Dispersion Equations for Harmonic Waves Propagating along a Cylindrical Shell Reinforced with A Rib Mesh (Single-Mode Approximation)

2009

Self Cite

We obtain the exact solution describing the propagation of harmonic waves along an open cylindrical shell reinforced with a quasiregular set of discrete longitudinal ribs. Numerical examples are used to examine the effect of discrete ribs on the number and shape of dispersion curves and the effect of the stiffness and inertial characteristics of the ribs on the excitation frequency for given wave parameters Introduction. The propagation of harmonic waves along closed circular cylindrical shells reinforced with a regular set of discrete longitudinal ribs is now well understood [3, 12-14, etc.] owing to the exact solution of the equations of motion in the form of a trigonometric series in powers of the coordinate orthogonal to the ribs. A number of new effects due to the discrete arrangement of ribs were revealed, including increased number and changed shape of dispersion curves.In what follows, we will consider, as a numerical example, an open circular cylindrical shell hinged at the longitudinal edges and reinforced with a quasiregular set of discrete longitudinal ribs. We will examine the influence of the discrete arrangement of ribs on the number and shape of dispersion curves for harmonic waves. A set of ribs will be quasiregular if all the geometrical and mechanical characteristics of all ribs are equal, the ribs are equally spaced, and the distance from the extreme ribs to the longitudinal edges of the shell are equal to half the distance between ribs. Such an arrangement of ribs is widely used in mechanical engineering. Rib-reinforced open cylindrical shells were analyzed in [4,7] in the case of a regular set of longitudinal ribs and in [1,2] in the case of a quasiregular set of longitudinal ribs. Similar problems were solved in [8][9][10].

Section: Influence Of Discrete Arrangement Stiffness and Inertial Csupporting

confidence: 83%

Section: Influence Of Discrete Arrangement Stiffness and Inertial Cmentioning

confidence: 99%

Section: Influence Of Discrete Arrangement Stiffness and Inertial Cmentioning

confidence: 99%

Section: Influence Of Discrete Arrangement Stiffness and Inertial Cmentioning

confidence: 99%

“…Figure 3 shows the curves plotted after solving Eq. (14) for n = 1. The curves obtained by solving Eq.…”

Section: Influence Of Discrete Arrangement Stiffness and Inertial Cmentioning

confidence: 99%

See 3 more Smart Citations

Propagation of harmonic waves along open circular cylindrical shells reinforced with a quasiregular set of discrete longitudinal ribs

Abramovich

2009

Self Cite

Natural Vibrations of Ribbed Cylindrical Shells with Low Shear Stiffness

Prokopenko

2005

Self Cite

A technique is proposed to determine the natural frequencies of rib-reinforced cylindrical shells with low shear stiffness. The equations of motion based on the Timoshenko model are used. The influence of the transverse shear moduli of the shell and ribs on the minimum natural frequencies and corresponding modes is studied by way of numerical examples. It is shown that the effect of the discrete ribs is different from that predicted by the classical theory of ribbed shells Keywords: cylindrical shell, grid of ribs, natural frequency, Timoshenko model, transverse shear 1. Introduction. The paper sets out to study the influence of discrete ribs and transverse-shear strains on the natural frequencies and vibration modes of rib-reinforced orthotropic cylindrical shells with low shear stiffness.To describe the deformation of such shells, we will use the equations of motion from the refined theory of shells and rods. The equations are based on the Timoshenko models and account for transverse-shear strains [5,7]. The natural vibrations of ribbed shells made of traditional materials were earlier studied using the equations of motion from the classical theory of ribbed shells [2][3][4]8].The influence of transverse-shear strains on the natural frequencies was examined only for shells reinforced with ribs of one type (stringers or rings) in [6,9,10], where simplified exact solutions of the equations of motion were used. We are unaware of other solutions of this problem. The method used below allows us to cancel some of the assumptions adopted in the above-cited studies.The method to be used to solve the equations of motion is similar to that proposed in [11], where the natural vibrations and stability of a shallow ribbed rectangular shell were analyzed using the classical theory of ribbed shells.The results discussed below are one of the necessary stages in solving a more complicated problem on harmonic waves in a ribbed shell with low shear stiffness. A similar problem was solved in [12][13][14][15] using the classical theory of ribbed shells.2. Original Relations. Consider a closed orthotropic symmetric laminated circular cylindrical shell reinforced with longitudinal and ring ribs. The equations of motion of such a shell are based on the Timoshenko model describing the deformation of the shell and ribs (one-dimensional elastic elements) [5]. Assuming that the grid of ribs is regular (the geometrical and mechanical characteristics of the ribs of one type are equal, the ribs are equally spaced, and the distance between the ring nearest to the shell end and this end is equal to the distance between rings) and introducing dimensionless coordinates and dimensionless geometrical and mechanical characteristics, we write the equations of motion [5]

Edge Resonance in Structurally Orthotropic Cylindrical Shells

2005

Self Cite

Possibilities for edge resonances to occur in structurally orthotropic cylindrical shells through which harmonic waves propagate are studied. It is shown that such resonances may be generated by axisymmetric longitudinal flexural waves propagating in a rigidly clamped semi-infinite shell Keywords: harmonic wave, structurally orthotropic cylindrical shell, edge resonance, axisymmetric longitudinal flexural wave, semi-infinite shell A harmonic force on finite bodies is known to be capable of generating standing modes, along with traveling waves, which, in turn, may cause edge resonances [2]. These resonances in thin shells have been studied inadequately. The only exclusion is the studies cited in [3]. In this connection, we will look into the possibilities for such resonances to occur in reinforced cylindrical shells. Harmonic waves in such shells have been addressed in many publications. Structurally orthotropic shells were considered in [4], and shells reinforced with discrete ribs in [5][6][7][8].We will consider a cylindrical shell reinforced with a rib grid. Its equations of motion are derived from the theory of structurally orthotropic shells on the assumption that both the shell itself (casing) and the ribs are described by the classical theories of shells and rods. It is also assumed that the rib grid is regular, i.e., the ribs of each direction have equal geometrical and mechanical characteristics and are equidistant, and the distance from the shell edge to the nearest ring rib is equal to the distance between rings. The equations of motion can be written as follows [1]: