Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

Abstract

Introduction.Extensive literature is devoted to the problem of vibrations of, mainly, perfect smooth and ribbed shells. First results on free and forced vibrations of plates and smooth shells are reported in [8,19,20]. Dynamic problems for shallow shells with deflections of high amplitudes are reviewed and experimental results are presented in [22,24]. The paper [7] proposes an approach to study the free vibrations of a wide class of shallow isotropic and anisotropic shells with arbitrarily varying thickness and complex boundary conditions. The vibrations of shell structures are studied in [21,31,32], where the method of spline functions is used. The paper [33] uses R-functions and variational methods to study the free vibrations of shallow shells of complex shape in plan and to solve a number of problems for shallow shells with canonical and compound planforms.Vibrations of shells with design features are studied in [1-4, 26, 28, 32, 35, 36], where the design features are reinforcing elements in the form of one-dimensional rods resisting tension/compression, bending, and torsion.In [1,26], expressions for the potential and kinetic energies of structurally orthotropic shells were derived, the natural frequencies of conical shells reinforced with arbitrarily spaced elastic ribs were determined, and theoretical and experimental minimum frequencies were presented. The fundamental tone of vibrations corresponded to a nodeless longitudinal mode. The theoretical and experimental frequencies differed by 10-12% (depending on the number of ring ribs). Design procedures for reinforced shells are outlined in [2-4, 17, 18, 23, 25, 29, 34, 35]. The paper [17] proposed a procedure to analyze the free vibrations of ribbed cylindrical shells taking into account the shell-rib interaction and the eccentricity of ribs, derived an analytic formula to determine the natural frequencies, and reported data for shells with reinforcements of various types. It was revealed that the number of rings has the strongest effect on the minimum natural frequency, and the greater the number of stringers, the less this frequency. The natural frequencies of reinforced conical shells were studied in [18,29] taking into account the eccentricity of ribs. Studies on the dynamic characteristics of shells with discrete inclusions are reviewed in [5].A special research area in dynamics of shells is the vibrations of shells with added masses [3,28]. The paper [28] proposed an approximate method to calculate the minimum natural frequency of a spherical shell with an added mass taking into account the contact area. Theoretical results were compared with experimental data. It was revealed that even in the presence of a small mass, the minimum natural frequency corresponds to an axisymmetric mode strongly localized near the contact area. 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 agre...

Simulation of dynamic processes of shell structures with viscoelastic elements

“…In article [8], a method is proposed for calculating the natural frequencies of ribbed cylindrical shells with local axisymmetric deflections. The influence of the initial imperfections of two types on the minimum vibration frequencies is analyzed.…”

Effect of Static Loads on the Natural Vibrations of Ribbed Shells

“…Problems of stability and natural vibrations of shallow panels are classical in the theory of thin elastic shells. Numerous literatures are devoted to their study [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Methods and algorithms for solving nonlinear stability problems and determining the parameters of natural vibrations are investigated on this type of shells, mainly of constant thickness.…”

“…Methods and algorithms for solving nonlinear stability problems and determining the parameters of natural vibrations are investigated on this type of shells, mainly of constant thickness. The shells are designed step-variable thickness (reinforced with ribs and overlays) to increase the overall rigidity of the thin-walled structure (and, correspondingly, its loadbearing capacity) [1][2][3][4][10][11][12]. Static loads significantly affect both the stressstrain state of the structure and its dynamic characteristics, which include frequencies and forms of natural vibrations [5-8, 15, 16].…”