Experimental study of the influence of rectangular plates stiffening a cylindrical shell on its natural frequencies and modes

Abstract

The results are presented of studying the influence of rectangular plates on the natural frequencies and modes of a fluid-filled cylindrical shell with different end conditions Experimental data collected so far [1] indicate that the effect of longitudinal ribs on the natural frequencies and vibration modes of shells has been studied well enough. The natural vibrations of ribbed shells were theoretically analyzed in [4][5][6]. However, despite a great many studies in this area, the problem remains open, in particular, for shells stiffened with high ribs or with rectangular plates. A problem similar to that stated below was addressed earlier in [3]. This paper analyzed the stability of an axially compressed elastic system consisting of a ribbed cylindrical shell and rectangular plates inserted into it. The purpose of the present paper is to study experimentally the influence of stiffening plates and end conditions on the natural frequencies and modes of shells.1. Characteristics of the Test Shells. Two cylindrical shells were tested. Shell No. 1 has radius R = 15 cm, length L = 45 cm, and thickness h = 0.05 cm. Shell No. 2 was made from shell No. 1 by fastening six plates with screws to the inside surface of the shell along its meridians. The plates have length L 1 = 43 cm, width b = 15.5 cm, and thickness h 1 = 0.05 cm. Each plate has two 0.8 cm flanges along its entire length. Each flange has five screw holes spaced at 8.7 cm. The shells are stiffened with aluminum bands, 1 cm wide and 0.05 cm thick, on the outside surface near the ends. The shells, plates, and bands are made of AMg-6M aluminum alloy. The ready-assembled shell No. 2 is schematically shown in Fig. 1 without the bands.2. Experimental Results. A schematic of the experimental setup was presented in [2]. Figure 2 shows the arrangement of the shells. Shell No. 3 was vertically inserted into the circular slots of steel disks 2 filled with Wood's metal melt to a depth of 0.5 cm, which, when hardened, rigidly fixed the lower end of the shell. The disks are rigidly attached to massive bedplate 1. The upper end of the shell was left free to provide the first variant of end conditions (Fig. 2à) and was inserted into the circular slot of massive disk 4 and also filled with Wood's metal melt to provide the second variant of end conditions (Fig. 2b). Shells Nos. 1 and 2 were filled with service water. The water level was varied from Í 1 = 0 to Í 1 = 1 (Í 1 = Í/L, H is the water level). The natural frequencies and modes of the shells were determined by the resonance method. The vibrations of the shells were excited with an electrodynamic vibrator. Its mobile coil, 5.42 g in mass, was rigidly fixed to the shell's wall, in its midsection. In Fig. 2, the point of attachment of the coil is indicated by an arrow. The methods of excitation and measurement of natural frequencies and modes were detailed in [2]. The experiments were conducted at fixed levels of excitation. Figure 3 shows the dependence of the experimental minimum natural frequencies f e min on the water...

Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

“…New buckling problems for systems consisting of ribbed shells and plates were solved in [36][37][38]. The stability and vibrations of an elastic system consisting of a ribbed cylindrical shell and rectangular plates inserted into it were analyzed in [37,…”

“…In this case, almost all of the shell surface is not involved in the vibratory process and its inertial properties can be neglected. It was shown that experimental and theoretical data on vibration frequencies are in better agreement when a finite contact area is considered.New buckling problems for systems consisting of ribbed shells and plates were solved in [36][37][38]. The stability and vibrations of an elastic system consisting of a ribbed cylindrical shell and rectangular plates inserted into it were analyzed in [37,…”

“…The vibration frequencies and modes of cylindrical shells connected with rectangular plates and containing fluid were experimentally determined in [36]. It was shown that the vibration mode is strongly dependent on the boundary conditions.…”

Experimental analysis of the natural vibrations and stability of cylindrical shells reinforced with rectangular plates

“…Experimental data of the natural vibrations and stability of rib-reinforced cylindrical shells are reported in many publications [2][3][4][5][6]8]. However, there are very view experimental studies on other types of reinforcement.…”

“…The shells of the second set were tested on a 30-ton Baldwin testing machine (USA, 1950). The loading method and the set-up were detailed in [3,4]. The local buckling of all the shells was accompanied by snaps and occurrence of dents, which deepened with increasing load.…”