Small vibrations of thin incomplete circular rings

Effect of Compression Ring Elastodynamics Behaviour upon Blowby and Power Loss

“…The inextensional vibrations of incomplete rings with small cross sections were discussed by Archer [5], with clamped boundary conditions. Modal results were presented, showing both the natural frequencies and mode shapes.…”

“…Figure 1. Ring in-plane degrees of freedom [6] The out-of-plane modal solution was presented by Ojalvo [7], who built on the previous work of Archer [5]. Figure 2 depicts a cross section of the mechanical model used by Ojalvo.…”

Analytical Evaluation of Fitted Piston Compression Ring: Modal Behaviour and Frictional Assessment

“…Figure 9 shows the in-plane motion degrees of freedom for an incomplete circular ring, with a radius significantly larger than its facewidth (thin structure). By neglecting rotary inertia, and considering the radial and tangential forces, as well as bending moments, the equations of motion for radial and tangential displacements are: Both equations need to be separated as performed by Archer (1960), into space and time expressions. This gives three solution forms for v and w, where the appropriate solution is determined by the nature of λ value in:…”

“…The ring was considered with different types of applied normal loads. Archer (1960) studied the in-plane in-extensional vibrations of incomplete rings with small cross-sections. The results were obtained using classical equations of motion, considering only in-plane forces.…”

Extensional Vibration Analysis of Curved Beams Including Rotatory Inertia and Shear Deformation Using DQM

“…Den Hartog [4] used the Rayleigh-Ritz method for finding the lowest natural frequency of circular arcs with simply supported or clamped ends, and his work was extended by Volterra and Morell [5] for the vibrations of arches having center lines in the form of cycloids, catenaries, or parabolas. Archer [6] carried out for a mathematical study of the in-plane inextensional vibrations of an incomplete circular ring of small cross section with the basic equations of motion as given in Love [2] and gave a prescribed time-dependent displacement at the other end for the case of clamped ends. Veletsos et al [7] used a theory which accurately considered the extensibility of the arch axis and the curved beam effect but neglects the effects of rotatory inertia and shearing deformation.…”