This paper is focused on the study of nonlinear vibration of Rotating laminated composite cross-ply cylindrical shells on a nonlinear Rotating elastic foundation. In this study, FSDT is employed while the geometrical nonlinearity of the cylindrical shell is modeled considering the von Karman approach. It should be mentioned that this study is accomplished considering the influences of initial hoop tension as well as Coriolis and Centrifugal accelerations. The nonlinear equation of the Rotating laminated composite cross-ply cylindrical shell is extracted via the Ritz method and then is written in the state space form. Then, modal analysis and the multiple scales method are applied to the nonlinear vibration equation in the state space form to obtain relations for nonlinear forward and backward frequency ratios. Validation of the results of this study is investigated considering some results published in the literature and good agreement is observed. Finally, the effects of the nonlinear and linear constants of the Rotating foundation, radius, total thickness, length, and rotation speed on the linear frequencies, nonlinear parameters, and the curves of nonlinear frequency ratios versus amplitude parameters are acquired. The results show that the increase of the nonlinear constant of the Rotating foundation doesn’t influence the linear frequencies. Besides, linear frequencies increase with increase of the linear constants of the Rotating elastic foundation and decrease with increase of the radius or total thickness. Furthermore, the increase of the nonlinear constant of the Rotating elastic foundation or total thickness leads to an increase in nonlinear parameters and nonlinear frequency ratios. Conversely, the increase of the linear constants of the Rotating foundation or the radius leads to a decrease in nonlinear parameters and frequency ratios. Moreover, the increase in amplitude parameters leads to an increase in the nonlinear frequency ratios.

Rotating cylindrical shells are applied in different industrial applications, such as gas turbine engines, electric motors, rotary kilns and rotor systems. So, it is of great interest to conduct some researches to improve the understanding of vibrational characteristics of Rotating cylindrical shells. Grid stiffened laminated composite cylindrical shells are used as components of aerospace, marine industries and civil engineering structures. In this research free vibration of Rotating grid stiffened composite cylindrical shell with various boundary conditions using the Fourier series expansion method is presented. Smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of shell in order to obtain the equivalent stiffness parameters of the whole structure. The stiffeners are considered as a beam and support shear loads and bending moments in addition to the axial loads. Strain displacement relations from Sanders's shell theory are employed in the analysis. Using the Fourier series expansion and Stokes’ transformation, frequency determinant of laminated cylindrical shells is derived.The effects of shell geometrical parameters and changes in the cross stiffeners angle and axial loading on the natural frequencies are investigated. Results given are novel and can be used as a benchmark for further studies.

Hybrid laminates, materials that consist of alternate aluminium alloy and composite laminae, are functionally graded material systems of particular interest to the aerospace industry. In this study, the use of genetic algorithm in stacking sequence optimization of thin Rotating hybrid laminated cylindrical shells is studied. The centrifugal and Coriolis forces are included in the theory and the Navier-type solutions are presented for simply supported boundary conditions. To validate the formulation, results are compared to those from other shell theories. For the optimization problem, two different objective functions that include the weight and Natural frequency of the Rotating cylinder are considered. the objective functions are constrained for the maximum number of contiguous plies. Optimal stacking sequences at different rotational speeds are presented.

In this study, active control of free and forced vibration of Rotating thin laminated composite cylindrical shells embedded with two magnetostrictive layers is investigated by means of classical shell theory. The shell is subjected to harmonic load which is exerted to inner surface of the shell in thickness direction. The velocity feedback control method is used in order to obtain the control law. The vibration equations of the Rotating cylindrical shell are extracted by means of Hamilton principle while the effects of initial hoop tension, centrifugal and Coriolis accelerations are considered in the vibration equations. The differential equations of the Rotating cylindrical shell are converted to ordinary differential equations by means of modified Galerkin method. The displacement of the shell is obtained using modal analysis. The free vibration results of this study are validated by comparison with the results of open literature. Also, the validity of the forced vibration results is proved by comparison with the fourth order Runge-Kutta method's result. Finally, the effects of several parameters including circumferential wave number, rotational velocity, the whole orthotropic layers thickness, magnetostrictive layers thickness, length, the amplitude and exciting frequency of the load on the vibration characteristics of the Rotating cylindrical shell are investigated.

This study provides an approach to predict the springback phenomenon during post-solidification coolingin a functionally graded hybrid composite cylindrical shell with a transverse isotropic structure. Here, thematerial properties are given with a general parabolic power-law function. During the theoretical analysis, an appropriate transformation is introduced in the equilibrium equation, which is resulting in ahypergeometrical differential equation. Thermoelastic solutions are obtained and analyzed for ahomogeneous, nonhomogeneous, and elastic-plastic state. The solution is validated by applying it to themultilayered functionally graded cylindrical shell using the transfer or propagator matrix method.

In this paper, the dynamics and vibration analysis of cylindrical shells made of graphite epoxy layers with two piezoelectric layers at both internal and external surfaces are investigated. Extraction of motion equations is based on Sanders theory for thin shells. Equations of motion, obtained by partial derivatives, are solved by fourth-order Runge– Kutta method. First, we examine a number of geometric parameters of the problem, including shell thickness, radius, length of the shell, and the angle of the fiber in the change of the fundamental frequencies. Finally, the effect of piezoelectric parameters on the vibrational and dynamic response of cylindrical shells has been investigated. In all cases investigated, with an increasing ratio of length to the radius, the effect of piezoelectric coefficients has increased. The results show that among the piezoelectric parameters, the parameter C11 has the most effect on the frequency response so that C11 has a direct relation and C12 has an inverse relationship with the natural frequency. The influence of other piezoelectric parameters has also been evaluated in relation to this parameter in frequency response is negligible.

Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE) -based micromechanical model. This study indicates how buckling resistance of composite cylindrical shell may vary by applying thermal and electrical loads. Applying the reverse voltage or decreasing the temperature, also, increases the critical axial buckling load. This work showed that the piezoelectric BNNT generally enhances the buckling resistance of the composite cylindrical shell.

In the investigation, the vibrations of a Rotating functionally graded cylindrical shell under axial and internal pressure with ring and stringer stiffened and simply supported boundary condition based on Love's shell theory is studied. The cylindrical shell with ring and stringer stiffened widely used in structures such as rockets, submarines and fuel tank of aircraft. The material properties of the Rotating functionally graded (FG) cylindrical shell vary continuously across the thickness according to the power law distribution. In this study considers functionally graded material composed of Nickel and stainless steel, in which FG cylindrical shell has Nickel on its inner surface and stainless steel on its outer surface. The governing equations of a cylindrical shell are derived using Hamilton's principle and energy method and the effect of various parameters such as angular speed, ring and stringer stiffened, axial load, internal pressure and the functionally graded material are investigated. The validity of the results by comparing them with the results of previous research is investigated, in which there is a very good agreement between the results of the present work and previous studies.

Curls and curves of a shell interweave its various strain modes and link them together. This interactional behavior has yet frustrated all attempts for the construction of shell templates, which needs for an individual element test in traditional approaches. Such a test fails to work for shell elements and must be reconstructed. In this paper, it is tried to study shell interactional behavior and strain entanglements via a microscopic investigation. This new view to the shell behavior reveals a simple method, in which shell templates are constructed by partitioning the stiffness matrix of a sample shell element into its components. Surly, sample elements have been qualified for their convergence in practice. The method is examined for axisymmetric cylindrical shell element.