ABSTRACT

The elastic behavior of a system can be expressed either in terms of the stiffness or the flexibility. The orthogonal property of normal modes is one of the most important concepts in vibration analysis. The orthogonality of normal modes forms the basis of many of the more efficient methods for the calculation of the natural frequencies and mode shapes. Associated with these methods is the concept of the modal matrix, which is essential in the matrix development of equations. Engineering structures are generally composed of beam elements. If the ends of the elements are rigidly connected to the adjoining structure instead of being pinned, the element will act like a beam with moments and lateral forces acting at the ends. The normal modes, or the eigenvectors of the system, can be shown to be orthogonal with respect to the mass and stiffness matrices.