MS07.5: Nonlinear Phenomena in Mechanical and Structural Systems

In the present work nonlinear vibrations of a circular plate under dynamic and thermal loading are investigated. The model of the plate is based on the geometrically nonlinear Mindlin plate theory. It is accepted that the plate gets elevated temperature instantaneously and it is subjected to harmonic loading. The theoretical model is represented by a set of partial differential equations and is reduced consecutively to one and to three degrees of freedom system by Galerkin method based on the first vibration mode or on the first three vibration modes. The obtained reduced nonlinear ordinary differential equations with cubic non-linearity and temperature influence is studied analytically by harmonic balance method. The influence of the amplitude of the loading and the elevated temperature on the frequency response functions is studied and selected bifurcation diagrams are computed. The analytical results are compared with numerical solutions obtained by the one-mode reduction model.

Soft robotics is an attractive and rapidly emerging field, in which actuation is coupled with the elastic response of the robot’s structure to achieve complex deformation patterns. A crucial challenge is the need for multiple control inputs, which adds significant complication to the system. We propose a novel concept of single-input control of an actuator composed of interconnected bi-stable elements. Dynamic response of the actuator and pre-designed differences between the elements are exploited to facilitate any desired multi-state transition, using a single dynamic input. We show formulation and analysis of the control system’s dynamics and predesign of its multiple equilibrium states, as well as their stability. Then we fabricate and demonstrate experimentally on single-input control of two- and four-element actuators, where the latter can achieve transitions between up to 48 desired states. Our work paves the way for next-generation soft robotic actuators with minimal actuation and maximal dexterity.

A neural network is designed and trained using a supervised learning approach to localize damages on plates. Mindlin's theory is used to derive the plate's equation of motion, and the finite element method is used to discretize it. Damages are simulated by reducing the thickness (or stiffness) of the plate in the damaged area. The equation of motion is solved in the time domain for various locations of damage and different external forces for generating the training data for the supervised learning method. Transverse displacements are stored for multiple instants of time along the entire plate's surface. The data is converted into a one-dimensional vector and utilized as training data. Neural networks are demonstrated to be able to localize damages well even for excitation frequencies that are not utilized in the training set.