Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force

Zhang, W.; S., W.; Zhang, Y. F.; Liu, Y. Z.

doi:10.1063/5.0014142

Cited by 21 publications

(3 citation statements)

References 54 publications

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“…On the basis of the previous experimental research, Arrieta et al [32] established a non-smooth double-well dynamic model with the lateral displacement as the variable and the critical snapthrough displacement as the dividing point, and found that double-well dynamics of a bistable plate exhibited dynamic snapthrough motions and chaotic responses. Dynamic snapthrough motions and nonlinear vibrations of bistable unsymmetric composite laminates under the foundation excitation were studied [33,34]. Emam et al [35] investigated snapthrough motions of bistable orthogonal composite laminates under the concentrated moment, the normal force and the tangential force respectively.…”

Section: Introductionmentioning

confidence: 99%

The Intra-well and Inter-well Dynamics of the Unsymmetric Bistable Composite Laminated Shells

Dong,

Cao,

et al. 2024

Preprint

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In this paper, the theoretical shell model of the bistable unsymmetric composite laminates is elucidated, elaborating the intra-well and inter-well dynamics. Deploying initial displacements delivered by the bistable plate model and utilizing the Reddy′s third-order shear deformation theory, the bistable shell model is introduced. Applying multiple sets of base excitation accelerations, sweeping frequency and sweeping amplitude, the intra-well and inter-well dynamics are detected. The intra-well dynamics are activated by the inadequate energy, while the inter-well dynamics are activated by the sufficient energy. The intra-well dynamics are characterized by the 1-cycle single-well vibration, the 2-cycle single-well vibration, the 3-cycle single-well vibration and the 4-cycle single-well vibration. The cycle-doubling bifurcation and the secondary Hopf bifurcation can be identified. The evolution process from the 1-cycle single-well vibration to dynamic snapthrough motions is judged to follow the cycle-doubling bifurcation which tends to generate all-around dynamic regimes. The frequency-amplitude response curve exhibits the softening nonlinear stiffness effect owing to the negative stiffness. The 1/2 subharmonic resonance actually represents superimposed responses which are constituted by the forced response activated by the high-level excitation frequency and the induced harmonic response equivalent to the primary resonance of the low-level mode frequency. The 1/2 subharmonic resonance is caused by quadratic nonlinear terms. The inter-well dynamics are characterized by limit-cycle oscillations, multiple-cycle snapthrough motions and chaotic snapthrough motions, which are attributed to loading conditions. The appearance of limit-cycle oscillations is decided by the level of initial displacements. The increasing level of initial displacements leads to the disappearance of limit-cycle oscillations. The first few mode frequencies tend to be the optimal excitation frequencies activating dynamic snapthrough motions. Limit-cycle oscillations are related to the first mode frequency while multiple-cycle and chaotic snapthrough motions are related to the third mode frequency. The discrepancies for different initial conditions are actually caused by the phase difference between the displacement response and the frequency sweeping, which denotes the hysteresis. With the increase of the number of layers, the actuation amplitude for dynamic snapthrough motions increases while the bandwidth of the actuation frequency range for dynamic snapthrough motions broadens correspondingly. The development of bistable energy harvesters and morphing aircrafts can be supported by the theoretical research.

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Section: Introductionmentioning

confidence: 99%

The Intra-well and Inter-well Dynamics of the Unsymmetric Bistable Composite Laminated Shells

Dong,

Cao,

et al. 2024

Preprint

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“…Multipulse chaotic motions are very common in highdimensional systems. With the extended Melnikov method, Zhang et al [14] investigated multipulse jumping chaotic vibrations of the bistable asymmetric laminated composite square panel under foundation force. e energy-phase method [15][16][17][18][19], proposed by Haller, is a global perturbation method for analyzing multipulse chaotic motions of high-dimensional nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of Piezoelectric Composite Laminated Beams

Zhou

Wang

2021

Shock and Vibration

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Chaos in piezoelectric composite laminated beams has significant implications in the design of this model. Some results for this model have been obtained numerically. With the energy-phase method and numerical simulations, global dynamics of piezoelectric composite laminated beams is investigated in this paper. The average equation of the piezoelectric composite laminated beam is obtained by the normal form theory. The existence of multipulse homoclinic orbits for undisturbed and dissipative cases is analyzed by the energy-phase method, and the mechanism of chaotic motion of the system is given. The effect of the dissipation factor on pulse sequence and layer radius is studied in detail. The chaotic motion of the system is verified by numerical simulations.

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“…They also verified the theoretical results with experiments. Zhang et al [57] predicted chaotic vibrations of a bi-stable asymmetric laminated composite square panel under foundation forces for the first time.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis for anti-symmetric laminated composite plates resting on visco-elastic foundation with temperature effects

Rahmani

Faroughi

Friswell

2021

Applied Mathematical Modelling

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Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force

Cited by 21 publications

References 54 publications

The Intra-well and Inter-well Dynamics of the Unsymmetric Bistable Composite Laminated Shells

The Intra-well and Inter-well Dynamics of the Unsymmetric Bistable Composite Laminated Shells

Chaotic Dynamics of Piezoelectric Composite Laminated Beams

Vibration analysis for anti-symmetric laminated composite plates resting on visco-elastic foundation with temperature effects

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