Free Vibrations of Laminated Composite Noncircular Thin Cylindrical Shells

This paper focuses on an analysis of free vibration of thick rotating stiffened composite cylindrical shells with different boundary conditions. The analysis is performed on the basis of a three-dimensional theory by using the layerwise-differential quadrature method (LW-DQM). The equations of motion are derived employing Hamilton’s principle. In order to accurately allow for the thickness effects, a layerwise theory is used to discretize the equations of motion and related boundary conditions through the thickness of the shells. Then, the equations of motion and the boundary conditions are transformed into a set of algebraic equations by using the DQM in the longitudinal direction. This study demonstrates the applicability, accuracy, stability, and fast rate of convergence of the present method in free vibration analyses of rotating stiffened cylindrical shells. The presented results are compared with those of other shell theories obtained by conventional methods and with a special case where the number of stiffeners approaches zero, i.e., an nonstiffened cylindrical shell, and excellent agreements are achieved. Finally, some new results are presented, which can be used as benchmark solutions for future investigations.

A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures

The composite cylindrical shell pressure structure is widely used for autonomous underwater vehicle (AUV). To analyze the critical buckling problem of variable stiffness (VS) composite pressure structure of AUV, a discrete finite element (DFE) method based on the curve fiber path function is developed in this work. A design and optimization method based on the radial basis function surrogate method is proposed to optimize the critical buckling pressure for a VS composite cylindrical shell. Both the DFE and surrogate methods are verified to be valid by comparison with the experimental data from the listed references. The effects of the geometric parameter and fiber angle on the critical buckling pressure are studied for different cylindrical shell cases. The results indicate that the proposed simulation model and optimization method are accurate and efficient for the buckling analysis and optimization of a VS composite cylindrical shell. Optimization result shows that the optimum critical buckling pressure for the VS cylindrical shell is improved and is 21.1% larger than that of the constant stiffness cylindrical shell under the same geometric and boundary condition.

This paper presents a methodology for designing piezoelectric sensors/ actuators in an application to monitor/generate flexural and torsional vibrations of cylindrical Shells. Based upon the classical laminate theory the equations of the electro-mechanical interactions, the constitutive, and the strain-displacement relations of piezoelectric composite cylindrical shells are derived. With these relations the piezoelectric sensor and actuator equations of the cylindrical shell are then developed. The modal sensors/actuators fabricated with PVDF embedded in the composite cylindrical shell capable of monitoring and generating vibrations of a particular mode or several combined modes are also developed. Finally, an experimental rig is designed to generate both the flexural and the torsional vibrations of a. circular cylindrical shaft for examining the capabilities of the modal sensors.

A comparison between the vibration of fiber-metal laminate (FML) and composite cylindrical shells has been studied in this manuscript. Love’s first approximation shell theory has been applied to obtain Strain-displacement relations. In addition, beam modal function model has been used to analyze the cylindrical shell with different boundary conditions. In this manuscript, the frequencies of FML and composite cylindrical shells have been compared to each other for different materials, lay-ups, boundary conditions, axial and circumferential wave numbers. The most commercially available FMLs are CARALL (carbon reinforced aluminium laminate), and GLARE (glass reinforced aluminium laminate), which are studied in this research. The results showed although the frequencies of carbon/epoxy are greater than glass/epoxy for all of the n, this process is not constant for FML. Also, with increasing the n, the frequencies of FML cylindrical shells are converged more faster than the composite one. Moreover, the frequencies of both boundary conditions are converged with increasing n for both FML and composite cylindrical shells.

This work investigates nonlinear harmonic resonance behaviors of graded graphene-reinforced composite spinning thin cylindrical shells subjected to a thermal load and an external excitation. The volume fraction of graphene platelets varies continuously in the shell’s thickness direction, which generates position-dependent useful material properties. Natural frequencies of shell traveling waves are derived by considering influences of the initial hoop tension, centrifugal and Coriolis forces, thermal expansion deformation, and thermal conductivity. A new Airy stress function is introduced. Harmonic resonance behaviors and their stable solutions for the spinning cylindrical shell are analyzed based on an equation of motion which is established by adopting Donnell’s nonlinear shell theory. The necessary and sufficient conditions for the existence of the subharmonic resonance of the spinning composite cylindrical shell are given. Besides the shell’s intrinsic structural damping, the Coriolis effect due to the spinning motion has a contribution to the damping terms of the system as well. Comparisons between the present analytical results and those in other papers are made to validate the existing solutions. Influences of main factors on vibration characteristics, primary resonance, and subharmonic resonance behaviors of the novel composite cylindrical shell are discussed. Furthermore, the mechanism of how the spinning motion affects the amplitude–frequency curves of harmonic resonances of the cylindrical shell is analyzed.

A new closed form formulation of three-dimensional (3-D) refined higher-order shell theory (RHOST) to analyze the free vibration of composite circular cylindrical shells has been presented in this article. The shell is considered to be laminated with orthotropic layers and simply supported boundary conditions. The proposed theory is used to investigate the effects of the in-plane and rotary inertias as well as transverse normal and shear strains on the dynamic response of thick composite cylindrical shells. The trapezoidal shape factor of the shell element is incorporated to obtain accurate stress-resultants. Using Hamilton’s principle, the equations of motion are obtained and solved in terms of the Galerkin method. Numerical results for the natural frequencies are verified by making comparison with the 3-D exact elasticity iterative solutions in the literature. In addition, the validity of the results is further verified by ABAQUS. According to the results, for thick composite cylinders with large length-to-radius and orthotropic ratios, through thickness exact integration yields accurate stress-resultants for proper prediction of the natural frequencies.

Axially compressed composite cylindrical shells can attain multiple bifurcation points in their post-buckling procedure because of the natural transverse deformation restraint provided by their geometry. In this paper, the post-buckling analysis of functionally graded (FG) multilayer graphene platelets reinforced composite (GPLRC) cylindrical shells under axial compression is carried out to investigate the stability of such shells. Rather than the critical buckling limit, the focus of the present study is to obtain convergence post-buckling response curves of axially compressed FG multilayer GPLRC cylindrical shells. By introducing a unified shell theory, the nonlinear large deflection governing equations for post-buckling of FG multilayer GPLRC cylindrical shells with wide range of thickness are established, which can be easily changed into three widely used shell theories. Load-shortening curves for both symmetric and asymmetric post-buckling modes are obtained by Galerkin's method. Numerical results illustrate that the present solutions agree well with the existing theoretical and experimental data. The effects of geometries and material properties on the post-buckling behaviours of FG multilayer GPLRC cylindrical shells are investigated. The differences in the three shell theories and their scopes are discussed also.

The dynamic stability behavior of rotating functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells under combined static and periodic axial forces is investigated. The governing equations are derived based on the first-order shear deformation theory (FSDT) of shells. The initial mechanical stresses due to the steady state rotation of the shell are evaluated by solving the dynamic equilibrium equations. The equations of motion under different boundary conditions are discretized in the spatial domain and transformed into a system of Mathieu–Hill type equations using the differential quadrature method (DQM) together with the trigonometric series. The influences of both the initial mechanical stresses and Coriolis acceleration are considered. Then, the parametric resonance is analyzed and the dynamic instability regions are determined by employing the Bolotin’s first approximation. After validating the approach, the effects of rotational speed, Coriolis acceleration, carbon nanotubes (CNTs) distribution in the thickness direction, CNTs volume fraction, length and thickness-to-mean radius ratios on the principal dynamic instability regions are examined in detail.

A higher order theory for vibration of shear deformable cylindrical shallow shells

3D braided composite is gaining popularity over the traditional composite because it has a higher impact resistance, fatigue strength, stiffness in the thickness direction, anti-delamination capability, etc. Based on bridging models, the fibers are considered as transversely isotropic and matrix isotropic. The equivalent material properties of the composites are computed using a volume averaging method (VAM). The four steps 1 × 1 braided technique are introduced to manufacture the 3D braided singly and doubly curved shell panels. The bridging model claimed to be more accurate in predicting mechanical properties and shear modulus in comparison with the other method. In the present study, the free vibration response of 3D braided curved panels is obtained using finite element methods (FEM). A third-order shear deformation (TSDT) with twelve degrees of freedom per node is for the first time employed in 3D braided panels using eight nodded isoparametric formulation. In this theory, the transverse displacement is the function of the thickness coordinate. In reality, the normal stress of the thick shells in the thickness direction can't be neglected. This theory having the capability of predicts the normal stress in the thickness direction. Hence, to predict the accurate results of the 3D braided shell, it has more capability compared to the other shell theory. The free vibration results of the shell panels' viz. cylindrical shells (CYS), elliptical paraboloid shells (EPS), and hyperbolic paraboloid shells (HPS) are computed at a different braided angle, braided volume fraction, aspect ratio, thickness ratio, curvature ratio, and boundary conditions, etc. HIGHLIGHTS The equivalent material properties of the 3D braided composites are calculated using bridging models based on a volume averaging method (VAM). The bridging model claimed to be more accurate in predicting mechanical properties and shear modulus in comparison with the other method. A third-order shear deformation (TSDT) with twelve degrees of freedom per node is for the first time employed in 3D braided panels using eight nodded isoparametric formulation. In this theory, the transverse displacement is the function of the thickness coordinate. To predict the 3D braided shell's accurate results, it has more capability than the other shell theory. The free vibration results of the shell panels' viz. cylindrical shells (CYS), elliptical paraboloid shells (EPS), and hyperbolic paraboloid shells (HPS) are computed at a different braided angle, braided volume fraction, aspect ratio, thickness ratio, curvature ratio, and boundary conditions, etc.

Free vibration of thin-walled composite box beams

Micropolar beam models for lattice grids with rigid joints

Geometrically nonlinear transient analysis of laminated composite super-elliptic shell structures with generalized differential quadrature method

Compression buckling of elastically supported cylindrical shells with Bend/Twist coupling