Lump” mass analysis

The pressure-time variation in the driver section can be approximated by a quasi-steady model consisting of a single lumped-mass system with choked outflow at the minimum throat area when the ratio of the driver volume to the throat area is equal to 20 ft3/ft2 (6.1 m3/m2) or more. For smaller values of the ratio, the representation by a quasi-steady model becomes less accurate, and the numerical wave analysis approach is more suitable. 

Consider a body of arbitrary shape of mass m, volume J, surface area density p, and specific heat initially at a uniform temperature 7) (Fig. 4-2). At time t = 0, the body is placed into a medium at temperature T., and heat transfer takes place between the body and its environment, with a heat transfer coefficient h. For the sake of discussion, we assume that 7) > 7), but the analysis is equally valid for the opposite case. We assume lumped system analysis to be applicable, so lhat the temperature remains uniform wilhin the body at all times and changes with time only, T T t). 

To produce the seismic analysis model for the reactor internal structures, the lumped-mass modeling technique is used From the 3-dimensional finite element model of KALIMER reactor internal structures, the detail local stiffness analyses are performed to construct the lumped-mass seismic analysis model The seismic analysis and evaluation of KALIMER are presented through the modal analysis, the seismic time history analvsis, and the equivalent seismic stiess analysis Table 3 shows the natural frequencies of the reactor structures resulted from the modal analysis for the seismic analysis model shown in Fig 13... 

The seismic analysis of the core is performed with the two-dimensional special purpose computer codes CRUNCH-2D and MCOCO, which account for the non-linearities in the structural design. Both CRUNCH-2D and MCOCO are based on the use of lumped masses and inertia concepts. A core element, therefore, is created as a rigid body while the element flexibilities are input as discrete springs and dampers at the corners of the element. CRUNCH-2D models a horizontal layer of the core and the core barrel structures (Figure 3.7-7). The model is one element deep and can represent a section of the core at any elevation, MCOCO models a strip of columns in a vertical plane along a core diameter and includes column support posts and core barrel structures (Figure 3.7-8). The strip has a width equal to the width of a permanent reflector block. Both models extend out to the reactor vessel,... 

In order to explore how shaft depth influences conveyance motion, it is necessary to adopt a fundamental approach to the analysis of this motion. The approach has been explained before (Greenway et al. 2000). A summary reminder of the elements of a dynamic model set up for this purpose is appropriate. The conveyance can be treated as a rigid body (lumped mass) acted on by disturbing forces and restoring forces. The equations of motion of the conveyance can then be represented as shown in Figure 4. 

Using a model with lumped masses at two characteristic levels (top and level 1), a nonlinear dynamic analysis was performed with a complex hysteretic (IZIIS) model (Fig. 8.5, Shendova 1998). To calibrate the computations in defining the capacity degradation in hysteretic models, the results from seismic shaking table testing of the model were used. With this, an attempt was made to model the dynamic response in a simple way, suitable for everyday analyses, resulting however in satisfactory final results on the behavior at individual levels. 

In a complete coupled analysis (Fig. 24.17) the 6 DOF motions of the floating vessel is solved at a given time step. The loads and motions of the top of each of the riser/mooring fine are determined. A finite element (or lumped mass) method for... 

The dynamic response analysis of an offshore tower, subjected to nonstationary ice forces, is presented for single-degree-of freedom and multi-degree-of-freedom, lumped mass, models based on evolutionary covariance matrices. The ice force excitation is idealized by i) equivalent evolutionary white noise, and ii) physical spectra. The mean square responses are computed in the time domain using the linear (state space formulation). The relationship between the physical spectrum and instantaneous spectrum analysis is discussed, and the need indicated for a study of the influence of ice force physical spectrum parameters on the response. 

The structure analyzed is a fixed offshore tower idealized by a lumped mass model shown in Fig. 5, considered by Sundararajan and Reddy (1977). The analysis is restricted to the first three modes. 

Static Analysis for Natural Frequency of an Overhung Shaft. The elements that determine the lateral natural frequency are the magnitudes and locations of concenbated and distributed masses, the tensile modulus of elasticity of the material, and the moment of inertia of the shaft. Ramsey and Zoller (1976) presented the basic elements of natural frequency for a shaft and impeller system like the one shown in Figure 21-32. That method uses a lumped mass, static technique for computing the critical speed of a shaft and impeller system. The mass of the individual impellers and the distributed mass of the shaft is lumped into a single mass at the end of... 

Multibody dynamics formulations can be applied to the crashworthiness analysis. In fact they can treat easily lumped mass models, generating automatically the equations of motion and may include flexibility effects [2], that can be applied efficiently and used as an alternative to the classical nonlinear finite elements methodologies. 

The sensitivity analysis and optimization techniques are used in many fields of engineering, but very little work as been applied directly to the vehicle crashworthiness design. However, some studies are reported in the literature where optimization techniques have been applied in crashworthiness design using simplified lumped mass models [3-5]. 

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. 

Actions Modeling and Analysis, Fig. 14 (a) Modal as lumped masses. Periods (sec) 0.49,0.159,0.09 shape direct modeling of the equipment. Periods (sec) ... 

The complex soil-structure interaction of underground structures during seismic loading can be simulated using numerical analysis tools which include lumped mass/stif iess methods and finite-element/difference methods. 

The analysis of the K-Reactor building was based on the FREDA computer code. This solution used a lumped mass stick model of the structure connected to the free-field through SSI frequency dependent functions. The basic model did not include vertical and torsional responses. The SSI coefficients used in the basic model satisfy the restart criterion except for the consideration of layering and high-frequency effects. The staff concludes that free-field input motion generated by URS/Blume and the damping values used satisfy the restart criteria. 

Aside from the original assumption of a lumped analysis, thus far there have been no other assumptions or approximations to the model. The model relies completely on basic thermodynamic principles, a known cell performance R(I), and rigorous mathematical operations. To solve the model, we need to know the bulk mass and heat capacity of the cell, M and C, respectively the reactant supply flow rate (m = fuel flow + air flow) the inlet temperature and pressure and the change in stream composition due to the electrochemical reaction, AX, so that the change in enthalpy can be calculated the electrical load current, / and the inlet and exit temperatures, Tm and rout. 

In order to check various model assumptions a first step in the analysis requires to perform mass balance calculations involving the amount of gas oil injected and the amount of hydrocarbons obtained by pressure difference under vacuum conditions, with the key hypothesis that no hydrocarbons remain on catalyst surface at 2 psia. Given mass balance closure was within typically 5-7% error for all experiments conducted, the following was validated a) the total mass of hydrocarbons including various lumps during the reaction... 

Because of the latter considerations another approach was undertaken. Mandelbaum and Bohm (] ) characterized mass transfer in the mixed region by two lumped expressions Sh/(Sc.Gr)l/ and Re/Gr /, This analysis is... 

The drawback of this approach compared with that described in Section 6.5.2 is that all errors are lumped into the isotherm parameters rather than the effective mass transfer coefficient, because either the wrong column or isotherm model is chosen. This approach is thus recommended to get a quick first idea of system behavior using only little amounts of sample, and not for a complete analysis, especially if binary mixtures with component interactions are investigated. The significance of the results decreases even further if some plant and packing parameters are only guessed or even neglected. 

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