System Stiffness and Natural Frequencies
In this assignment, the system stiffness was computed for a model involving cantilevers, springs, and propped beams in both series and parallel configurations. MATLAB was used to calculate the undamped and damped natural frequencies, as well as the system’s free vibration response. ANSYS was employed to validate the results.

(Homework 1)

Multi-Degree-of-Freedom Systems
This assignment focused on determining the natural frequencies of multi-degree-of-freedom (MDOF) systems, such as beams. By applying the generalized SDOF system approach, stiffness and mass matrices were calculated, and modal analysis was performed in ANSYS to validate the theoretical results.

(Homework 2)

Modal Analysis
Explored modal analysis of a structure subjected to various loading conditions. The assignment included performing a mesh sensitivity analysis and extracting the first few modes to evaluate the impact of boundary conditions and mesh refinement on the results.

(Homework 3)

Response to Harmonic Loading
This exercise involved analyzing the response of a structure under harmonic loading conditions using ANSYS. The amplitude and phase of the system's response were calculated at different excitation frequencies, and the results were compared with theoretical predictions.

(Homework 4)

Response Spectrum and PSD Analysis
Two separate analyses were performed to evaluate the system's response under different mode conditions using a response spectrum method. The results from 3-mode and 10-mode analysis were compared to evaluate vertical accelerations and mode participation factors.

(Homework 5)

Time-Domain Analysis
This assignment focused on solving time-domain responses for different dynamic loads using the numerical Newmark method. Simulations were run in MATLAB to model displacement and velocity over time for a multi-degree-of-freedom system, comparing the Newmark method results with analytical solutions.

(Homework 6)

Final Exam: Transient Structural and Modal Superposition

The final exam included two main parts: a transient structural analysis and a modal superposition analysis.

• Transient Structural Analysis
  A structure was modeled with a transient load applied, and the response was calculated over time. The simulation focused on evaluating the system's dynamic displacement response, accounting for both horizontal and vertical excitations. The effects of damping and large deflections were also explored, comparing results with and without these considerations.

• Modal Superposition Analysis
  Modal analysis was performed to determine the natural frequencies and mode shapes of the structure. The results were then used in a transient dynamic analysis to evaluate the system’s response to external loading. Displacements were tracked across various modes, demonstrating how mode shapes influence the overall dynamic response.