Sharif Digital Repository

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton's principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all... 

In this study, the buckling of two joined isotropic conical shells under axial compression and simply supported boundary conditions is investigated. The governing equations are obtained using thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved by assuming trigonometric response in circumferential and series solution in meridional direction. The results are validated in comparison with the available results in the literature. Effects of semi-vertex angles and meridional lengths on the buckling load... 

In the present study, a simple analytical method is introduced for determination of natural frequencies of generally laminated conical and cylindrical shells with arbitrary boundary conditions. The governing equations of motion employed are those of thin-walled shell theory of Donnell. The free-vibration equations are solved using state space method and series solution in meridional direction. The results are compared and validated with the available especial results in the literature. The effects of bending-stretching coupling, semi-vertex angle, meridional length, shell thickness, fiber directions of composite plies, and lamination sequences on the natural frequency of conical and... 

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of... 

Nonlinear vibrations of viscoelastic thin cylindrical shells are studied in this paper. The viscoelastic properties are modeled using the Kelvin–Voigt fractional-order constitutive relationship. Based on the nonlinear Love thin shell theory, the structural dynamics of the cylindrical shell is modeled by using the Newton’s second law, and the Galerkin method is used to discretize the nonlinear partial differential equations into the set of nonlinear ordinary differential equations. The method of multiple scales is used to solve the nonlinear ordinary differential equations, and the amplitude–frequency and phase–frequency equations are extracted. The obtained results are verified with... 

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to... 

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to... 

Design and performance of a beam shaping device based on a simple flexible plastic fiber-bundle stripe and a prism duct is described in this study. Such a system offers practical means to modify and change the output beam shape and also provides quantitative information concerning the transmitted power. It is possible to measure transmitted power signal by using a precise photodetector and also analyze beam images taken by a digital camera. The photograph picture of the illuminating LED beam just at its output point shows a circular shape with a radius of about 4 mm and the fiber-bundle output beam is rectangular shape with a dimension of 22.5×2 mm. A regular duct is tested in this study and... 

In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton's principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted.... 

This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. Specially, the feasibility problem of the position norm constraints is considered in this paper. Under assumptions, it is proved that if a position vector be reachable, then the reach time and the corresponding time of impulses are unique. The trajectory boundedness of the spacecraft between adjacent impulses are analyzed using the Gerschgorin and the Rayleigh-Ritz theorems as well as a finite form of the Jensen's inequality. Some... 

A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying... 

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous 'competing' buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are... 

This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical... 

Buckling of generally laminated conical shells under uniform torsion with simply-supported boundary conditions is investigated. The Donnel type strain displacement relations are used to obtain potential strain energy of the shell and membrane stability equation is applied to acquire the external work done by torsion. The Ritz method is used to solve the governing equations and critical buckling loads are obtained. The accuracy of the results is validated in comparison of with other investigations and finite element method. The effects of lamination sequence, semi-vertex angle and length to radius ratio of the cone are evaluated and mode shapes are presented for two types of lamination... 

This paper presents an orbit estimation using non-simultaneous horizon detector measurements in the presence of uncertainties in the celestial body rotational velocity and its geometrical characteristics. The celestial body is modeled as a tri-axial ellipsoid with a three-dimensional force field. The non-simultaneous modelling provides the possibility to consider the time gap between horizon measurements. An unscented Kalman filter is used to estimate the spacecraft state variables and the geometric characteristics as well as the rotational velocity vector of the celestial body. A Monte-Carlo simulation is implemented to verify the results. Simulations showed that using non-simultaneous... 

A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only effective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Furthermore, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on... 

A new shape-based geometric method (SBGM) is proposed for generation of multi-impulse transfer trajectories between arbitrary coplanar oblique orbits via a heuristic algorithm. The key advantage of the proposed SBGM includes a significant reduction in the number of design variables for an N-impulse orbital maneuver leading to a lower computational effort and energy requirement. The SBGM generates a smooth transfer trajectory by joining a number of confocal elliptic arcs such that the intersections share common tangent directions. It is proven that the well-known classic Hohmann transfer and its bi-elliptic counterpart between circular orbits are special cases of the proposed SBGM. The... 

This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground or a space-based station. The current study is particularly useful for small private launching companies with limited access to global observations around the Earth and for orbital maneuvers around other planets for which the orbital observations are limited to the in situ equipment. An appropriate cost function is introduced for the sake of minimizing the total control/impulse effort as well as the orbital uncertainty. It is subsequently proved that for a... 

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz... 

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz...