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Turan, Ferruh/0000-0002-4160-712X WOS: 000467538600005 This paper investigates the parametric instability (PI) of multilayered composite conical shells (MLCCSs) under axial load periodically varying the time, using the first order shear deformation theory (FOSDT). The basic equations for the MLCCSs are derived and then the Galerkin method is used to obtain the ordinary differential equation of the motion. The equation of motion converted to the Mathieu-Hill type differential equation, in which the DI is examined employing the Bolotin's method. The expressions for left and right limits of dimensionless parametric instability regions (PIRs) of MLCCSs based on the FOSDT are obtained. Finally, the influence of various parameters; lay-up, shear deformations (SDs), aspect ratio, as well as loading factors on the borders of the PIRs are examined.

Allahverdiev, Bilender P./0000-0002-9315-4652; Turan, Ferruh/0000-0002-4160-712X; Zerin, Zihni/0000-0001-7906-8136 WOS: 000417616500006 The dynamic instability of truncated conical shells subjected to dynamic axial load within first order shear deformation theory (FSDT) is examined. The conical shell is made from functionally graded (FG) orthotropic material. In the formulation of problem a dynamic version of Donnell's shell theory is used. The equations are converted to a Mathieu-Hill type differential equation employing Galerkin's method. The boundaries of main instability zones are found applying the method proposed by Bolotin. To verify these results, the results of other studies in the literature were compared. The influences of material gradient, orthotropy, as well as changing the geometric dimensions on the borders of the main areas of the instability are investigated.

The stability of elastic cylindrical thin shells of variable thickness along the directrix and of elastic properties varying continuously depending on the thickness coordinates, subject to a uniform external pressure which is a power function of time, was investigated. Firstly, fundamental relations and the modified Donell-type stability equations of the non-homogeneous elastic cylindrical thin shells with variable thickness were derived. Applying Galerkin's method, a differential equation having a variable coefficient depending on time wass obtained and by applying the method of Sachenkov and Baktieva (1978) to these equations, general formulas for static and dynamic critical loads, corresponding wave numbers, and the dynamic factor were obtained. The appropriate formulas for elastic cylindrical thin shells made of homogeneous and non-homogeneous materials with uniform thickness were specifically obtained from these formulas.Finally, performing the computations, the effects of linear and sinusoidal variation of shell thickness, linear, parabolic, and exponential variation of elastic properties, and the variation of variation factor due to time on critical parameters were investigated.

The buckling of laminated orthotropic cylindrical thin shells under torsion, which is a linear function of time, has been investigated. First, fundamental relations and the modified Donnell type stability equations of the laminated cylindrical thin shells are derived. Applying Galerkin's method, a differential equation having a variable coefficient depending on time is obtained and by applying the Ritz-type variational method to these equations, general formulas for static and dynamic critical loads, corresponding wave numbers and the dynamic factor are obtained. Finally after performing the computations, the effects of the variations of the numbers and ordering of layers, loading speed, and the ratio of radius to thickness on the critical parameters are investigated.

In this study, the dynamic stability of a laminated orthotropic truncated conical shell, subjected to an external pressure which is a power function of time, was considered. First, the modified Donnell-type dynamic stability and compatibility equations of a laminated orthotropic truncated conical shell, subjected to an external pressure, were obtained. Applying the Galerkin and Sachenkov and Baktieva (1978) methods one after the other, the static and dynamic critical external pressures, the pertinent wave numbers and the dynamic factor were found explicitly. Finally, carrying out some computations for cross-ply laminated truncated conical shells, the effects of the variation of the number and orientation of the layers and the power function of time in the external pressure expression on the critical parameter were studied.

The dynamic stability of a non-homogeneous elastic conical shell under a time dependent uniform external pressure varying as a power function is investigated in this study. Dynamic stability and displacement compatibility equations of the non-homogeneous elastic conical shell under external pressure are obtained. Applying Galerkin's method, fundamental equations are reduced to a time dependent differential equation with variable coefficients. Then, by applying the method of Sachenkov and Baktieva (1978), general formulas for dynamic and static critical loads, wave numbers, and the corresponding critical time, critical impulse and dynamic factor are obtained. From these formulas, formulas for a homogeneous isotropic elastic shell are found. The effects of non-homogeneity and the power of time in the external pressure expression on the critical parameters are studied through pertinent computations. It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading.

The dynamic stability of orthotropic cylindrical thin shells of exponentially variable geometric and mechanical parameters is studied by using Galerkin and Ritz type variotional methods. The qualitative and quantitative effects of the external geometry, material properties, and design features on the critical loads, corresponding wave numbers, and the dynamic factor are evaluated. Comparing results with those in the literature validates the present analysis. © 2006, Emerald Group Publishing Limited

This article deals with the vibrational behavior of composite conical shells (CCSs) reinforced with carbon nanotubes (CNTs) resting on Winkler- and Pasternak-type foundations. A generalized version of the Ambartsumian's first-order shear deformation theory (FSDT) is here proposed to handle the vibration problems for CCSs reinforced with CNTs, resting on an elastic foundation, while considering a uniform and functionally graded (FG) distribution for the reinforcement phase throughout the shell thickness. The basic equations of the problem are determined and solved in closed form by means of the Galerkin procedure. First, we check for the reliability and accuracy of the proposed formulation with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the foundation stiffness, the type of distribution, and the volume fraction of CNTs.