Random Vibration Analysis

However, for a large number of observed data points, repeated evaluations of the factor p(V 0, C) for different values of 0 becomes computationally prohibitive. It is obvious from Equation (4.9) that it requires the computation of the solution X of the algebraic equation F( )X = Y and the determinant of the x matrix F( ). This task is computationally very expensive for large N even though the former can be done efficiently by pre-conditioners [43,49,124]. Repeated evaluations of the likelihood function for thousands of times in the optimization process is computationally prohibitive for large N. Therefore, the exact Bayesian approach described above, based on direct use of the measured data V, becomes practically infeasible. In the next section, the model updating problem will be formulated with a nonsta-tionary response measurement. Standard random vibration analysis will be reviewed. Then, an approximated approach is introduced and it overcomes the computational obstacles and renders the problem practically feasible. 

Der Kiureghian A(1981)A response spectrum method for random vibration analysis of MDF systems. Earthq Eng Struct Dyn 9 419-435... 

Lutes LD, Sarkani S (2004) Random vibrations - analysis of structural and mechanical vibrations. Elsevier, Boston Michaelov G, Sarkani S, Lutes LD (1999a) Spectral characteristics of nonstationary random processes - a critical review. Struct Saf 21 223-244 Michaelov G, Sarkani S, Lutes LD (1999b) Spectral characteristics of nonstationary random processes -response of a simple oscillator. Struct Saf 21 245-267 Muscolino G (1991) Nonstationary pre-envelope covariances of nonclassically damped systems. J Sound Vib 149 107-123... 

Both deterministic and stochastic simulations can be used for response-history dynamic analysis, but only stochastic simulations can be utilized for stochastic dynamic (i.e., random vibration) analysis, because the latter analysis method requires a random process model of the earthquake ground motion. Synthetic ground motions are particularly useful for nonlinear dynamic analysis due to the scarcity of recorded motions for large-magnitude earthquakes that are capable of causing nonlinear responses. Two approaches are available for nonlinear dynamic analysis of structures subjected to earthquakes (1) nonlinear response-history analysis by the use of a selected set of ground motion time series and (2) nonlinear stochastic dynamic analysis by the use of a stochastic representation of the ground motion. 

Newland, D. E. 1975 An Introduction to Random Vibrations and Spectra Analysis. London Longman. 

Motion of fluids in which local velocities and pressures fluctuate irregularly, in a random manner. Predictive maintenance technique that uses principles similar to those of vibration analysis to monitor the noise generated by plant machinery or systems to determine their actual operating condition. Ultrasonics is used to monitor the higher frequencies (i.e., ultrasound) that range between 20,000 Hertz and 100 kiloHertz. 

There are defect limits that are associated with random failure modes. For example, if there is a leak from a mechanical seal on a pump, where do we decide that the leakage is excessive and requires immediate maintenance Vibration analysis severity levels are also typical examples of when do we have severe enough conditions to warrant equipment shutdown and overhaul. In such circumstances, the defect limit is dependent upon individual subjective judgment. 

A. Preumont Random Vibration and Spectral Analysis. 1994 ISBN 0-7923-3036-6... 

Modern methods of vibrational analysis have shown themselves to be unexpectedly powerful tools to study two-dimensional monomolecular films at gas/liquid interfaces. In particular, current work with external reflection-absorbance infrared spectroscopy has been able to derive detailed conformational and orientational information concerning the nature of the monolayer film. The LE-LC first order phase transition as seen by IR involves a conformational gauche-trans isomerization of the hydrocarbon chains a second transition in the acyl chains is seen at low molecular areas that may be related to a solid-solid type hydrocarbon phase change. Orientations and tilt angles of the hydrocarbon chains are able to be calculated from the polarized external reflectance spectra. These calculations find that the lipid acyl chains are relatively unoriented (or possibly randomly oriented) at low-to-intermediate surface pressures, while the orientation at high surface pressures is similar to that of the solid (gel phase) bulk lipid. 

The important problem of metal-nitrogen frequencies is unlikely to be resolved without at least a vibrational analysis of the ligands (no easy task) more extensive Raman data would also help. It has, in fact, been suggested that the bands discussed above are possibly ligand modes excited on complex formation (162), although it is not clear why this should occur so randomly. Tentative assignments of r(MN) above 200 cm have been made for a number of bipyridyl and phenanthroline complexes (e.g., 253, 254, 452, 502). 

Acoustic analysis is done in three steps 1) determination of source strength, 2) calculation of sound pressure levels throughout the primary coolant system, and 3) calculation of random vibration response of components and structures. 

For the seismic analysis using random vibration theory, floor response spectra in power density functions have been generated at all the important locations. 

Analysis of the maximnm deflection calculation formula reveals (as expected) that components with some compliance built into their component mounting and electrical terminations (such as the DIP and PGA) can be subjected to about twice the vibrational deflection as an SMT CLCC, provided component size, PB size, and PB thickness are equivalent.The latest equation for maximum deflection calculations is rated for 10 million stress reversals when subjected to harmonic (sinusoidal) vibration, and 20 million stress reversals when subjected to random vibration. It must be understood that this equation is a first approximation for predicting solder joint life. There are many factors that must be included for a more rigorous analysis and prediction. A more thorongh discussion is found in Barker. ... 

Detailed vibration data were also accumulated from the water experiment with the stainless steel pipe. With the accumulated data, conservative design power spectmm density for stress analysis on random vibration has been defined as is shown in Fig. 11.7. Random vibration in the hot-leg piping has been analyzed, and the maximum stress is evaluated to be lower than the criteria of high cycle fatigue stress. 

In the late fifties, Eringen and his co-workers [1-3] have analyzed the responses of beams and plates to random loads. Since these pioneering works, response analysis of structures subjected to random excitations has attracted considerable attention in the past thirty years. An extensive review of the recent developments have been provided by Crandall and Zhu [4]. Most of the earlier studies on nonstationary random vibrations were concerned with the analysis of mean-square response statistics [5,6]. Recently, evaluation of the time-dependent power spectra of structural response has attracted considerable interest. Priestley [7] introduced the orthogonal representation of a random function. Hammond [5], Corotis and Vanmarcke [8] and To [9] have studied the time-dependent spectral content of responses of single- and multi-degree-of-freedom structures. 

Fault diagnosis Nonstationary random vibration Signal-based modeling (identification) Structural Health Monitoring Time-dependent ARMA modeling Time-frequency analysis... 

Parametric SPE and DPE modelings of nonstationary random vibration are more involved than their nonparametric coimter-parts but offer unique opportunities for more accurate and compact representations, improved time-frequency resolution, analysis, and SHM. Other areas such as... 

Preumont A (1994) Random vibration and spectral analysis. Kluwer, Dordrecht... 

Spiridonakos M, Fassois S (2014b) Non-stationary random vibration modelling and analysis via functional series time dependent ARMA (FS-TARMA) models -a critical survey. Mech Syst Signal Pr 47(1-3) 175-224... 

Wen YK (1976) Method for random vibration of hysteretic systems. ASCE J Eng Mech Div 102(2) 249-263 Zeris C, Mahin SA (1988) Analysis of reinforced concrete beam-columns imder uniaxial excitation. J Struct Eng 114(4) 804-820... 

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