Transient stability of empty and fluid-filled cylindrical shells

Abstract

In the present work a qualitatively accurate low dimensional model is used to study the non-linear dynamic behavior of shallow cylindrical shells under axial loading. The dynamic version of the Donnell non-linear shallow shell equations are discretized by the Galerkin method. The shell is considered to be initially at rest, in a position corresponding to a pre-buckling configuration. Then, a harmonic excitation is applied and conditions to escape from this configuration are sought. By defining steady state and transient stability boundaries, frequency regimes of instability may be identified such that they may be avoided in design. Initially a steady state analysis is performed; resonance response curves in the forcing plane are presented and the main instabilities are identified. Finally, the global transient response of the system is investigated in order to quantify the degree of safety of the shell in the presence of small perturbations. Since the initial conditions, or even the shell parameters, may vary widely, and indeed are often unknown, attention is given to all possible transient motions. As parameters are varied, transient basins of attraction can undergo quantitative and qualitative changes; hence a stability analysis which only considers the steady-state and neglects this global transient behavior, may be seriously non-conservative

Vibration Characteristics of Fluid-Filled Functionally Graded Cylindrical Material with Ring Supports

“…Figure 2(b) exhibits a good coincidence between respective counters of the frequencies. The values at n = 8, 9 are less significant and on enhancing the value of n, the present numerical values are smaller than those of Gonçalves and Batista [10] and Gonçalves et al [11] and Gasser [12]. This difference is the result of two separate analytical techniques.…”

“…They are varied with axial wave number, m for circumferential wave mode, n = 2, 3. For the same shell, the present results for a fluid-filled shell are compared with those numerical results obtained by Gonçalves and Batista [10], Gonçalves et al [11] and obtained experimentally by Gasser [12] in Figure 2(b). They are varied with circumferential wave mode, n for axial wave number, m =1 .…”

“…This difference is the result of two separate analytical techniques. Present data Goncalves and Batista data [10] Goncalves et al data [11] Gasser data [12] (b) …”

“…In Figure 6 From the previous data, the shell frequencies are affected highly as the fluid quantities [11,[31][32][33][34][35] and ring supports are appended [2,5,27,36]. A beam type vibration of CSs crops up when the addition of ring supports are made.…”

“…Simply supported end conditions were imposed on both edges. Goncalves et al [11] investigated the transient stability of empty and fluid-filled cylindrical shells and used to study the non-linear dynamic behavior of shallow cylindrical shells under axial loading. Gasser [12] studied the frequency spectra of bi-layered cylindrical shells by taking different materials in both layers such as isotropic as well as functionally graded material (FGM) and by taking two different FGM at the inner and outer layers of the CSs respectively.…”