Abstract
In-plane free vibrations of an elastic and isotropic annular disk with elastic constraints at the inner and outer boundaries, which are applied either along the entire periphery of the disk or at a point are investigated. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. Boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to account for different boundary conditions. The frequency parameters for different boundary conditions of the outer edge are evaluated and compared with those available in the published studies and computed from a finite element model. The computed mode shapes are presented for a disk clamped at the inner edge and point supported at the outer edge to illustrate the free in-plane vibration behavior of the disk. Results show that addition of point clamped support causes some of the higher modes to split into two different frequencies with different mode shapes.
Highlights
The vibration characteristics of circular disks subject to classical boundary conditions have been widely reported
For a disk with non-uniform boundary conditions, nature of coupling between the modes would differ from those observed under classical boundary conditions, :
The frequency parameters and the corresponding mode shapes of the annular disk with different edge constraints are obtained by solving the eigenvalue problem in Eq (2.1)
Summary
The vibration characteristics of circular disks subject to classical boundary conditions have been widely reported. Another study evaluated the frequency parameters and associated mode shapes of in-plane vibration of solid disks clamped at the outer edge using assumed deflection modes in terms of trigonometric and Bessel functions [8]. Irie et al [10] evaluated the natural frequencies of in-plane vibration of annular disks using transfer matrix formulation with combinations of free and clamped conditions at the inner and outer edges,. The studies on in-plane vibration of disks, have not yet considered the effects of partial constraints, while the effect of flexible boundary conditions have been reported by the authors [22]. The present study is an attempt to understand the effect of partial constraints and flexible boundary conditions on the in-plane free vibration of circular disks. The frequency parameters are tabulated and the mode shapes are depicted to illustrate the in-plane free vibration behavior of circular disks. The results are compared with the reported data and those obtained from finite element analysis to illustrate the validity of the present method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
