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http://dx.doi.org/10.12989/sem.2002.13.3.329

The dynamic stability of a nonhomogeneous orthotropic elastic truncated conical shell under a time dependent external pressure  

Sofiyev, A.H. (Ondokuz Mayis University, Civil Engineering Department)
Aksogan, O. (Cukurova University, Civil Engineering Department)
Publication Information
Structural Engineering and Mechanics / v.13, no.3, 2002 , pp. 329-343 More about this Journal
Abstract
In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli and density varying in the thickness direction, subject to a uniform external pressure which is a power function of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have been derived. Applying Galerkin's method, these equations have been transformed to a pair of time dependent differential equations with variable coefficients. These differential equations are solved using the method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for the dynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressure impulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, the loading speed, the variation of the semi-vertex angle and the power of time in the external pressure expression on the critical parameters have been studied.
Keywords
dynamic stability; nonhomogeneous; orthotropic; truncated; conical shell; external pressure; Galerkin's method; dynamic critical load; dynamic factor; wave number;
Citations & Related Records

Times Cited By Web Of Science : 9  (Related Records In Web of Science)
Times Cited By SCOPUS : 12
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1 Heyliger, P.R., and Julani, A. (1992), "The free vibrations of inhomogeneous elastic cylinders and spheres", Int. J. Solids and Struct., 29, 2689-2708.   DOI   ScienceOn
2 Lomakin, V.A. (1976), The Elasticity Theory of Nonhomogeneous Materials, Moscow, Nauka. (in Russian)
3 Baruch, M., Harari, O., and Singer, J. (1970), "Low buckling loads of axially compressed conical shells", J. Appl. Mech., 37, 384-392.   DOI
4 Sivadas, K.R., and Ganesan, N. (1991), "Vibration analysis of laminated conical shells with variable thickness", J. Sound and Vibrations, 148, 477-491.   DOI   ScienceOn
5 Tong, L., Tabarrok, B., and Wang, T.K. (1992), "Simple solution for buckling of orthotropic conical shells", J. Solids and Struct., 29, 933-946.   DOI   ScienceOn
6 Tani, J. (1981), "Dynamic stability of truncated conical shells under pulsating torsion", Transactions of the J. Appl. Mech., ASME, 48, 391-398.   DOI
7 Sachenkov, A.V., and Baktieva, L.U. (1978), Research on the theory of plates and shells, "Approach to the Solution of Dynamic Stability Problems of Thin Shells", Kazan State University, Kazan, 13, 137-152. (in Russian)
8 Gutierrez, R.H., Laura, P.A.A., Bambill, D.V., Jederlinic, V.A., and Hodges, D.H. (1998), "Axisymmetric vibrations of solid circular and annular membranes with continuously varying density", J. Sound and Vibrations, 212(4), 611-622.   DOI   ScienceOn
9 Brinkman, J.A. (1954), "On the nature of radiation damage in metals", J. Applied Physics, 25, 961-970.   DOI
10 Delale, F., and Erdogan, F. (1983), "The crack problem for a nonhomogeneous plane", J. Appl. Mech., ASME, 50, 609-614.   DOI
11 Massalas, C., Dalamanagas, D., and Tzivanidis, G. (1981), "Dynamic instability of truncated conical shells with variable modulus of elasticity under periodic compressive forces", J. Sound and Vibrations, 79, 519-528.   DOI   ScienceOn
12 Lam, K.Y., and Hua, L. (1999), "Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell", J. Sound and Vibrations, 223, 171-195.   DOI   ScienceOn
13 Aksogan, O., and Sofiyev, A. (2000), "The dynamic stability of a laminated nonhomogeneous orthotropic elastic cylindrical shell under a time dependent external pressure", Int. Conf. on Modern Practice in Stress and Vibration Analysis, Nottingham, UK, 349-360.
14 Sofiyev, A., and Aksogan, O. (1999), "Dynamic stability of a nonhomogeneous orthotropic elastic cylindrical shell under a time dependent external pressure", Technical Journal, Chamber of Civil Engineers of Turkey, 10, 2011-2028.
15 Tani, J. (1973), "Dynamic stability of truncated conical shells under periodic external pressure", The Report of the Institute of High Speed Mechanics, Tohoku University, Japan, 28, 135-147.
16 Singer, J. (1966), "Buckling of damped conical shells under external pressure", American Institute of Aeronautics and Astronautics J., 4, 328-337.
17 Yakushev, A.N. (1990), "The stability of orthotropic cylindrical shells under dynamic pressure", Research on the Theory of Plates and Shells, Kazan State University, Kazan, 20, 215-222. (in Russian)
18 Massalas, C., Dalamanagas, D., and Raptis, A. (1982), "Dynamic characteristics of conical shell with variable modulus of elasticity", Review Roumanie Sciences Techniques, Mechanics Applications, Bucharest, 27, 609-628.
19 Irie, T., Yamada, G., and Kaneko,Y. (1984), "Natural frequencies of truncated conical shells", J. Sound and Vibrations, 92, 447-453.   DOI   ScienceOn
20 Mecitoglu, Z. (1996), "Governing equations of a stiffened laminated inhomogeneous conical shell", American Institute of Aeronautics and Astronautics J., 34, 2118-2125.   DOI   ScienceOn
21 Sachenkov, A.V., and Aganesov, L.G (1964), "The stability and vibration of circular conical and cylindrical shells at different boundary conditions", Research on the Theory of Plates and Shells, Kazan State University, Kazan, 2, 111-126. (in Russian)
22 Singer, J. (1961), "Buckling of circular conical shells under axisymmetrical external pressure", J. Mech. Eng. Sci., 3, 330-339.   DOI
23 Volmir, A.S. (1967), The Stability of Deformable Systems, Nauka, Moscow. (in Russian)
24 Zhang, X., and Hasebe, N. (1999), "Elasticity solution for a radially nonhomogeneous hollow circular cylinder", J. Appl. Mech., ASME, 66, 598-606.   DOI
25 Sachenkov, A.V. (1976), "The dynamic criterion of the stability of plates and shells", Research on the Theory of Plates and Shells, Kazan State University, Kazan, 12, 281-293. (in Russian)
26 Mushtari, K.M., and Sachenkov, A.V. (1958), Stability of Cylindrical and Conical Shells of Circular Cross Section with Simultaneous Action of Axial Compression and External Normal Pressure, NASA TM-1433.
27 Baktieva, L.U., Jigalko, YU. P., Konoplev, YU. G., Mitryaikin, V.I., Sachenkov, A.V., and Filippov, E.B. (1988), "The stability and vibrations of shells under impulsive distribution and local loads", Research on the Theory of Plates and Shells, Kazan State University, Kazan, l, 113-130. (in Russian)
28 Sachenkov, A.V., and Klementev, G.G. (1980), "Research of the stability of conical shells by theoreticalexperimental method under impulsive load", Research on the Theory of Plates and Shells, Kazan State University, Kazan, 15, 115-125. (in Russian)
29 Tong, L. (1993), "Free vibration of orthotropic conical shells", Int. J. Eng. Sci., 31, 719-733.   DOI   ScienceOn
30 Leissa, A.W. (1973), Vibration of Shells, NASA SP-288.
31 Lekhnitski, S.G. (1980), Theory of Elasticity of an Anisotropic Elastic Body, Holden Day, San Francisco, Also Mir Publishers, Moscow.