20 / 12 / 2022 - 14:30 – 15:10

Roman Starosta

Poznan University of Technology, Poland

Multiple Scale Methods in Predicting Nonlinear Vibrations of Discrete Mechanical Systems

Abstract

It has been observed over time that various asymptotic methods, including the multiple scale method (MSM), can be very attractive to engineers and scientists in solving nonlinear problems despite significant progress in numerical techniques. MSM allows one not only to solve many problems of physics and technology, but also to predict essential features of the analyzed nonlinear vibrations. The latter may have either harmful effects from the point of view of applications or may give some benefits depending on needs and expectations. Although MSM has its roots in the development of nonlinear science, it raises new questions and problems that science and technology must face and can be understood as a competition to recently developed and widely used computational techniques based on the numerical approaches. The MSM may not only predict archetypical features of nonlinear dynamic phenomena but also compete with the results accuracy of the classical numerical methods. This lecture concerns discrete mechanical systems in the form of coupled oscillators with several degrees of freedom. The motion of systems is governed by second-order equations transformed into their dimensionless counterparts. The latter can be obtained either by direct physical and mathematical modeling of numerous engineering problems where one may clearly separate the mass objects linked by massless stiffness and damping elements or via considering the continuous mass distribution of mechanical systems like rods, strings, beams, plates and shells governed by nonlinear PDEs.