Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

Abstract

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak's elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented Keywords: dynamic problems, inhomogeneous shell structures, moving and impulsive loads, Pasternak's elastic foundation, perforated and ribbed shells of revolution, sandwich shell structuresIntroduction. An analysis of the dynamic behavior of real thin-walled structures indicates that their strength is strongly affected by structural inhomogeneities such as ribs, added masses, or layers. The need for improved design models of modern structures necessitates the development of refined methods to design such systems. In this review, we use the vibration equations [3] derived from the classical theories of plates, shells, and beams to analyze and generalize results on the effect of discrete ribs on the natural frequencies and vibration modes of ribbed plates and shells [2,8,68,70,71] and on the number and shape of dispersion curves for harmonic waves in plates and shells [72][73][74][75]. An extensive bibliography on theories and specific dynamic problems for ribbed shells can be found in [9,10,29]. Modified classical and refined theories of shells are used to study the effect of the cement sheath on the wave processes in wells with fluid [15,17,20,23], dynamics of perforated cylindrical manifolds [19,22], and critical velocities of explosive loads in cylindrical shells of different purpose [13,14,16,18,31]. The behavior of various elements of layered shell structures under various impulsive loads is studied in [36, 39, 42-48, 51-55, 67]. Influence of Discrete Ribs on the Dynamic Characteristics of Rectangular Plates and Cylindrical Shells.The influence of discrete ribs on the natural frequencies and vibration modes of ribbed plates and shells is adequately understood [2,68]. However, there remained several important issues that have been addressed only recently. For example, natural frequencies lying close to multiple ones and having very different natural modes were discovered in [8,70,71]. The influence of discrete ribs on the number and shape of dispersion curves for harmonic waves in plates and cylindrical shells was examined in [72][73][74][75]. The relevant studies are analyzed and generalized below using the equations of motion derived in [3] based on the classical theories of plates, shells, and beams. Influence of Discrete Ribs on the Vibration of Rectangular Plates.Let us solve two dynamic problems for ribb...

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.…”

Influence of reinforcement and elastic foundation on the vibrations of shallow shells with rectangular planform

“…Shallow shells with rectangular planform are often used in various fields of engineering. This is why their dynamic behavior is studied in a great many publications [1,2,6,7,[9][10][11]. In this paper, we study the influence of the elastic foundation and the number of ribs on the natural frequencies and modes of such shells.…”

Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

“…Here, we will vary it to analyze in more detail the effect of ribs on the stress-strain state of the shell. The equations to be used to determine the minimum natural frequencies and critical stresses are borrowed from [3,4].We will show that the phenomenon (first discovered in [4]) of significant decrease in the minimum natural frequencies for certain vibration modes and number of ribs is independent of their stiffness.Similar problems of statics, dynamics, and static stability of shells were solved in [5][6][7][8]. …”

“…,(8), and (10) make it possible to determine the critical stresses under axial compression (w 1 0 = ) and natural frequencies ( p = 0).2. Effect of the Stiffness of Ribs on the Minimum Natural Frequencies.Six cases of reinforcement with ribs with rectangular cross-section with an aspect ratio of 10 are considered.…”