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Investigated in this paper is the nonlinear forced vibration response of axially moving graphene platelet-reinforced metal foams (GPLRMF) conical shells. According to Reddy’s high-order shear deformation theory and von Karman’s geometric nonlinearity, the governing equations with highly nonlinear terms for the GPLRMF conical shells are obtained and discretized by Galerkin principle. Subsequently, considering the simply supported boundary condition, the multiple scale method is employed to determine the amplitude-frequency response curves of GPLRMF conical shells. Numerical analyses are performed to verify the correctness of present method. In the end, the effects of porosity distribution form, graphene platelets (GPLs) distribution pattern, damping coefficient, porosity coefficient, coning angle, GPLs weight fraction, geometrical dimensions and the position of the external load, axially moving velocity as well as pre-stressing force on the nonlinear-forced vibration response curves of the GPLRMF conical shells are presented.

The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied. A step function and a porosity volume fraction are introduced to describe the porosities in FGM layers of sandwich shells. Using the Donnell’s nonlinear shallow shell theory and Hamilton’s principle, an energy approach is employed to gain the nonlinear equations of motion. Afterwards, the multi-degree-of-freedom nonlinear ordinary differential equations are carried out by using Galerkin scheme, and subsequently the pseudo-arclength continuation method is utilized to perform the bifurcation analysis. Finally, the effects of the core-to-thickness ratio, porosity volume fraction, power-law exponent, and external excitation on nonlinear forced vibration characteristics of FGM sandwich shells with porosities are investigated in detail.

Vortex-induced vibration (VIV) systems with stiffness nonlinearity have received increasing attention because the stiffness nonlinearity can broaden the effective flow velocity range for energy harvesting or achieve broadband VIV suppression. Reduced-order mathematical models are useful when it is necessary to analyze and optimize a VIV-based system with stiffness nonlinearity. However, the accuracy of existing reduced-order models in simulating the VIV of a structure with nonlinear stiffness remains unknown. This investigation proposes to predict the VIV of a circular cylinder with nonlinear stiffness using harmonically forced vibration data. The transverse force coefficients of a circular cylinder at a Reynolds number of Re  = 150 are identified based on computational fluid dynamics (CFD) simulations with harmonically forced vibrations. The forced vibration data are utilized to predict the VIV responses of a circular cylinder with cubic nonlinear stiffness and a circular cylinder with a nonlinear energy sink (NES) attachment. The predictions based on forced vibration data are compared with free vibration CFD simulations to validate the accuracy of the proposed method. Numerical examples suggest that the forced vibration data can qualitatively and to some extent quantitatively predict the VIV responses of the considered nonlinear systems. Hence, the reduced-order model with forced vibration data can serve as an effective tool for analyzing and optimizing VIV systems with stiffness nonlinearities.

Multi-harmonic excitations are commonly observed in rotor systems and affect their nonlinear characteristics significantly. However, most of the published nonlinear studies on rotating structures only consider single-harmonic excitation. Compared with single-harmonic issues, multi-harmonic excitations increase the difficulty of calculation and solution exponentially. The purpose of this paper is to establish the nonlinear coupled mechanical model and analyze nonlinear forced vibrations of rotating shells subjected to multi-harmonic excitations in thermal environment. The nonlinear governing equations, considering the Coriolis forces, centrifugal force, initial hoop tension and thermal effect, are obtained by the improved Donnell nonlinear shell theory and Hamilton principle, and then, the multi-mode Galerkin technique is introduced to transform the partial differential equations into multi-degree-of-freedom nonlinear ordinary differential equations (ODEs). Afterward, numerical simulations are conducted by the pseudo-arc-length continuation algorithm. The verification of the solutions with available results in the literature and the convergency of the results are presented. At last, the effects of main factors on nonlinear dynamic response of rotating shells are evaluated. It can be observed that since the multi-DOF coupled system, which is excited by multi-harmonics, exhibits complex nonlinear dynamic responses of rotating shells, the nonlinear multiple internal resonances occur.

This paper aims to investigate the nonlinear forced vibration characteristics of hybrid fiber/graphene nanoplatelets/polymer composite sandwich cylindrical shells with hexagon honeycomb core (HHC) in a hygrothermal environment. Firstly, an analytical model for such shells is proposed, where the equivalent material parameters of skins are determined based on the law of the mixture and homogenization approach, and the improved Gibson's technique is adopted to estimate the equivalent material properties of HHC. Furthermore, the first-order shear deformation theory together with von Kármán geometric nonlinearity terms and Hamilton’s principle is utilized to obtain the nonlinear governing equations that consider the effect of hygrothermal and mechanical loads, which are further discretized into a series of ordinary differential equations via the Galerkin approach. Subsequently, the static condensation technique and the multiple scale method are utilized to solve the nonlinear forced vibration responses, including primary, super- and sub-harmonic resonances. The results obtained by the present model are compared to the ones from the literature to prove the effectiveness of the proposed model. Also, the influences of key parameters on the nonlinear dynamic performance of the structure are evaluated, with some critical conclusions related to reducing the nonlinear resonance amplitude and resonance region of the structure being summarized.

In the paper, a novel magneto-electro-elastic model of bi-directional (2D) functionally graded materials (FGMs) beams is developed for investigating the nonlinear dynamics. It is shown that the asymmetric modes induced by the 2D FGMs may significantly affect the nonlinear dynamic responses, which is tremendously different from previous studies. Taking into account the geometric nonlinearity, the nonlinear equation of motion and associated boundary conditions for the beams are derived according to the Hamilton’s principle. The natural frequencies and numerical modes of the beams are calculated by the generalized differential quadrature method. The frequency responses of the nonlinear forced vibration are constructed based on the Galerkin technique incorporating with the incremental harmonic balance approach. The influences of the material distributions, length–thickness ratio, electric voltage, magnetic potential as well as boundary condition on the nonlinear resonant frequency and response amplitude are discussed in details. It is notable that increasing in the axial and thickness FG indexes, negative electric potential and positive magnetic potential can lead to decline the nonlinear resonance frequency and amplitude peak, which is usually applied to accurately design the multi-ferroic composite structures. Furthermore, the nonlinear characteristics of motion can be regulated by tuning/tailoring the 2D FG materials.

Combining the spectral geometry method and the incremental harmonic balance method (IHB), the nonlinear analytical model of functionally graded graphene platelet reinforced composite (FG-GPLRC) beams is developed in this paper. Nonlinear free and forced vibration characteristics are studied based on this model containing viscoelastic foundation and geometric nonlinear factors. Geometric nonlinear strain–displacement relationship and Lagrangian energy generalization for the FG-GPLRC beam structure are derived according to the Von-Kármán and Timoshenko theories. The IHB method is applied to track the nonlinear vibration response solution of the reduced-order model, which is constructed by introducing linear modal components into the overall nonlinear dynamic equation of the FG-GPLRC beam. Through comparison of the present solution with those from numerical method and literature, the correctness of the established nonlinear analytical model is evidenced. Further, the influence of material-, geometry-, foundation-related parameters and boundary constraints on the nonlinear frequency parameter and amplitude-frequency response of FG-GPLRC beams rested on viscoelastic foundation is analyzed, which can serve as a theoretical guide for designing and evaluating the dynamic environment adaptation of FG-GPLRC beams.

Significant advances in the field of composite structures continue to be made on a variety of fronts, including theoretical studies based on advances in structural theory kinematics and computer models of structural elements employing advanced theories and unique formulations. Plate vibration is a persistently interesting subject owing to its wider usage as a structural component in the industry. The current study was carried out using the Co continuous eight-noded quadrilateral shear-flexible element having five nodal degrees of freedom, which is ground on first-order shear deformation theory (FSDT). For small strain and sufficiently large deformation, the geometric nonlinearity is integrated using the Von Kármán assumption. The governing equations in the time domain are solved employing the modified shooting technique along with an arc-length and pseudo-arc-length continuation strategy. This work explored the effect of fiber angle on the steady-state nonlinear forced vibration response. To explain hardening nonlinearity, the strain and stress fluctuation throughout the thickness for a rectangular laminated composite plate is determined. The cyclic fluctuation of the steady-state nonlinear normal stress during a time period at the centre of the top/bottom surfaces is also provided at the forcing frequency ratio of peak amplitude in a nonlinear response. Because of the variation in restoring forces, the frequency spectra for all fiber angle orientations show significantly enhanced harmonic participation in addition to the fundamental harmonic.

In recent years, there has been a growing trend in the application of hyperelastic pipes across several engineering fields, especially in bioengineering and biomedical engineering. For further understanding the dynamic behavior of hyperelastic pipes conveying fluid, this study proposes a mathematical model for the nonlinear forced vibrations of simply supported hyperelastic pipes based on the Yeoh's hyperelastic model. Some numerical methods are employed for verification purposes and to solve the dynamical system. In the discussion part, a series of significantly different results can be drawn about the hyperelastic pipe compared with linearelastic ones. Particularly, compared with the linearelastic pipe system with cubic nonlinearity only, the coupled effect of the nonlinear geometric relations and hyperelastic constitutive relations lead to the simultaneous existence of different order nonlinearities in the hyperelastic pipe model, including quadratic, cubic, quartic or quantic nonlinearities. Softening behaviors of the hyperelastic pipe can be observed, which are mainly caused by the combined influence of nonlinear constitutive relation (used hyperelastic model) and nonlinear geometric relation. Additionally, linear and low-order nonlinear terms in the hyperelastic pipe model play much more important roles in influencing nonlinear dynamic responses than high-order nonlinear ones. Furthermore, it is clarified that fluid–structure interactions (FSIs) between the internal fluid and the hyperelastic pipe have a significant influence on nonlinear dynamic responses by dominating the linear characters instead of the nonlinear ones.

Most studies on the nanoscale mainly focus on regular rectangular nanoplates, but according to the synthesis of nanostructures, the dynamic response of non-rectangular nanoplates is noticeable and there are not many works on these complex nanostructures. This work presents energy absorption, and forced and free vibrations of sandwich non-rectangular nanoplates with a single sinusoidal edge resting on a fractional torsional viscoelastic medium. The nanostructure is made from alumina reinforced by graphene platelets (GPLs) as a core covered by the flexoelectric and magnetostrictive materials as top and bottom layers, respectively. The consideration of size effects is derived from the innovative theory of local/nonlocal phenomena in a two-phase context. The Halpin–Tsai micromechanical and Kelvin–Voigt models are applied for the effective characteristics of the material in the nanocomposite layer and structural damping, respectively. Based on Hamilton’s principle and refined zigzag theory (RZT), the coupled electro-magneto-mechanical equations of motion are gained and analyzed by Galerkin’s and Newmark’s procedures. The effects of different components, including factors related to both the nonlocal and local phase fractions, the volume fraction of GPLs, various elastic mediums, electric field, structural damping, magnetic field, piezoelectric and flexoelectric effects on the absorption of energy, and forced and free vibrations of the sandwich nanostructure. Numerical simulations demonstrate that optimal energy absorption occurs when the flexoelectric factor is set to zero and the piezoelectric constant is non-zero but of opposite polarity. Additionally, it is concluded that when the coefficient of the local phase fraction is zero, increasing the nonlocal factor has more influence on the energy absorption and vibration of the nanostructure.