This paper researches the dynamic snap-through phenomena and the coexistence of the multi-pulse jumping chaotic dynamics in bistable equilibrium positions and the large amplitude nonlinear vibrations for a simply supported buckled 3D-kagome truss core sandwich rectangular plate under combined transverse and in-plane excitations based on the extended high-dimensional Melnikov method. According to the two-degree-of-freedom non-autonomous nonlinear dynamical system of the buckled truss core sandwich rectangular plate and the theory of normal form, it is found that some nonlinear terms have less effects on the nonlinear dynamic responses than other nonlinear terms. The extended high-dimensional Melnikov method is employed to investigate the dynamic snap-through phenomena and the bistable multi-pulse jumping chaotic vibrations around the upper-mode and the lower-mode for two different cases of buckling in the truss core sandwich rectangular plate. A numerical method is used to detect the bistable multi-pulse jumping chaotic vibrations around two stable equilibrium positions for the non-autonomous buckled truss core sandwich rectangular plate. The obtained theoretical and numerical results indicate that there exists the coexistence of the bistable multi-pulse jumping chaotic vibrations and the large amplitude nonlinear vibrations in the buckled truss core sandwich rectangular plate under combined transverse and in-plane excitations.

The nonlinear resonant responses, mode interactions, and multitime periodic and chaotic oscillations of the cantilevered pipe conveying pulsating fluid are studied under the harmonic external force in this research. According to the nonlinear dynamic model of the cantilevered beam derived using Hamilton’s principle under the uniformly distributed external harmonic excitation, we combine Galerkin technique and the method of multiple scales together to obtain the average equation of the cantilevered pipe conveying pulsating fluid under 1 : 3 internal resonance and principal parametric resonance. Based on the average equation in the polar form, several amplitude-frequency response curves are obtained corresponding to the certain parameters. It is found that there exist the hardening-spring type behaviors and jumping phenomena in the cantilevered pipe conveying pulsating fluid. The nonlinear oscillations of the cantilevered pipe conveying pulsating fluid can be excited more easily with the increase of the flow velocity, external excitation, and coupling degree of two order modes. Numerical simulations are performed to study the chaos of the cantilevered pipe conveying pulsating fluid with the external harmonic excitation. The simulation results exhibit the existence of the period, multiperiod, and chaotic responses with the variations of the fluid velocity or excitation. It is found that, in the cantilevered pipe conveying pulsating fluid, there are the multitime nonlinear vibrations around the left-mode and the right-mode positions, respectively. We also observe that there exist alternately the periodic and chaotic vibrations of the cantilevered pipe conveying pulsating fluid in the certain range.

The double excitation multi-stability and Shilnikov-type multi-pulse jumping chaotic vibrations are analyzed for the bistable asymmetric laminated composite square panel under foundation force for the first time. Based on the extended new high-dimensional Melnikov function, the explicit sufficient conditions are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations in the bistable asymmetric laminated composite square panel, which implies that multi-pulse jumping chaotic vibrations may occur in the sense of Smale horseshoes. The extended new high-dimensional Melnikov function gives the parameters domain of the intersection for the homoclinic orbits, which illustrates the relationship among the coefficients of damping, parametric, and external excitations. Numerical simulations including the bifurcation diagrams, largest Lyapunov exponents, phase portraits, waveforms, and Poincaré sections are utilized to study the double excitation multi-pulse jumping and metastable chaotic vibrations and dynamic snap-through phenomena. The numerical results demonstrate that double excitation Shilinikov multi-pulse jumping chaotic and small metastable chaotic vibrations coexist in the bistable asymmetric laminated composite square panel. It is found that the external excitation changes the complexity of the chaos, while the parameter excitation changes the type of chaos. It is verified that the bistable asymmetric laminated composite square panel with small damping is easier to produce double excitation Shilinikov multi-pulse jumping chaotic vibrations.

The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP) reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns. The FGGP reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet. It is novel to simplify the leakage of the air flow in the tip clearance to the non-uniform axial excitation. The rotating speed of the steady-state adding a small periodic perturbation is considered. The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation. Utilizing the first-order shear deformation theory, von-Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations. The primary resonance and nonlinear dynamic behaviors of the FGGP reinforced rotating pretwisted composite cantilever plate are analyzed by Runge-Kutta method. The amplitude-frequency response curves，force-frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations.

A widespread internal resonance phenomenon is detected in axially moving functionally graded material (FGM) rectangular plates. The geometrical nonlinearity is taken into account with the consideration of von Kármán nonlinear geometric equations. Using d’Alembert’s principle, governing equation of the transverse motion is derived. The obtained equation is further discretized to ordinary differential equations using the Galerkin technique. The harmonic balance method is adopted to solve the above equations. Additionally, stability analysis of steady-state solutions is presented. Research shows that a one-to-one internal resonance phenomenon widely exists in a large range of constituent volume distribution in moving FGM plates. Moreover, it is found that this internal resonance phenomenon can easily happen even though the FGM plates are under extremely small external excitation or with very large damping.

The primary resonance and nonlinear vibrations of the functionally graded graphene platelet (FGGP) reinforced rotating pretwisted composite blade under combined the external and multiple parametric excitations are investigated with three different distribution patterns. The FGGP reinforced rotating pretwisted composite blade is simplified to the rotating pretwisted composite cantilever plate reinforced by the functionally graded graphene platelet. It is novel to simplify the leakage of the air flow in the tip clearance to the non-uniform axial excitation. The rotating speed of the steady-state adding a small periodic perturbation is considered. The aerodynamic load subjecting to the surface of the plate is simulated as the transverse excitation. Utilizing the first-order shear deformation theory, von-Karman nonlinear geometric relationship, Lagrange equation and mode functions satisfying the boundary conditions, three-degree-of-freedom nonlinear ordinary differential equations of motion are derived for the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations. The primary resonance and nonlinear dynamic behaviors of the FGGP reinforced rotating pretwisted composite cantilever plate are analyzed by Runge-Kutta method. The amplitude-frequency response curves，force-frequency response curves, bifurcation diagrams, maximum Lyapunov exponent, phase portraits, waveforms and Poincare map are obtained to investigate the nonlinear dynamic responses of the FGGP reinforced rotating pretwisted composite cantilever plate under combined the external and multiple parametric excitations.

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In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for the blisk structure with the lumped parameter model under combined the aerodynamic force and varying rotating speed. The varying rotating speed and aerodynamic force are respectively simplified to the parametric and external excitations. The nonlinear governing equations of motion for the rotating blisk are established by using Hamilton's principle.The free vibration and mode localization phenomena are studied for the tuning and mistuning blisks. Due to the mistuning, the periodic characteristics of the blisk structure are destroyed and uniform distribution of the energy is broken. It is found that there is a positive correlation between the mistuning variable and mode localization factor to exhibit the large vibration of the blisk in a certain region. The method of multiple scales is applied to derive four-dimensional averaged equations of the blisk under 1:1 internal and principal parametric resonances. The amplitude-frequency response curves of the blisk are studied, which illustrate the influence of different parameters on the bandwidth and vibration amplitudes of the blisk. Lyapunov exponent, bifurcation diagrams, phase portraits, waveforms and Poincare maps are depicted. The dual-parameter Lyapunov exponents and bifurcation diagrams of the blisk reveal the paths leading to the chaos. The influences of different parameters on the bifurcation and chaotic vibrations are analyzed. The numerical results demonstrate that the parametric and external excitations, rotating speed and damping determine the occurrence of the chaotic vibrations and paths leading to the chaotic vibrations in the blisk.