Modal parameters

The model is based on both human and animal data. However, it is intended for applications to human dosimetry. Applications to other species would require consideration of species-specific adjustments in modal parameters. 

O Yottaqe source O Current source Ofltobal parameter Modal parameter... 

C yotaga source C Current source Global parameter C Modal parameter Iamparatura... 

C foliage tource Current source global parameter Modal parameter 9 Xemparature... 

Lingard JJN, Agus EL, Young DT, Andrews GE, Tomlin AS (2006) Observations of urban airborne particle number concentrations during rush-hour conditions analysis of the number based size distributions and modal parameters. J Environ Monit 8 1203-1218... 

Agus EL, Young DT, Lingard JJN, Smalley RJ, Tate EJ, Goodman PS, Tomlin AS (2007) Factors influencing particle number concentrations, size distributions and modal parameters at a roof-level and roadside site in Leicester, UK. Sci Total Environ 386 65-82... 

The modal approach assumes a shape for the particle-size distribution, typically one or more lognormal distributions, and represents evolution of the size distribution as evolution of the parameters characterizing the distribution, i.e., the amplitude, mode radius, and variance for the lognormal distribution (Binkowski and Shankar, 1995 Wilck and Stratmann, 1997). This approach offers the possibility of representing aerosol microphysical properties in models with far fewer variables (modal parameters) than are required in the sectional method (numbers of particles in each bin). 

FIGURE 8.12 Measured and fitted multimodal number distributions at different distances downwind from a major road in Los Angeles (a) 30 m downwind, (b) 60 m downwind, (c) 90 m downwind, and (d) 150 m downwind. Please note the different scale for the y axis. Modal parameters given are the geometric mean diameter and geometric standard deviation (Zhu et al. 2002). 

In the special case of modal updating, assume that only the lowest Nm modes contribute significantly to the model response and only the modal parameters of these modes are to be identified. Then, the uncertain structural parameters include the modal fi-equencies the modal damping ratios and the components of the measured DOFs of the mode shapes except the ones which are used for normalization, m = 1, 2,..., Nm, thus, there are a total number of Nm(No + 1) unknown modal parameters in modal identification. 

Beck, J. L., May, B. S. and Polidori, D. C. Determination of modal parameters from ambient vibration data for structural health monitoring. In Proceedings of 1st World Conference on Structural Control (Pasadena, CA, 1994),pp. TA3 3-TA3 12. 

Coppolino, R. N. A simultaneous frequency domain technique for estimation of modal parameters from measured data. SAE paper No. 811046, Aerospace Congress and Exposition (Anaheim, CA, 1981). 

Ebersbach, P. and hretier, H. On the application of modal parameter estimation using frequency domain algorithms. Journal of Analytical and Experimental Modal Analysis 4(4) (1989), 109—116. 

Juang, J. N. and Suzuki, H. An eigen-system realization algorithm in frequency domain for modal parameter identification. Journal cf Vibration, Acoustics, Stress and Reliability in Design 110(1) (1988), 24-29. 

Mayes, R. L. and Johansen, D. D. A modal parameter extraction algorithm using best-fit reciprocal vectors. In Proceedings of 16th International Modal Analysis Conference (Santa Barbara, CA, 1998), pp. 517-521. 

Topole, K. G. and Stubbs, N. Non-destructive damage evaluation in complex structures from a minimum of modal parameters. International Journal of Analytical and Experimental Modal Analysis 10(2) (1995), 95-103. 

Many recently published smdies are subjected to the evaluation of several functional parameters, either by direct measurements or by simulation, including tanperature prediction of rolling tires [126], in-plane [127] and rolling [128] deformations, other rolling tire modal parameter determinations [129] and estimations [130], influence of different parameters on tire power losses and CO2 emission (resistive loads and inflation pressure [131]), tire-road interface parameter measurements [132-138], and particularly the tractive performances for off-road vehicles [139-141]. Other examples refer to the optimization of air pressure in tires for fuel consumption minimization [142]. 

S. Palanivelu, K.V.N. Rao, K.K. Ramarathnam, Determination of rolling tyre modal parameters using finite element techniques and operational modal analysis, Mechanical Systems and Signal Processing, ISSN 0888-3270 64-65 (December 2015) 385 02. http //dx.doi.Org/10.1016/j.ymssp.2015.04.006. 

This can be represented in the modal parameter space of mode i, as illustrated by figure 5. The grey area represents a physically possible locus of k, nti) combinations. There is no general analytical description of the exact contour of this domain, but there area number of (conservative) numerical approximations ... 

The Modal Rectangle method (MR) neglects the coupling between the modal stiff-ness and the modal mass. The bounds on the ranges are calculated by minimising and maximising the modal parameters ki and nti over the domain... 

Modal envelope FRF calculation This step translates the range of the modal parameters into the modal envelope FRF, expressed as the range of the modal frequency response function ERP-f ... 

Since an FE solver can calculate all modal parameters for all modes of interest at once, the computational cost to calculate one objective function is equal to the computational cost to calculate all objective functions. Generic non-linear optimisers use only one of these objective functions. Other results however can be useful for other optimisations, for instance to select a suitable start vector. In most cases some optima - especially these located on a vertex - can even be found without performing additional FE analyses. Especially for larger FE models, storing all EE analysis results can cut the computational cost significantly. 

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