neemo14-15
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10 years ago This chapter provides a brief overview of structural waves and discusses their relation to the modal response of finite structures. Different forms of waves can exist in structures. The waveform corresponds to a transverse wave where the string particle motion is perpendicular to the wave direction. Another important characteristic of waves in structures is the variation of the phase speed, with frequency. As most realistic structural systems are characterized by the ability to support transverse shear as well as having internal stiffness the focus is on longitudinal and flexural waves in thin beams. Longitudinal waves are characterized by a particle motion which is parallel to the direction of propagation. Many structures are excited by disturbances which are located off the central axis of the moment of inertia of the structure leading to wave motion which is transverse to the direction of propagation. In a relatively thin beam, for example, it is extremely difficult to excite purely longitudinal motion; the net result is a combination of both transverse and longitudinal displacements.
This chapter provides an introduction to mechanical vibrations. Terminology is discussed that is used in analyzing the vibratory response of mechanical systems. Mathematical methods are described for the linear response of vibrating systems. The equations of motion and linear behavior of single-degree-of-freedom systems are outlined for both free and forced response. All vibrations in realistic systems occur with some form of damping mechanism, where the energy of vibration is dissipated during a cycle of motion. The inclusion and characteristics of damping are very important to active control methods since it represents a process by which the response of a system can also be reduced by passive means. The chapter shows typical response versus time curves for an SDOF system with light, critical and heavy damping.