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In the present study, we analyze the nonlinear forced vibration of thin-walled metal foam cylindrical shells reinforced with functionally graded graphene platelets. Attention is focused on the 1:1:1:2 internal resonances, which is detected to exist in this novel nanocomposite structure. Three kinds of porosity distribution and different kinds of graphene platelet distribution are considered. The equations of motion and the compatibility equation are deduced according to the Donnell’s nonlinear shell theory. The stress function is introduced, and then, the four-degree-of-freedom nonlinear ordinary differential equations (ODEs) are obtained via the Galerkin method. The numerical analysis of nonlinear forced vibration responses is presented by using the pseudo-arclength continuation technique. The present results are validated by comparison with those in existing literature for special cases. Results demonstrate that the amplitude–frequency relations of the system are very complex due to the 1:1:1:2 internal resonances. Porosity distribution and graphene platelet (GPL) distribution influence obviously the nonlinear behavior of the shells. We also found that the inclusion of graphene platelets in the shells weakens the nonlinear coupling effect. Moreover, the effects of the porosity coefficient and GPL weight fraction on the nonlinear dynamical response are strongly related to the porosity distribution as well as graphene platelet distribution.

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two ‘self-equilibrated’ states, one natural and the other inside out (or ‘everted’). Though this is familiar from everyday life—an umbrella is remarkably stable, yet a contact lens can be easily turned inside out—the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite-element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more ‘robust’ to snap-through. Our work sheds new light on the robustness of the ‘mirror buckling’ symmetry of spherical shell caps.

This work mainly aims to analyze the natural vibration of the sandwich-structured cylindrical shells using a theoretical framework for the structral with a porous metal core layer. The theoretical model applies the modified thick shell theory (MTST), which includes the initial curvature effect. Designed to reduce structural weight, these shells are composed of a thick porous metal core sandwiched between thin layers of homogeneous metallic material. The comparative study has revealed the advantages of using the MTST over the classical shell theory (CST), emphasizing the limitations of the CST, particularly for large thickness structures with high-frequency modes. This combination in the free vibrational examination of sandwich porous metal shells underscores the accuracy, high reliability, and efficiency of the MTST and the theoretical approach. Furthermore, this work contributes to a deeper understanding of the evaluation and development of these structures for practical applications.

We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.

In this paper, the radial nonlinear vibrations are investigated for a thin-walled hyperelastic cylindrical shell composed of the classical incompressible Mooney–Rivlin materials subjected to a radial harmonic excitation. Using Lagrange equation, Donnell’s nonlinear shallow-shell theory and small strain assumption, the nonlinear differential governing equation of motion is obtained for the incompressible Mooney–Rivlin material thin-walled hyperelastic cylindrical shell. The differential governing equation of motion is simplified to a generalized Duffing equation with the quadratic term. The second-order approximate analytical solutions are obtained by using the modified Lindstedt–Poincaré (MLP) method. The impacts of the parameters on the amplitude–frequency response curves and number of the equilibrium points are analyzed. According to Runge–Kutta method, the bifurcation diagrams, Lyapunov exponents and Poincaré maps are obtained. The chaotic behaviors are found in the radial nonlinear vibrations of the incompressible Mooney–Rivlin material thin-walled hyperelastic cylindrical shell. The results demonstrate that the nonlinear dynamic responses of the incompressible Mooney–Rivlin material thin-walled hyperelastic cylindrical shell are highly sensitive to the structural parameters and external excitation.

We derive the equations for a thin, axisymmetric elastic shell subjected to an internal active stress giving rise to active tension and moments within the shell. We discuss the stability of a cylindrical elastic shell and its response to a localized change in internal active stress. This description is relevant to describe the cellular actomyosin cortex, a thin shell at the cell surface behaving elastically at a short timescale and subjected to active internal forces arising from myosin molecular motor activity. We show that the recent observations of cell deformation following detachment of adherent cells (Maître J-L et al 2012 Science 338 253-6) are well accounted for by this mechanical description. The actin cortex elastic and bending moduli can be obtained from a quantitative analysis of cell shapes observed in these experiments. Our approach thus provides a non-invasive, imaging-based method for the extraction of cellular physical parameters.

Based on the classical shell theory, the linear dynamic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundations subjected to dynamic loads is presented. The truncated conical shells are reinforced by single-walled carbon nanotubes (SWCNTs) that vary according to the linear functions of the shell thickness. The motion equations are solved by the Galerkin method and the fourth-order Runge–Kutta method. In numerical results, the influences of geometrical parameters, elastic foundations, natural frequency parameters, and nanotube volume fraction of FG-CNTRC truncated conical shells are investigated. The proposed results are validated by comparing them with those of other authors.

In this paper, wave propagation in fluid-conveying double-walled carbon nanotube (DWCNT) was investigated by using the nonlocal strain gradient theory. In so doing, the shear deformable shell theory was used, taking into consideration nonlocal and material length scale parameters. The effect of van der Waals force between the two intended walls and the DWCNT surroundings was modeled as Winkler foundation. The classical governing equations were derived from Hamilton’s principle. Results were validated by comparing them to the results of the references obtained through molecular dynamic method, and a remarkable consistency was found between the results. According to the findings, the effects of nonlocal and material length scale parameters, wave number, fluid velocity and stiffness of elastic foundation are more considerable in the nonlocal strain gradient theory than in classical theory.

This work reports the investigations of the electric potential impacts on the mechanical buckling of the piezoelectric nanocomposite doubly curved shallow shells reinforced by functionally gradient graphene platelets (FGGPLs). A four-variable shear deformation shell theory is utilized to describe the components of displacement. The present nanocomposite shells are presumed to be rested on an elastic foundation and subject to electric potential and in-plane compressive loads. These shells are composed of several bonded layers. Each layer is composed of piezoelectric materials strengthened by uniformly distributed GPLs. The Halpin–Tsai model is employed to calculate the Young’s modulus of each layer, whereas Poisson’s ratio, mass density, and piezoelectric coefficients are evaluated based on the mixture rule. The graphene components are graded from one layer to another according to four different piecewise laws. The stability differential equations are deduced based on the principle of virtual work. To test the validity of this work, the current mechanical buckling load is analogized with that available in the literature. Several parametric investigations have been performed to demonstrate the effects of the shell geometry elastic foundation stiffness, GPL volume fraction, and external electric voltage on the mechanical buckling load of the GPLs/piezoelectric nanocomposite doubly curved shallow shells. It is found that the buckling load of GPLs/piezoelectric nanocomposite doubly curved shallow shells without elastic foundations is reduced by increasing the external electric voltage. Moreover, by increasing the elastic foundation stiffness, the shell strength is enhanced, leading to an increase in the critical buckling load.

In this paper, for the first time, the nonlinear vibration response of toroidal shell segments with varying thickness subjected to external pressure is investigated analytically using Reddy’s third-order shear deformation shell theory. The variable thickness shells are made of functionally graded material (FGM) that is created from ceramic and metal constituents. The material properties of FGM shells are assumed to be gradually graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. Equations of motion of variable thickness FGM toroidal shell segments are established based on Reddy’s third-order shear deformation shell theory with von Kármán nonlinearity. The Galerkin method and the Runge–Kutta method are used to solve the governing system of partial differential equations of motion, and then the nonlinear vibration response of variable thickness FGM toroidal shell segment is analyzed. A numerical analysis is also performed to show the effects of material and geometrical parameters on the nonlinear vibration response of variable thickness FGM toroidal shell segments.