The One Degree of Freedom and Continuous Beam Models

Abstract

This chapter deals with the statistics for the vibration responses of a one degree of freedom model and also a simple beam model. In the first case, a tall offshore structure fixed to the ocean floor is assumed to vibrate in its first mode only when subjected to random wave forces. In the second case, a uniform, horizontal cross beam on a fixed ocean structure is assumed to vibrate in all modes under random forces. In each case, the statistical vibration analysis follows a definite pattern. Since the steps are rather lengthy, it is often easy to lose sight of the design goals of such an analysis. These steps to be followed are summarized: 1. Set up a reasonable mathematical model of the structure and formulate the governing equations of motion for this model. 2. Calculate the complex frequency response function where the applied force is harmonic« Deduce the response to a nonharmon-ic force. 3 Calculate the unit impulse response function where the applied force is step pulse. From this« deduce the response to a general type of force input. 4. Assume that the random input force is stationary and ergodic, and use the results of steps 2 and 3 to calculate the system’s responses.