In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyzed in this report: The Euler-Bernoulli beam theory, Rayleigh beam theory and Timoshenko beam theory. A comparison of the results show the difference between each theory and the advantages of using a more advanced beam theory for higher frequency vibrations.

Buildings and other structures, all components and cladding thereof, shall be designed and constructed to resist the wind loads are required in all wind codes. Simple quasi-static treatment of wind loads, which is universally applied to design of low to medium-rise structures, can be either overly conservative or erroneous under-estimated for design of high-rise structures. Dynamic response, vortex, wind directionality, and shedding from other structures are all complicated key factors suppose to be considered in design. Meanwhile, wind tunnel testing is expansive, difficult and sometimes inaccurate even if it is a widely used method in simulation of aerodynamic response. Computational Fluid dynamics (CFD), historically, were two-dimensional (2D) method using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s. A number of three-dimensional (3D) codes were developed, leading to numerous commercial packages, which is more accessible and economical for wind load analysis.

As more and more stadia structures nowadays are being built by making use of new high strength building materials which tend to be lighter than the "old" ones, composite systems and also the fact that engineers, contractors and clients want their structures as optimized as possible, in terms of minimal materials used, there is an inevitable side effect that comes with this. The result is that structures are more flexible, and thus they become susceptible to undergone vibration problems due to the action of dynamic loading. Pop/rock concerts, exhibitions, boxing matches, and so forth are staged to supplement the football/sport seasons. Consequently, stadia structures must resist not only static loading, but also dynamic loading, such as the human induced loads from various activities of the spectators which include, standing, jumping, stamping, clapping and dancing, particularly in response to touchdowns (in football matches) or musical beats (during concerts). Active and passive models of humans are studied to see how they influence the response in TCF Bank Stadium for different ranges in excitation frequencies, by performing dynamic analyses and comparing the results with the ones obtained from static analysis. Parameter estimation and system identification in mechanical sciences and structural engineering have become increasingly important areas of research in the last three decades. Many nondestructive testing methods are based on the concepts of system identification and parameter estimation. In this document, two parameter estimation algorithms are studied, namely the Equation Error Estimator and the Output Error Estimator, through the simulation of modal data obtained from a computer structural analysis program and comparisons of their results are presented so that future researchers are better informed about the two and therefore can decide which one would give the best results for their application.