MS12.6: Nonlinear Dynamics for Engineering Design

This paper aims to examine the feasibility of using the static condensation approach to derive an integral equation commonly used in literature to describe the nonlinear dynamics of initially curved beams, similar to rectilinear beams. The focus is on establishing a solid theoretical foundation for this equation.

The paper presents a piezoelectric floating mass transducer with variable stiffness element which is used to connect the transducer with the middle ear. A magnetorheological elastomer and variable stiffness polymer can be used as connecting element to get an effect of variable natural frequency of the system. Numerical simulations are performed using the Bouc-Wen model of elastomer which exhibit a hysteresis effect. Finally, some conclusions are drawn for future research

In the face of the growing relevance of Unmanned Aerial Vehicle (UAV) applications, especially quadcopter drones, this paper presents the application of the State-Dependent Riccati Equation (SDRE) nonlinear optimal control technique for attitude control of a quadcopter in aggressive trajectories. In simulation, three cascaded control configurations are compared: one system using a Proportional-Integral-Derivative (PID) attitude controller, another with a Linear Quadratic Tracking (LQT) controller, and finally, one with a nonlinear SDRE controller. The configurations were subjected to an aggressive trajectory, and the results indicate the effectiveness of the SDRE controller compared to other linear techniques.

Cable-stayed bridges have gained significant attention in large-span bridge construction due to their robust structures, aesthetic appeal, and impressive spanning capabilities. These structures, however, are susceptible to considerable vibrations and internal resonance when subjected to load conditions. Accordingly, this study concentrates on the vibrations and nonlinear modal interactions in cable-stayed beam under primary resonance, with a special emphasis on the 2:1 internal resonance. Utilizing Hamilton’s principle for the development of the model and the method of multi-scale for solving, the motion equations and second-order approximate displacement expressions of cable-stayed beam were deduced. Based on these findings, equilibrium and dynamic solutions under different primary resonance conditions were explored to analyze the nonlinear responses of cable-stayed beam. To validate these theoretical insights, corresponding experimental models of cable-stayed beam and testing systems were designed, allowing for a comparative analysis between the experimental and theoretical results.

This research aims to investigate the dynamic behaviors of Carbon Nanotubes (CNTs) under conditions of geometric nonlinearity, taking into account size effects through the utilization of the Second Strain Gradient (SSG) elasticity theory. The study derives the dynamic equation in the nonlinear context. The weak form is clarified by employing C^3 continuum Hermite interpolation functions. Subsequently, a perturbation methodology is introduced, incorporating nonlinear phenomena within the framework of linear wave propagation. Combining nonlinear SSG theory with the higher-order finite element method is essential for gaining insight into the wave propagation characteristics of CNTs.