Modal interactions in primary and subharmonic resonant dynamics of imperfect microplates with geometric nonlinearities

This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff＇s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct timeintegration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed.Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.

Nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric structures.It is also an important tool to guide the piezoelectric damping design of linear structures.Advanced aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on structures.Geometric and contact nonlinearities of thin-walled structures and joint structures are often activated.To achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear structures.Therefore,this paper defines the Nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric structures.Three candidate definitions of the NMEMCF are given,including two frequency definitions and one energy definition.The energy definition is the most promising one.It is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear MEMCF.In addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit state.The analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is observed.The results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.

The effect of nozzle layout on droplet ejection of a piezo-electrically actuated micro-atomizer

We study here effects of nozzle layout on the droplet ejection of a micro atomizer, which was fabricated with the arrayed nozzles by the MEMS technology and actuated by a piezoelectric disc. A theoretical model was first built for this piezoelectric-liquid-structure coupling system to characterize the acoustic wave propagation in the liquid chamber, which determined the droplet formation out of nozzles. The modal analysis was carried out numerically to predict resonant frequencies and simulate the corresponding pressure wave field. By comparing the amplitude contours of pressure wave on the liquid-solid interface at nozzle inlets with the designed nozzle layout, behaviors of the device under different vibration modes can be predicted. Experimentally, an impedance analyzer was used to measure the resonant frequencies of the system. Three types of atomizers with different nozzle layouts were fabricated for measuring the effect of nozzle distribution on the ejection performance. The visualization experiment of droplet generation was carried out and volume flow rates of these devices were measured. The good agreement between the experiment and the prediction proved that only the increase of nozzles may not enhance the droplet generation and a design of nozzle distribution from a view-point of frequency is necessary for a resonant related atomizer.

Study on modal characteristics and vibration reduction of an aircraft rotor–stator brake-induced squeal system

Based on the modal coupling theory,the rotor and stator contact stiffness and axial relative velocity are considered to build an electric aircraft brake dynamic system model in this study.Both the complex modal analysis and transient dynamic analysis methods are used to study the aircraft brake squeal performance and vibratory mechanism.The unstable vibration modes indicate that the out-of-plane vibration plays an important role and the feed-in energy is larger than the output energy in the brake rotor–stator module so that brake squeal takes place.Then the influences of the contact stiffness,friction damping and frictional coefficient on the brake squeal system are carried out,laying the foundation for the three proposed vibration suppression methods.Results show that the coefficient negative-slope condition will intensify the vibration.Also,a linear relationship between the squeal factor and the frictional coefficient is obtained to provide a guidance to predict squeal stability under more conditions.Vibration reduction design shows that adding a damping layer to the brake mechanism and chamfering the edge of braking stators both can reduce brake squeal effectively,while slotting braking stators is invalid in aircraft braking system.