MS09.6: Nonlinear Dynamics in Engineering Systems

This study investigates linear and geometrically nonlinear vibrations of the sandwich plate with auxetic honeycomb core and functionally graded material (FGM) face sheets. The first order shear deformation theory (FSDT) is applied to construct mathematical model. The R-functions theory, variational Ritz method, procedure by Bubnov-Galerkin and Runge-Kutta method are used to solve the given problem for plates with a complex form and different boundary conditions. The effective material properties of the FGM plates made of mixture metal and ceramics are determined by Voight power law. The reliability and accuracy of the proposed method have been validated via comparisons of the present results with known ones for the case of simply supported rectangular plates. Solution structures are constructed for the plates with mixed boundary conditions. The effect of geometric parameters of auxetic material, volume fraction index of FGMs, the thickness ratio of layers, the parameters of the elastic foundation on linear and nonlinear frequencies was investigated for plates with the mixed boundary conditions.

The goal of this work is to extend the developed by the authors of this study a theoretical model of the vibration of bi-material beams subjected the combined action of mechanical and thermal loads. The geometrically nonlinear version of the Timoshenko beam theory is used to describe the theoretical model of the problem. Starting from the geometrical, constitutive and equilibrium governing equations of each layer of the bi-material beam are derived with respect to one coordinate system. In a contrast with the previously developed model, where a generalized properties of the beam were used, here the properties of each layer were taken into the equations of motion. Then reduced order models for the equations of each layer were developed using the normal forms of vibration. The relation between the generalized coordinates in time of the layers were obtained which was used in the solution of the equations of motion. Numerical results for the response of the beam in time and frequency domains were obtained and stability and bifurcation of the beam due to elevated temperature and loading parameters were studied.

Nonlinear mechanisms leverage nonlinear kinematics to enhance the efficacy of isolators, maintaining controlled static deflections while keeping natural frequencies low. Despite extensive examination of their performance under harmonic base excitation, there is a scarcity of applications incorporating real seismic signals, and few experimental validations exist for real-world scenarios. This study substantiates the advantageous impact of High Static Low Dynamic Stiffness isolators vs. linear counterparts in diminishing transmitted vibrations to a suspended mass during near-fault earthquakes through experimental demonstrations. Additionally, a lumped parameter model is devised, incorporating a piecewise nonlinear-linear stiffness, and accounting for dissipation through viscous and dry friction forces. Preliminary tests encompass harmonic base motion scenarios to assess isolator transmissibility in various cases. The model exhibits outstanding agreement with experimental measurements.

We investigate the multistable dynamics of a simple model of reed musical instrument written as a system of four ordinary differential equations. A bifurcation analysis is performed considering the blowing pressure – which is the main control parameter for the musician – as a bifurcation parameter. This unveils that several stable periodic solutions corresponding to different musical notes coexist on a range of the blowing pressure. We employ a machine learning technique (namely an explicit design space decomposition technique combined with an support-vector learning machine) to construct, in an well-chosen 3D subspace of the phase space, the boundary between the basins of attraction of the coexisting periodic solutions. Basins are of particular interest from a practical point of view: they relate to the playability of the regimes and to their sensitivity to perturbations.

The method for the numerical simulation of complex process of interaction between nonlinear oscillations, creep and wear in fuel rod claddings is presented. Geometrically nonlinear oscillations of the fuel rod are modelled by Galerkin and time integration methods. The cyclic creep governing equation was obtained by use of the asymptotic expansions and averaging in a period of fuel rod’s oscillations. The approach for estimating the power value of the friction forces, which vary over time in creep conditions, is proposed. The examples of the calculation results are presented.