Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.

THE MEASUREMENT AND STUDY OF BLASTING VIBRATION AFFECTING IN SITU CAST CONCRETE LINING OF VERTICAL SHAFT

Vertical shaft is main form of drivage in deep mineral depoist. They also serve as the entrance into and the exit from the underground mine. The main problems in shaft and tunnel engineering is to solve the contradiction between drivage and lining. The measurement of blasting vibration affecting concrete lining strength of vertical shaft is carried out in experiment and theory in this paper.

Bandgap Properties for the Folded S-Type Periodic Structure:Numerical Simulation and Experiment

The central wavelength of the first Bragg scattering bandgap is approximately twice that of the lattice.Therefore,a low-frequency Bragg scattering bandgap with a small structural dimension for phononic crystals is difficult to obtain.In this study,a folded S-type periodic structure is developed to reduce the dimension in the direction of vibration suppression by folding unit cells.According to the foregoing,an improved folded S-type periodic structure with different unit cell arrangements is designed to widen the bandgap frequency range.Energy band diagrams and frequency responses are calculated based on the Bloch theory and using the finite element method.Furthermore,a prototype of the improved folded S-type periodic structure is fabricated using a three-dimensional printing technique,and a vibration experiment is conducted.To verify the vibration reduction performance of the structure,numerical simulation and experimental results are compared.This type of folded periodic structure can effectively reduce dimensions to satisfy the dimension requirements pertaining to the direction of vibration suppression.Hence,the foregoing can aid in promoting the use of elastic bandgap structures in engineering.

Band-gap Properties of Elastic Sandwich Metamaterial Plates with Composite Periodic Rod Core

A novel elastic sandwich metamaterial plate with composite periodic rod core is designed,and the frequency band-gap characteristics are numerically and experimentally investigated.The finite element and spectral element hybrid method(FE-SEHM)is developed to obtain the dynamic stiffness matrix of the sandwich metamaterial plate.The frequency response curves of the plate structure under the harmonic excitation are calculated using the presented numerical method and validated by the vibration experiment.By comparing with the frequency response curves of sandwich metamaterial plate with pure elastic rod core,improved band-gap properties are achieved from the designed metamaterial plate with composite periodic rod core.The elastic metamaterial plate with composite periodic rod core can generate more band-gaps,so it can suppress the vibration and elastic wave propagation in the structure more effectively.