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

Abstract

The paper presents experimental results on the effect of reinforcing cylindrical shells with rectangular plates on the axial compressive critical loads and the natural frequencies and modes of two sets of shells Introduction. 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. For example, the effect of reinforcement of shells with rectangular plates has not been examined at all. In this connection, the present paper discusses the results from an analysis of the influence of such reinforcement plates on the natural frequencies and modes of cylindrical shells and their critical loads under axial compression. The efficiency of this type of reinforcement will be demonstrated. Similar results were obtained in [7] by calculation.1. Characteristics of Test Shells. Two sets of cylindrical shells were tested. Their geometry is summarized in Table 1. Three shells of the first set (Nos. 1-3) were made from a lavsan film. The nonreinforced shell No. 1 was made by bonding a film with BF-2 adhesive on a precision cylindrical mandrel. Shells Nos. 2 and 3 were made by reinforcing shell No. 1 with plates k = 6and k = 9in number and b = 10.3 and b = 7.3 ñm in width, respectively. The lengths and thicknesses of all plates were equal: L = 23.8 cm and h = 0.0175 ñm. All plates had both long edges flanged, flanges being 1 cm wide. The plates were bonded to the inside surface of the shells with BF-2 adhesive. After testing shell No. 2, the plates were removed and the shell was wiped clean with acetone. After that, the plates with b = 7.3 ñm were bonded to shell No. 2 to make it No. 3. The cross section of one of the plate-reinforced shells ( ) k = 6 is shown in Fig. 1. Three shells of the second set (Nos. 4-6) were made from a ÎÒ4-1 titanium alloy rolled sheet. Shell No. 4 was not reinforced. Shells Nos. 5 and 6 were reinforced with plates attached along meridians. The plates of shell No. 5 had length L =37.5 ñm, width b =27.3 ñm, and thickness h =0.03 ñm, while the plates of shell No. 6 had length L =37.5 ñm, width b = 16ñm, and thickness h =0.03 ñm. All the plates had two 1 cm flanges on both long edges. It is by these flanges that the plates were fixed to the inside surface of the shell with five screws spaced at 8.7 cm. Shells Nos. 5 and 6 were reinforced with three and six plates, respectively.2. Determination of Critical Loads. The shells of the first set were tested on a set-up described in [1]. 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. Local buckling occurred under loads of approximately 0.8P (P is the global buckling load) in the shells of the first set and 0.75P in the shells of the second set. The test was stopped once the...

Influence of discretely arranged longitudinal ribs on the stability and vibrations of open circular cylindrical shells

“…These frequencies are strongly dependent on the number and eccentricity of ribs, inner ribs decreasing these frequencies, while outer ribs increasing them. In special cases of deformation, the minimum natural frequencies determined by (1) and (5) are higher than c = 0.7 and the minimum resonant frequencies are higher than c = 0.25, with both being higher than those calculated by (10) in the general case of deformation. The only exception is the minimum natural and resonant frequencies calculated by (1) for shells reinforced with eight ribs.…”

“…Figures 2 and 3 show how the number and discrete arrangement of ribs influence the minimum natural and resonance frequencies calculated by (10) in the general case of deformation. Here the triangles and squares represent outer ribs and inner ribs, respectively; the solid lines represent shells with discrete ribs and the dashed lines structurally orthotropic shells for c = 10 2 1 2 ( ) min w .…”

“…Some other problems for open shells reinforced with either regular or quasiregular sets of ribs were solved in [2,[5][6][7][8]. Similar problems were also addressed in [9,10].In what follows, we will discuss how the discrete arrangement and number of ribs affect the stability of shells subjected to longitudinal compression and vibrations (natural vibrations and resonant states caused by longitudinal compressive stresses close to critical, the associated frequencies being called resonant). …”

“…Some other problems for open shells reinforced with either regular or quasiregular sets of ribs were solved in [2,[5][6][7][8]. Similar problems were also addressed in [9,10].…”

Experimental research of the vibrations of a cylindrical shell filled with some medium and subjected to impulsive loading

“…It is established that the vibroaccelerations are maximum at resonance Introduction. Theoretical and experimental results on the dynamics of thin-walled shell structures are presented in [2][3][4][5][6][7][8]. The ray method was used in [4] to analyze the stress-strain state of mine workings subject to the action of discontinuous waves.…”