Nonlinear targeted energy transfer in mechanical and structural systems. 2 Vols.
Two volumes of this monograph present an original approach to the problems of passive vibration control of dissipative mechanical and structural systems subjected to broadband transient inputs, including topics of targeted energy transfer (TET) and nonlinear energy sink (NES). The authors explain experimental, analytical and computational methods needed to formulate and study TET and NES phenomena in mechanical and structural systems. Natural processes involve to a certain extent some types of energy transfer. TETs, where energy of some form is directed from a source (donor) to a receiver (recipient) in a one-way irreversible fashion, govern a broad range of physical phenomena. Such flow of energy from the linear system to an attachment, which acts, in effect, as a NES, can be considered as a passive adaptive broadband boundary controller. This monograph is intended for scientists and mechanical and civil engineers who have a general knowledge of analytical dynamics and ordinary and partial differential equations, as well as integro-differential equations. Systems of such equations are used by the authors to describe TET and NES phenomena in mechanical and structural systems, what determines the advantage of this monograph from mathematical point of view. The first and second volumes consist of eleven chapters including introduction as Chapter 1 and postscript as Chapter 11. Chapter 2 includes the topics for discussion of localisation in mechanical systems, the concepts of nonlinear normal modes and resonance capture, as well as a survey of the complexification-averaging technique which is frequently employed here. Chapter 3 provides a theoretical basis for the study of TET including the analysis in the simplest system that can exhibit this phenomenon, namely a single-degree-of-freedom (SDOF) linear oscillator, as well as theoretical results on TET in multi-degree-of-freedom (MDOF) linear oscillators. Chapter 4 analyzes discrete linear oscillators with MDOF essentially nonlinear attachments and demonstrates more complex forms of TET for this type of dynamical systems. Theoretical analysis of TET is extended to flexible structures in Chapter 5 by considering beams, rods and plates with basically nonlinear SDOF and MDOF attachments, where TET can be beneficial for shock isolation. Chapter 6 treats TET in discrete oscillators under periodic external excitations, some of which turn out also to be favourable in the context of vibration isolation. The analysis in Chapter 7 concerns TET in systems with attachments that possess non-smooth nonlinearities including vibro-impact nonlinearities, since these systems are especially suitable for shock isolation on a fast time scale. Experimental validations of nonlinear TET phenomena are reviewed in Chapter 8, which also includes practical implementation of TET in engineering applications. Chapter 9 describes passive suppression of aeroelastic instabilities by means of TET in SDOF and MDOF lightweight nonlinear attachments. Applications of TET to seismic mitigation problems are presented in Chapter 10 which includes passive suppression of drill-string instabilities in oil drilling applications. Concluding remarks on TET with some perspectives of passive designs are presented in Chapter 11. The monograph contains also some practical engineering applications, such as passive energy harvesting, flutter suppression, vortex shedding control, enhanced reliability designs of power grids, and suppression of instabilities in drilling operations.
scientific article; zbMATH DE number 5380157