Session: 16-01-01: Government Agency Student Poster Competition

Paper Number: 148997

148997 - Stability and Oscillatory Response of Beck's Column With Nonlinear Constitutive Laws 

Introduction:

This research investigates the complex dynamics of Beck's column, a cantilever beam subjected to nonconservative follower forces, focusing on the interplay between nonlinear constitutive laws and fluid-structure interactions. The motivation for this study stems from the need to understand the stability and oscillatory behavior of slender structures under dynamic loading conditions, which is crucial for applications ranging from engineering structures to biological filaments.

Contribution:

The primary contribution of this work lies in advancing the understanding of nonlinear post-buckling behavior and the effect of follower forces on the stability of elastic structures. By incorporating a nonlinear softening constitutive law and considering fluid drag effects, the study provides insights into the dynamic response and stability characteristics that were previously unexplored in the context of Beck's column.

Methodology:

The mathematical formulation of the model employs the dynamic equilibrium equations, compatibility conditions along with the constitutive law. The set of coupled partial differential equations are discretized and solved numerically using MATLAB. The model is benchmarked against known critical buckling force values to validate its accuracy. The study uses the Morison drag model to account for the fluid-structure interaction, describing the drag force as a function of the rod's motion through the fluid. The nonlinear constitutive law is defined to capture the softening behavior of the material, which is crucial for understanding the post-buckling dynamics.

Results:

The results reveal several key findings. Firstly, the critical buckling force calculated by the computational model is within 1% from the reported value, confirming the model's validity. Frequency analysis under fluid drag indicates that the oscillation frequency scales with the magnitude of the follower force, following a theoretical power law. The results from the computational model show good agreement with this theoretical prediction.

In the nonlinear regime, the study finds that the post-buckling oscillations of Beck's column exhibit complex behavior. The frequency of oscillation is lower in the nonlinear case compared to the linear case for a given force, due to the reduced stiffness from nonlinear softening. However, as the force increases, the frequency also increases, surpassing the linear case at higher forces. This behavior is attributed to the excitation of higher energy modes in the nonlinear case, which is confirmed by the increase in the number of inflection points in the rod's deformation profile.

Moreover, the study explores the propulsion dynamics of the rod in a fluid environment. It is found that the nonlinear rod generates a higher active propulsion force compared to the linear rod, especially at larger follower forces. This increased propulsion force is linked to the greater deformation and higher frequency of oscillation in the nonlinear case, suggesting potential applications in the design of bio-inspired propulsion systems.

Conclusion:

In conclusion, this research significantly advances the understanding of the dynamic stability and nonlinear behavior of slender structures under follower forces. The incorporation of nonlinear constitutive laws and fluid-structure interaction provides a more comprehensive picture of the post-buckling dynamics, with implications for both engineering and biological applications​.

Presenting Author: Muhammad Hassaan Ahmed University of California Merced

Presenting Author Biography: In 2018, I earned my B.E. degree in Mechanical Engineering from the National University of Science and Technology (NUST), Pakistan, securing GPA-based scholarships throughout all eight semesters. During my academic journey, I also served as a Research Assistant (RA) at the National Centre of Robotics and Automation (NCRA). My diverse research interests encompass biomedical devices, robotics, and computational dynamics, with a particular focus on microscope biological systems.
The crux of my research revolves around investigating the impact of constitutive laws on slender structures, modeled as continuum beams or rods, and their dynamics of deformation in bending and torsion. Specifically, I will delve into scenarios where the constitutive law exhibits non-linear and/or non-homogeneous characteristics. This exploration is propelled by a fundamental question: how do the features of non-linearity and non-homogeneity in constitutive laws influence the dynamics of deformation in biological filaments, subsequently shaping their biological activity or functions?
Although the exact application of this study may be elusive, I plan to define mechanics-based problems that intricately address engineering and mathematical challenges. This strategic approach serves as a foundational stepping stone toward achieving the overarching goal of understanding the intricate relationship between the structure and function of biological filaments.
Moreover, my research aims to develop inverse methods for identifying the constitutive laws governing slender filaments. To achieve this, I will leverage experimental data from real systems, employing it to discern the constitutive laws. The accuracy of these identified laws will be rigorously validated through molecular dynamics simulations on software platforms, ensuring the reliability and applicability of the research outcomes.

Authors:

Muhammad Hassaan Ahmed University of California Merced
Soheil Fatehiboroujeni Colorado State University
Sachin Goyal University of California Merced