Research on a cascade model synthesis with the use of classical and non-classical methods in the context of new piezoelectric stack applications

Abstract

Abstract. Active audio noise cancellation technology using piezoelements is fairly new and emerging technology on the market in recent years and is still gaining in popularity. The ability to use piezoelectric devices to gather information about vibration spectrum and to create interfering waves, to cancel out the noise, allows for the reduction in passive vibration methods and gives more flexibility in terms of space and application. The idea of using this technique on larger scales such as industrial equipment is the focus of ongoing research conducted by the authors of this article. This work is intended as the first part of a larger project and focuses solely on theoretical approach to the problem of modelling mechatronic systems capable of creating complex vibration spectrums and using piezoelectric components. The authors have focused on creating a mix of classical and non-classical methods to synthesize model systems based on input resonance frequencies. A classical calculation through matrix equations was also done to validate the accuracy of obtained results through the structural number method. The resulting model is still awaiting the empirical verification through extensive testing on real-life models, and that part of the research is still being developed. When validated and checked, this technology could bring new solutions in the vibration damping of industrial equipment, potentially increasing its flexibility and effectiveness.

Analytical approach to piezoelectric model synthesis with the use of Cauer’s method for system design

“…The classical matrix method served as a reference for an additional method using structural numbers. 2,11,16,29,30,31 The use of a second method is considered as part of the ongoing research 32 aimed at evaluating the accuracy and computational load of structural numbers in comparison to the matrix calculation. Current state of the algorithm based on structural numbers should still not be considered as final as there are more improvements to be made in terms of its compatibility with computation software.…”

“…A detailed description of this method in the context of solving mechanical cascade systems without damping was presented in Ref. 32. The structural number algebra is an entirely separate method of performing mathematical operations and therefore requires extensive explanation.…”

“…This time, in order to obtain absolute values of the displacements, the merging (similar to ( 12)) has to be performed for the whole structural number and all the simultaneity functions. 11,29,32 The amplitude response of each stage can be calculated by solving the equations:…”

“…The process of obtaining the necessary structural numbers to derive equations (14-16) and the meaning of a simultaneity function has been explained in more detail in. 29,32 The computer algorithm which was later used for this purpose is described in detail under the section dedicated to the algorithm testing. The nodes of each graph represent the degrees of freedom of the model they are describing.…”

“…30,31 More details can also be found in previous article published by authors. 32 The article also directly relates to adaptations of this method used by other researchers for analysis and synthesis of various systems. 2,11,16…”