Abstract
This paper derived the expression to estimate the effective line moment mobility of a non-deterministic thin plate under moment excitation by a piezoelectric patch actuator. The piezoelectric patch actuator is assumed to generate purely line moments at each of its edges and regarded as a finite number of point moments acting on an infinite plate, which is achieved by integration method. The theoretical model is validated using MATLAB simulation and compared with experimental measurements on a randomized thin plate. The derived effective line moment mobility managed to closely estimate high-frequency response while cutting significant computational time and resource. Results from this study can be used in many applications ranging from vibration isolation where power transmission between the isolator with an area distribution and its host structure can be determined more accurately, and to design the optimal shunt circuit of a piezoelectric shunt damper for maximum power dissipation in order to reduce vibration of a non-deterministic thin plate.
Highlights
Non-deterministic substructures (Non-DS) are structures that are subjected to short wavelength, vibrates at the high-frequency range and produce a response that cannot be determined using a deterministic method
The mid-frequency range (1 modal overlap factor (MOF) 2) is when the modal response is beginning to overlap and MOF 2 is the high-frequency range where: (i) the vibration response is increasingly sensitive to uncertainties [2, 3] and (ii) no distinct resonant peaks are visible in the response since the modal responses are combined to be broader peaks (Fig. 1)
The modal model for effective point mobility at ith connection on a thin plate under moment excitation by a PZT patch actuator, assuming the moment excitation point is uniform along the line is: Y
Summary
Non-deterministic substructures (Non-DS) are structures that are subjected to short wavelength, vibrates at the high-frequency range and produce a response that cannot be determined using a deterministic method. The concept of mobility is normally used in the study of vibration isolation, in determining the characteristics of power transmission over the contact region between the isolator and the host structure This knowledge can be applied to the concept of designing the optimal shunt circuit for PZT shunt damping; with the goal to maximize energy dissipation from a non-deterministic substructure [8]. A multi-point connection model is employed through integration method to determine the effective line mobility of an infinite thin plate excited by line moments induced by a PZT patch actuator. The modal model for effective point mobility at ith connection on a thin plate under moment excitation by a PZT patch actuator, assuming the moment excitation point is uniform along the line is:
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