The finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems. Starting from the system differential equations and its boundary conditions, what is referred to as a weak form of the problem (elaborated in the text) is developed in a variational sense. This variational statement is used to define elemental properties that may be written as matrices and vectors as well as to identify primary and secondary boundaries and all possible boundary...

Computational techniques for the analysis and design of structural dynamic systems using numerical methods have been the focus of an enormous amount of research for several decades. In general, the numerical methods utilized to solve these problems include two phases: (a) spatial discretization by either the finite element method (FEM) or the finite difference method (FDM), and (b) solution of systems of time dependent second-order ordinary differential equations. In addition, the significantly powerful advances in computer systems capabilities have put on the desks of structural systems...

There are various techniques to optimize either structural parameters, or structural controllers, but there are not many techniques that can simultaneously optimize the structural parameters and controller. The advantage of integrating the structural and controller optimization problems is that structure and controller interaction is taken into account in the design process and a more efficient overall design (lower control force/lighter weight) can be achieved, and also multidisciplinary design optimization can be performed. The down side is that the combined optimization problem is more...

Nonlinear structural dynamic systems which are multi-degree of freedom systems involve, for instance, matrix dynamic equilibrium equations, which can be of various order up to very high order. In these equations, the nonlinear quantities can be dependent on time and other terms, such as scalar variables, which are dependent on time. Frequency response and response time derivatives would also, of course, be involved. Nonlinear terms can account for dissipative phenomena and can be due to other physical phenomena. In fact, many engineering structures involve time-dependent properties such as,...