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.

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 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.

Rotating cylindrical shells have a wide range of practical applications; however, they are prone to vibrations. Despite numerous theoretical studies on vibration characteristics of Rotating cylindrical shells, experimental validation remains limited.  Using non-contact vibration sensors for an experimental study offers significant advantages, such as eliminating mass effects and avoiding complex wiring associated with attachment to Rotating shells. However, achieving an adequate data acquisition frequency by non-contact sensors in modal analysis of Rotating cylindrical shells necessitates deploying multiple sensors circumferentially, which makes it costly and complex. This difficulty could be mitigated by correct shell selection to enable experimental validation of theoretical studies. The primary objective of the present study is to determine with which dimensions and rotational velocities, an experimental result of vibration characteristics for a Rotating cylindrical shell could be attained by fewer non-contact sensors, which could be interpreted as a first pace toward experimental validation of theoretical methods. To achieve this innovative goal, a parametric study was conducted using an accurate finite element method (FEM) in ANSYS to illustrate how rotational velocity and dimensions affect the required number of sensors. Using the results of the parametric study, optimum values of rotational speed and dimensional parameters have been determined in a way that the experimental vibration analysis could be accomplished with a minimum number of required circumferential non-contact sensors. In the case of the present study, the number of required circumferential sensors is reduced from about 200 for an unsuitable choice to 24 for the choice of the present paper.

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.

In this study, free vibration analysis of a Rotating composite double-layer cylindrical shell has been carried out using first-order shear deformation theory. The shell is made of a thin magneto-electroelastic (MEE) top layer bonded to the functionally graded graphene platelet reinforced (FG-GPLR) porous layer and is subjected to the thermal environment. The two ends of the shell can be considered as pinned boundary conditions due to the presence of bearings that prevent transverse movement. At first, natural frequencies of the forward and backward modes for the Rotating composite shell were obtained and verified by the literature results. Then the effect of rotational speed, mode numbers, temperature change, porosity and GPLs mass fraction on the frequencies were investigated. This study then seeks to investigate the effect of uncertainties in the MEE layer properties on the free vibration of a Rotating composite shell exposed to electric and magnetic potentials. In this case, the uncertainties in the elastic modulus, piezoelectric and piezomagnetic coefficient of the smart layer, are introduced using a symmetric Gaussian fuzzy number. The governing equations for the uncertain system are obtained by combining Hamilton's principle and the dual parametric form of fuzzy numbers; Then the natural frequencies of the uncertain model are calculated using Navier's approach. Free vibration is also investigated by obtaining the natural frequency borders with respect to the various uncertain parameters. The results have shown that the porosity increased the frequencies. In the case of uncertain properties, with increasing of the electric potential, the frequency bounds decreased slightly, but they increased intensely with increasing of the magnetic potential.

The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additional rotational degree of freedom. The resulting element has 24 degrees of freedom, six essential external degrees of freedom at each of the four nodes and thus, avoiding the difficulties associated with internal degrees of freedom (the three translations and three rotations) and the displacement functions of the developed element satisfy the exact representation of the rigid body motion and constant strains (in so far as this allowed by compatibility equations). Numerical experiments analysis have been conducted to assess accuracy and reliability of the present element, this resulting element with the added degree of freedom is found to be numerically more efficient in practical problems than the corresponding Ashwell element [4].

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.