Hands-on Learning with Computer Simulation Modules for Dynamic Systems

While the mathematical development and solution of dynamic equations of motion for mechanical systems is readily accomplished by engineering students, physical insights based on these equations is not. Interactions of multiple degrees of freedom as well as the consequences of modeling assumptions for dynamic systems are especially difficult for many students to grasp. This paper presents a series of in-class computer simulation modules on modeling of dynamic systems for hands-on learning, suitable for undergraduate courses in dynamic systems or vibrations. Simulations provide a means for students to visualize solutions and investigate alternative modeling or simplifications such as linearization of small angles, via graphical tools for plotting acceleration, velocity, and displacement results. Comparisons between linearized models and more complex nonlinear models help students determine the appropriate application of nonlinear modeling. These computer-based, visualization modules also offer students a vehicle for further inquiry, improved comprehension, and increased learning opportunities both inside and outside of class. Simulation and modeling with Matlab® and Simulink®, of various mechanical systems was accomplished through four classroom modules. Module topics included: one degree of freedom (1-DOF) free vibration, 1-DOF forced vibration with harmonic forces, 2-DOF free and forced vibration, and simulation of an earthquake on a 4-DOF structure with actual acceleration data from the 1940 El Centro earthquake. Computer-generated solutions were compared to closed-form solutions for several of the studied systems, establishing a means for verification of results. Transfer function and state space representations of linear, time-independent, multiple DOF systems as well as graphical-based modeling of linear and nonlinear systems via a function block and signal flow diagrams were applied in the modules. Instructional materials for the classroom computer exercises and the associated semester project, forming the basis of the modules, are provided and discussed in the paper. While resources for this module were developed for specific software, the concepts and topical problems presented for investigation may be used with other modeling and analysis software. The module materials may also be used by students as self-paced tutorials on modeling and simulation of dynamic systems.