Modeling, Analysis, and Experimentation of Shape-Morphing Plates
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Authors
Reiner, David Leo
Issue Date
2025
Type
Thesis
Language
en_US
Keywords
Nonlinear , Plate Dynamics , Shape-Morphing , Vibrations
Alternative Title
Abstract
This thesis covers the exploration of numerical modeling, analysis, and experimentation of shape-morphing plates. The work is separated into three main sections to discuss three complementary topics. The first section investigates the analytical and numerical modeling of a nonlinear equation of motion with the addition of global and local optimization. Machine learning and parameter exploration is covered in the second section of this work. Finally, the third section describes and analyzes novel experimentation of physical moment-actuated plates employing modal excitation and actuation via Macro Fiber Composites (MFC). In the first section, an equivalent Duffing oscillator was proposed to interpret Finite Element Analysis (FEA) frequency response simulations of a shape-morphing plate. The equivalent oscillator parameters were identified using least squares and an analytical treatment of the Duffing equation through numerical optimization. In the second section, to devise a robust parameter identification framework, a methodology for determining the best machine learning model was explored. “Bagged Trees”, a form of ensemble machine learning, was quantitatively found to be the best method for the investigation. After this, randomized parameter data was generated, a machine-learning model was made, and comparisons to simulated FEA data were explored.
In the third section, we focused on the experimental investigation of MFC-actuated shape morphing plates. Several actuation architectures were studied. The architecture comprising a single MFC was found to be significantly less effective than that with two MFC actuators connected by an aluminum substrate, which resulted in an increase of 5.3 times displacement amplitude. Among the studied configurations, a soft plate excited at its third mode was found to produce viable controllable curvature for shape-morphing applications. Many shapes and materials were tested resulting in an optimized A-30 silicone rubber plate in the form of a bioinspired “emarginate tail” with a thickness of 0.25 inches. An embedded MFC was placed in the plate to modulate its stiffness and was found to be able to reduce displacement amplitudes of up to 31%, thereby demonstrating the principle of shape-morphing. Using constructive interference during another test, a 200% increase in displacement amplitude was obtained by matching the phase of the MFC to a base excitation. A 3.125% change in peak frequency at the third mode during a frequency sweep was observed by dynamically controlling the MFC signal. Overall advancements were made in the fields of modeling and physical design of nonlinear shape-morphing plates, with the first experimental demonstration of the system.