Oscillator with Hyperbolically Variable Inertia

• Main Authors: Zvonko Rakarić, Boris Stojić*
• Format: Article
• Language: English
• Published: Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek 2020-01-01
• Series: Tehnički Vjesnik
• Subjects: energy surface contraction; harmonic excitation of support; nonlinear oscillator; singular inertial coefficient; super-attenuation
• Online Access: https://hrcak.srce.hr/file/361321
• ISSN: 1330-3651; 1848-6339

Novel oscillator model is introduced whose kinetic energy is inversely proportional to the generalized coordinate. System is referred to as "Oscillator with Hyperbolically Variable Inertia" (OHVI), since its inertia undergoes hyperbolic growth. Concept of comparison of free OHVI with the behaviour of simple harmonic oscillator (HO) via contraction and deformation of a 3D energy surface is introduced. Analysis of phase orbits and fixed point is performed. Obtaining an exact analytical solution for motion of free OHVI is shown. Main features of the system are demonstrated by numerical experiment performed for kinematically excited OHVI using appropriate mechanism design. It is shown that OHVI has an exact solution in the form of Jacoby elliptic function. Also, phase orbits of OHVI show characteristic oval ("egglike") shape. Motiontime histories and amplitude-frequency (AF) characteristics for forced oscillations were determined. Analysis of solutions for free system indicates possibility of realization of oscillatory system that has very long period i.e. low natural frequency. Comparison of system behaviour with typical nonlinear oscillator with restoring force of hardening type was carried out. Presented analysis shows that such system can be successfully applied for attenuation of low frequency vibrations or their detection.