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The free vibration analysis of joined conical–spherical panels and shells of revolution is the primary aim of this investigation. The equations of motion are derived by considering Donnell’s kinematic assumptions and the first-order shear deformation theory (FSDT), which considers the effects of shear deformation as well as rotational inertia. The equations of motion are discretized by using the two-dimensional generalized differential quadratic (2D-GDQ) method in the (x,휃) and (φ,휃) directions for conical and spherical panels and shells, respectively. Natural frequencies of joined conical–spherical shells and panels are determined for different boundary conditions. The accuracy of results has been compared with the results of the other researchers and those obtained using Abaqus and Ansys, which showed good agreement. Moreover, the effects of length, thickness, and the angle of the semi-vertex of the conical shell on the dynamic behavior of joined spherical–conical panels/shells are investigated. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration behavior of a rotating functionally graded conical shell, reinforced by an anisogrid lattice structure. The material properties of the shell are assumed to be graded in the thickness direction. The governing equations have been derived based on classical shell theory and considering the effects of centrifugal and Coriolis accelerations as well as initial hoop tension due to shell rotation. The smeared method is also employed to superimpose the stiffness contribution of the stiffeners with those of the shell to obtain the whole structure's equivalent stiffness parameters. The resulting equations, which are the coupled set of three variable coefficient partial differential equations in terms of displacement components, are solved by the Galerkin method for different boundary conditions. The obtained frequencies are compared with the available literature and the finite element software results. Finally, new results are discussed to show the effect of various parameters such as shell geometrical and material properties, stiffeners, rotating speed, and boundary conditions on natural frequencies. [ABSTRACT FROM AUTHOR]

In this paper, the optimization of piezoelectric patch positions is conducted in order to improve vibration performance of an FG-truncated conical shell. This investigation is done based upon a new optimization trend on a rotating cone for the first time, as well as, the piezoelectric material has been considered functionally graded. The vibration model is based on the classical theory, and the governing equation is obtained using the Lagrange equation. The sensor voltage change rate is selected as feedback signal to vibration control. Four different piezoelectric sets considered with different numbers of piezoelectric Patches. The settling time of the system and position of the piezoelectric patches in longitudinal direction is assumed as an objective function and optimization variable, respectively. Optimization is carried out using sequential quadratic programming and pattern search algorithms. Also, the symmetrical and asymmetrical layouts of the piezoelectric patches in order to study the settling time have been considered. Then, the effect of piezoelectric lengths and arcs on the settling time has been studied. The results show that the best position for piezoelectric placement is in a range between the middle and the base of the cone. [ABSTRACT FROM AUTHOR]

In this study feedback control is applied to control the free vibration response of an isotropic truncated conical shell embedded with magnetostrictive layers. Classical shell theory is applied to derive the shell vibration equations. The results are derived based on the Galerkin method and the results are compared with published results and the results of finite element software in order to determine the accuracy of using method. The influence of several parameters such as the thickness of magnetostrictive layers, control gain, length and radius of the large edge of the shell on the vibration suppression of fundamental frequency is determined. [ABSTRACT FROM AUTHOR]

A theoretical model is presented to investigate the sound transmission through a thin-walled truncated circular conical shell excited by an oblique incident plane sound wave, which impinges on the outer surface of the shell. Love's theory is used to implement the governing equations of the shell motion, and a convergent power series solution is applied to obtain the exact dynamic response of the shell. In order to calculate the acoustic pressure loadings acting on the shell surfaces, the shell is divided into several narrow segments which can be considered to be locally cylindrical. At first, the model predictions are compared with their experimental and analytical counterparts reported in the literature. Then, the effects of crucial design parameters including different boundary conditions at the ends of the shell, cone angle, incident sound wave angle, length, radius, thickness and material properties of the shell, and the material properties of the fluid media are studied on the characteristics of the sound transmission loss. The proposed model can provide an effective tool in the acoustic design stage of the truncated circular conical shells. [ABSTRACT FROM AUTHOR]

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution. [ABSTRACT FROM AUTHOR]

The present study explores the frequency characteristics and critical speeds of rotating functionally graded truncated conical shells stiffened by anisogrid lattice structures. The shell and stiffener structures are transformed into an equivalent conical shell with variable stiffness and density using the smeared method. A dynamic model of the rotating equivalent structure is developed based on the first-order shear deformation theory in order to account for the effects of shear deformation and rotational inertia. By taking centrifugal and Coriolis accelerations and initial hoop tension into account, the motion equations with variable coefficients are derived using Hamilton's principle and then are solved numerically using the generalized differential quadrature method. The obtained results under different conditions are validated by comparing them with existing data in the literature, and reliable precision is observed. A comprehensive parametric study is conducted on the frequencies of backward and forward travelling waves, with a special focus on critical speeds of the proposed conical structure. • Dynamic behaviour of rotating Anisogrid stiffened structures with FG conical skins is investigated. • The shell structure is modelled by first-order shear deformation shell theory. • Bifurcation of frequencies and critical speeds caused by Coriolis effects are explored. • The effects of different parameters on vibration characteristics and critical speeds are studied. [ABSTRACT FROM AUTHOR]

In this paper, the supersonic flutter characteristics of truncated sandwich conical shells with the magnetorheological (MR) core and isotropic homogeneous host and constraining layers are studied. The mathematical modeling of the shell and the aerodynamic pressure sequentially are performed utilizing the first-order shear deformation theory (FSDT) and the supersonic piston theory incorporating the effects of curvature and aerodynamic damping. The set of the governing equations and associated boundary conditions are derived using Hamilton's principle. Through an analytical solution in the circumferential direction and a numerical solution in the meridional direction via the differential quadrature method (DQM), a semi-analytical solution is provided for various boundary conditions. After validation of the presented model, the effects of various parameters on the aeroelastic stability regions of the shell are examined such as magnetic field density, semi-vertex angle, length, total thickness, and thickness of the MR core. [ABSTRACT FROM AUTHOR]

Acoustic transmission through single- and double-walled truncated conical shells lined with poroelastic material is analytically studied. The thin isotropic shells are excited by an oblique plane acoustic wave. The equations of motion of the shells are governed by Love's theory, and the wave propagation within the elastic porous material is described by an equivalent fluid model based on Biot's theory. To extract the acoustic pressures exerting on the surfaces of the conical shells, the shells are divided into several truncated segments which are narrow enough to be considered locally cylindrical. By employing a convergent power series solution the exact dynamic response of the conical shells is obtained. At first, the transmission loss results of this study are validated against those of previous works. Then, the results of various configurations of the single-walled conical shell lined with porous material are compared with those of its double-walled counterpart with equal mass. It is found that the single-walled shell lined with a porous layer is appropriate for sound insulation purposes at low frequencies below the first ring frequency, whereas, at higher frequencies, the double-walled sandwich shell provides better performance and more options for tuning the sound insulation. It is also shown that, except for low frequencies, the effects of the porous material and the method for bonding it to the facing shell are significant to improve the acoustic insulation ability. Finally, the influence of the porous layer thickness is investigated on the sound transmission loss. [ABSTRACT FROM AUTHOR]

Nonlinear vibration control of laminated composite conical shells surrounded by elastic foundations through magnetostrictive layers is presented in this paper. The shell modeled via the consideration of the effects of shear deformation and rotary inertia while von Karman theory of nonlinearity is also employed. In order to suppress the nonlinear vibration, velocity feedback control method is adopted. Modified Galerkin method is exerted to obtain the nonlinear ordinary differential equation of the system from equations obtained via Hamilton principle. The results of this study are acquired with a combination of modal analysis and multiple scales method. The asymptotical stability of the system around zero equilibrium point is investigated based on Lyapunov's indirect method. The results for damping coefficients of nonlinear system and fundamental linear frequency as well as the curves of amplitude versus nonlinear frequency and nonlinear frequency ratio are obtained for different values of several parameters. • Nonlinear vibration control of laminated composite conical shells on elastic foundations has been considered. • Vibration control task has been done through smart magnetostrictive layers via feedback control law. • Modified Galerkin method is applied in order to obtain the shells' nonlinear vibration equation. • A combination of multiple scales method and modal analysis is utilized for obtain of the responses. • Asymptotical stability investigation around zero equilibrium point has been carried out through Lyapunov's indirect method. [ABSTRACT FROM AUTHOR]

• Nonlinear free vibration of laminated composite angle-ply cylindrical and conical shells was studied. • The Ritz method was used for obtaining the ordinary differential equations. • The combination of multiple scales method and modal analysis was used for obtaining the results. This paper presents the combination of multiple scale method and modal analysis in order to investigate nonlinear vibration of laminated composite angle-ply cylindrical and conical shells. The shells are modeled considering the shear deformation and rotary inertia while the geometrical nonlinearity is modeled using von Karman approach. Hamilton principle is used for obtaining the basic equations of the system. These equations are converted to nonlinear ordinary differential equations depending on time variable using Ritz method. The results of this study are validated against the results of open literature and good agreement is observed. The effects of several parameters including the layers' angle, the number of the layers, semi-vertex angle, length, radius and also each layer's thickness on nonlinear frequency ratio, fundamental linear frequency and nonlinear frequency are illustrated in details. [ABSTRACT FROM AUTHOR]