GAMM2025

Session

S05: Nonlinear Oscillations

S05

10 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S05: Nonlinear Oscillations: S05.01

• Roman Starosta
• Ulrich Römer

S05: Nonlinear Oscillations: S05.02

• Ulrich Römer
• Roman Starosta

S05: Nonlinear Oscillations: S05.03

• Ulrich Römer
• Roman Starosta

S05: Nonlinear Oscillations: S05.04

• Roman Starosta
• Ulrich Römer

Description

The section covers all fields of vibrational problems in solid mechanics or mechatronics including nonlinear effects. Submissions may address, for example, systems with nonlinear material behavior, nonlinearities in joints, mathematical solution methods (analytical or numerical), control or description of nonlinear behavior like bifurcations or chaos, or experimental idendification of nonlinearities.

119. Dynamics of Two Coupled Bodies on a Rough Horizontal Plane with Variable Coefficient of Friction

Alexander Prokopenya

10/04/2025, 08:30

Two bodies of the same mass attached to opposite ends of a massless spring of natural length l₀ move on a smooth semi-plane (x<0) of a horizontal plane with the same velocity v₀, and the spring is not deformed. Assume that at the initial instant of time, the second body crosses the line x=0 and starts to slide on the rough semi-plane (x>0) while the first body continues to move on a...

120. Pure Mobility: Rolling resistance in future vehicle-road systems

David Ruff

10/04/2025, 08:50

Today’s road traffic is characterized by an enormous effort in the consumption of space, energy, and resources. The initiative ”Pure Mobility” intends to develop a mobility system in addition to public transport based on small electric vehicles in combination with innovative roads made of water-permeable, sustainable, and resource-efficient materials. The driving resistances and in particular...

121. Secular Perturbations of the Orbital Elements in the Maby-Body System with Variable Masses

Moldir Saparova

10/04/2025, 09:10

The classical problem of (n+1) bodies with variable masses attracting each other according to Newton's law of universal gravitation is investigated. The central body P0 is assumed to lose mass isotropically, while the masses of the bodies P1,…, Pn can change anisotropically with different rates, which leads to the appearance of reactive forces. The laws of the masses change are arbitrary twice...

122. Frequency analysis of a Superconducting Magnetic Bearing system in ring spinning using an Eddy Current Damper

Yves Jesus Perez Delgado

10/04/2025, 09:30

The conventional ring-spinning process has been used for over a century, being one of the most used processes in the textile industry. However, this process has some disadvantages at high spindle speeds, such as friction in the traveler/ring components that generates heat, resulting in yarn breakages or lower-quality production.

New technological advances like superconducting magnetic...

123. Peculiarities of Amplitude-Frequency Characteristics in Geometrically Nonlinear Vibrations of Composite Shells and Plates under Various Deformation Models

Taras Goriachko, Mykhailo Marchuk

10/04/2025, 09:50

Composite thin-walled shell and plate elements are indispensable components of modern critical structures and technical devices for various purposes. This is due to their efficient material usage and ability to provide the required stiffness in specific directions under operational conditions. Intense cyclic loads cause geometrically nonlinear vibrations in these elements. Preventing resonance...

124. On the Influence of Cracks on the Dynamic Behavior of PICMA® Multilayer Actuators

Simon Riedel

10/04/2025, 10:10

Piezoelectric actuators are used to drive high-precision positioning systems. Ceramic actuators can withstand very high compressive loads but are susceptible to tensile forces. Cyclic loads and frequent load changes can cause cracks to form in the material over its lifespan. The influence of these cracks on the behavior and the durability of the actuator is the subject of current research. The...

130. Multi-Stable Systems: Nonlinear Dynamics and Energy Harvesting

Jerzy Warmiński

10/04/2025, 14:00

Systems with more than one equilibrium belong to a group of nonlinear multi-stable structures. The multi-stability can be created by specific devices, for example by a system producing nonlinear magnetic force and enabling to obtain the potential function with two or more potential minima (potential wells). Another option is to add axial force to the structure which shifts the vibrating system...

126. Forced response analysis of dynamic systems with inertia nonlinearity by applying the Multi-Harmonic-Balance Method

Sebastian Tatzko

10/04/2025, 14:40

Nonlinear mechanical vibrations under harmonic forcing can be well approximated by Fourier series. For a finite number of harmonics, the error is minimized over one period of vibration. This technique known as Fourier-Galerkin-Method (FGM) or Multi-Harmonic-Balance Method (MHBM) is today widely used in academics as well as industrial applications, e.g. friction damping in turbomachinery. The...

127. Integration of Base Excitation with non-linear Coupling within the Multiharmonic Balance Method

Tido Kubatschek

10/04/2025, 15:00

This paper presents a method for integrating base excitations into the harmonic balance method within the context of path continuation. Footpoint excitation can be applied via linear or non-linear elements to the mechanical system. First, a brief introduction into the harmonic balance method and the continuation procedure are given. Then, different types of base excitations are discussed:...

128. Stability analysis using predictor-corrector continuation to develop Ince-Strutt diagrams for a nonlinear parametric oscillator

Mirco Jonkeren

10/04/2025, 15:20

Time-varying physical properties of mechanical systems can lead to parametrically excited oscillations. A notable example of this is the time-varying stiffness of gear teeth meshing in the analysis of gearbox dynamics. In gear dynamics, the vibration behavior is a key design criterion, as it can lead to increased wear and noise. A mechanical model with two degrees of freedom can be used to...

129. A MATLAB Toolbox for the continuation of stationary solution branches

Julian Vogelei

10/04/2025, 15:40

Stationary solutions of dynamical systems play an important role in engineering and science. These solutions are characterised by the fact that their underlying solution type does not change for infinite time. Very well-known stationary solutions are equilibria and periodic solutions. Beyond that, quasi-periodic solutions may occur. This solution type can be understood as an extension of...

131. Slow-fast oscillations of an elastic double pendulum

Alois Steindl

10/04/2025, 16:30

We investigate the oscillations of a stiff longitudinally elastic double pendulum. The model is motivated by the oscillations of a tethered satellite system with negligible bending stiffness, where we expected, that the fast longitudinal oscillations have no significant influence on the slow transversal swingings. Numerical simulations show that even for very stiff pendula a significant amount...

132. Optimal lᵖ-Norm for Robust Integrity Measures of Safe Basins in High-Dimensional Systems

Nico Novelli

10/04/2025, 16:50

Evaluating the integrity measure of safe basins is a critical task in engineering, as it provides insight into the robustness of operational states in various machines and systems. A classical local approach involves determining the largest radius hypersphere (or, in a suitably scaled context, a hyperellipsoid) fully contained within the safe region. However, in high-dimensional spaces, even...

133. Mechanism of self excitation of silos for particles

Matthias Kröger

10/04/2025, 17:10

Bulk materials are used in many areas of technology and are often stored in silos. Examples can be found in mining, plastics technology or food technology.

In some cases, extremely loud noises can occur when silos are discharged, which are caused by self-excited vibrations. However, the excitation mechanism for these vibrations is still not clearly understood. The noise is emitted by...

134. Investigations on Sensitivity of AFM Cantilevers Using Parametric Resonance

Jonathan Ehrmann

10/04/2025, 17:30

Dynamic Atomic Force Microscopy (dAFM) uses a forced excited oscillating cantilever probe to image sample surface topography. The working principle uses the nonlinear interaction forces between probe and sample and has two operation modes, non-contact or intermittent contact between probe tip and sample surface. One of the most important key characteristics of dAFM is spatial vertical...

125. A new paradigm for multi-fidelity continuation using parallel model refinement

Johann Gross

10/04/2025, 17:50

CANCELLED
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Numerical path continuation is commonly applied to determine how limit states of complex nonlinear dynamical systems evolve with a free parameter. For high-fidelity models, the sequential nature inherent to continuation can become an unsurmountable obstacle. Recently, we proposed a seminal method for robustly obtaining the desired high-fidelity solution curves in a...

135. Inverse Problems for Weakly Nonlinear Boundary-Value Problems with Delay

Sergey Chuiko

11/04/2025, 08:30

We study a weakly nonlinear boundary-value problem for a system of delay differential equations. The initial function of the delay differential system contains an unknown eigenfunction that provides the solvability of the weakly nonlinear boundary-value problem. Due to the impossibility of defining solutions of weakly nonlinear boundary-value problems in terms of elementary functions, the...

137. Consideration of non-linear oscillations under uncertainties in the context of the electrical activity of pancreatic β-cells

Paula Clasen

11/04/2025, 08:50

Cell biological systems are characterized by complex relationships and non-linear processes. The modelling of these processes improves the understanding and represents a significant enrichment of the experimental investigation. An example of such a system is the regulation of blood glucose concentration by pancreatic β-cells through the secretion of insulin. β-cells are electrical active and...

138. An Analysis of Linear and Nonlinear Flexural Vibration of Bimodular Tapered Beams

Galeb El Chabaan

11/04/2025, 09:10

Certain materials exhibit different elastic behavior in tension and compression. These materials are typically modeled as bimodular, with different Young's moduli in tension and compression, as a simplified engineering approximation. Due to this material property, the neutral axis of a beam composed of bimodular material shifts away from the geometric centroid of the cross-section, with its...

136. Nonlinear Periodic Boundary Value Problems with Switching at Non-Fixed Points in Time

Olga Nesmelova

11/04/2025, 09:30

We analyze the relationship between boundary value problems with impulsive action at fixed points in time and boundary value problems with switching at fixed and non-fixed points in time. We derive constructive conditions for the solvability of these problems and a scheme for constructing solutions to a nonlinear periodic boundary value problem with switching at non-fixed points in time. Both...