elastic circular rings

Abstract

This paper treats free nonlinear flexural vibrations of circular elastic rings in the context of a geometrically exact formulation accounting for the effects of nonlinear material behavior. A direct asymptotic approach based on the method of multiple scales is used to investigate such vibrations. It is shown that the flexural motions are softening for linearly elastic rings, in agreement with previous results in the literature, while there are nonlinearly elastic rings for which the motions are hardening. There are thresholds in the nonlinear constitutive laws separating softening from hardening behaviors

Internal resonance in forced vibration of coupled cantilevers subjected to magnetic interaction

“…To address the lack of research in the aspect, the present investigation focuses on internal resonance of elastically connected cantilevers under magnetic interaction via the method of multiple scales. Although the method of multiple scales has been well developed to treat continuous systems without discretization [25], internal resonances in continuous systems are usually treated after the discretization via the Galerkin method [26,27] and the finite element method [28,29]. In the following, the method of multiple scales will be applied to the partial differential equations with nonlinear boundary conditions to derive solvability condition in the external resonance and the internal resonance.…”

Vibrational characteristics of size dependent vibrating ring gyroscope

“…Elastic rings are the main components of vibrating ring gyroscopes; therefore, many researchers modeled and analyzed the mechanical behavior of these components [16][17][18][19]. Wu and Parker [16] presented the natural frequency analysis of rings resting on the general elastic foundation.…”

Vibration of Elastic Functionally Graded Thick Rings

“…Their applications can be found in planetary gears, rotors, gyroscopic actuators, measuring instruments, and hollow axle used on subway and high-speed trains. Their mechanical performances have been investigated extensively, among which the vibration characteristics are one of the most important aspects [1][2][3][4][5][6][7].…”

“…Wong et al [2] considered inplane vibration problem for thermoelastic damping rings. Lacarbonara et al [7] analyzed flexural vibration problem of elastic circular rings considering nonlinearity of structural deformation.…”