Finite Elements: Special Problems in Solid Mechanics, Vol. V

Chapter 7 focuses upon response of continuous systems. The shear beam is used as the prime example. As a previous chapters, deterministic vibration via modal solutions initiates the subject. Stationary and concentrated random excitation follow in order. The author touches upon random vibration of a thin plate. Our next topic is the alternative solution of shear beams, where again, the uncoupled SDOF systems are applied in either time or frequency domain. The random vibration of a dam reservoir system subjected to vertical ground acceleration is exploited. The alternative impulse response function solves the dam problem where the hydrodynamic pressure cor­ responds to the shear force. The frequency response function and power spectral density response conclude this section. In a similar manner, the dam-reservior is excited by a horizontal acceleration simulating an earthquake event. A very good chapter! The next chapter covers the design of structures for random excitations. The stationary Gaussian process (random variable) is defined. The probability of upcrossings over a specified level and probability density of the peaks introduce this phase of the subject. The author applies this to the con­ cept of structural design against yield failure using an SDOF and a dam-reservoir subjected to vertical ground acceleration. The chapter concludes with structural damage against fatigue and includes the Palmgren-Miner (PM) rule and stationary narrow band random loading. The reviewer would have preferred seeing actual random test data since PM is limited as to excitations and may be unconservativ e at times. Chapter 9 treats nonstationary response which is a time dependent response of structures. Beginning with an SDOF system having stationary excitation, we again utilize the damreservoir system (vertical acceleration excitation). This con­ tinues into systems with nonstationary excitation containing Priestley's complex integral model. Zero damped and lightly damped SDOF systems inaugurate this topic. An alternative approach is Bendat and Piersol's model which employs the autocorrelation function for zero mean excitation and nonsta­ tionary specturm. The dam-reservoir with nonstationary ex­ citation concludes the chapter. The last chapter develops random vibration of structures in the plastic range. The random walk model is the eye-opener. It encompasses basic probability definitions (mass probability, mass function, conditional probability) and then derives the Chapman-Kalmagarov-Smolchoewski equation applied to structural response. Application of random walk model to a nonlinear structure and solution of the Fokker-Plunck equa­ tion complete the chapter. The appendices include Fast Fourier Transform (FFT) in random vibration and Monte Carlo simulation plus references. In summary, this is a good book. The author spares no ef­ fort in making the reader understand random vibration. The