1 Introduction
3
Fig. 1.1d. The system has an infinite number of degrees of freedom and is referred
to as continuous system or system with distributed mass.
As stated, the developments on MDOF/continuous systems (Chaps. 4 and 5)
are based on methods for solving SDOF systems (Chap. 2) and representations
of the deformations of MDOF/continuous systems in eigenvector/eigenfunction
coordinates developed in Chap. 3 and involve the following three steps. First, the displacement vectors/functions of MDOF/continuous systems are viewed as elements
of the linear spaces spanned by the eigenvectors/eigenfunctions of these systems.
The methods of Chap. 3 are employed to construct eigenvector/eigenfunction
coordinates. The displacement functions are completely defined by their projections
on these coordinates, which are finite for MDOF systems and (countable) infinite
for continuous systems. Second, differential equations are developed for the projections of the displacement vectors/functions of MDOF/continuous systems on their
eigenvectors/eigenfunctions. These equations are uncoupled and have the structure
of the equations of motion for SDOF systems. They can be solved one-by-one by
using the methods developed in Chap. 2. Third, the displacement vectors/functions
of MDOF/continuous systems are assembled from their representations in the
eigenvector/eigenfunction coordinates and their projections of these coordinates.
The problems at the ends of the chapters are intended to facilitate the understanding of basic concepts and tools for solutions. The instructor is encouraged to develop
and discuss, in addition to these problems, field-specific problems.
Finally, I would like to acknowledge the significant contributions of the many
students enrolled in my class on dynamics and the teaching assistants participating
in this class for their questions and comments. Their input was essential to the
completion of this work and is highly appreciated.
3
Fig. 1.1d. The system has an infinite number of degrees of freedom and is referred
to as continuous system or system with distributed mass.
As stated, the developments on MDOF/continuous systems (Chaps. 4 and 5)
are based on methods for solving SDOF systems (Chap. 2) and representations
of the deformations of MDOF/continuous systems in eigenvector/eigenfunction
coordinates developed in Chap. 3 and involve the following three steps. First, the displacement vectors/functions of MDOF/continuous systems are viewed as elements
of the linear spaces spanned by the eigenvectors/eigenfunctions of these systems.
The methods of Chap. 3 are employed to construct eigenvector/eigenfunction
coordinates. The displacement functions are completely defined by their projections
on these coordinates, which are finite for MDOF systems and (countable) infinite
for continuous systems. Second, differential equations are developed for the projections of the displacement vectors/functions of MDOF/continuous systems on their
eigenvectors/eigenfunctions. These equations are uncoupled and have the structure
of the equations of motion for SDOF systems. They can be solved one-by-one by
using the methods developed in Chap. 2. Third, the displacement vectors/functions
of MDOF/continuous systems are assembled from their representations in the
eigenvector/eigenfunction coordinates and their projections of these coordinates.
The problems at the ends of the chapters are intended to facilitate the understanding of basic concepts and tools for solutions. The instructor is encouraged to develop
and discuss, in addition to these problems, field-specific problems.
Finally, I would like to acknowledge the significant contributions of the many
students enrolled in my class on dynamics and the teaching assistants participating
in this class for their questions and comments. Their input was essential to the
completion of this work and is highly appreciated.