Nonlinear structural dynamics

Kitada, Y. Identification of nonlinear structural dynamic systems using wavelets. Journal of Engineering Mechanics (ASCE) 124(10) (1998), 1059-1066. 

Hughes, T.J.R. 1979. A note on the stability of Newmark s algorithm in nonlinear structural dynamics. International Journal for Numerical Methods in Engineering, 11, 383-386. 

Hajjar, J.F. Abel, J.F. 1988. Parallel processing for transient nonlinear structural dynamics of three-dimensional framed structures using domain decomposition. Computers Structures, 30(6) 1237-1254. 

W. K. Liu, T. Belytschko, and A. Mani, Probabilistic Finite Elements for Nonlinear Structural Dynamics, Computer Methods in Applied Mechanics and Engineering, no. 56, pp. 61-86, 1986. 

Yang JN, Lin S, Huang H, Zhou L (2006) An adaptive extended Kahnan filter for stmctural damage identification. J Struct Contr Health Monit 13(4) 849-867 Yu JX, Tang YL, Liu WJ (2010) Adaptive mutation particle filter based on diversity guidance. In 2010 international conference on machine learning and cybernetics (ICMLC), TBD Qingdao, China, vol 1, 11-14 July 2010, pp 369-374 Yun CB, Shinozuka M (1980) Identification of nonlinear structural dynamics systems. J Struct Mech 8(2) 187-203... 

Li J, Chen JB, Sun W, Peng YB (2012) Advances of probability density evolution method for nonlinear stochastic systems. Probab Eng Mech 28 132-142 liu WK, Belytschko T, Mani A (1986) Probability finite elements for nonlinear structural dynamics. Comput Methods Appl Mech Eng 56 61-81 Manolis GD, Koliopoulos PK (2001) Stochastic structural dynamics in earthquake tatgineering. WIT Press, Boston... 

In Ouypomprasert et al. (1989), it has been pointed out that for reliability analysis, it is most important to obtain support points for the response surface very close to or exactly at the limit state g(x) = 0. This finding has been further extended in Kim and Na (1997) and Zheng and Das (2000). In Brenner and Bucher (1995), the response surface concept has been applied to problems involving random fields and nonlinear structural dynamics. Besides polynomials of different orders, piecewise continuous functions such as hyperplanes or simplexes can also be utilized as response surface models. 

Sajeeb R, Manohar CS, Roy D (2009) A conditionally linearized Monte Carlo filter in nonlinear structural dynamics. Int J Nonlinear Mech 44 776-790 Saouma VE, Sivaselvan MV (eds) (2008) Hybrid simulation theory, implementation and applications. CRC Press, London... 

In blast analyses, the resistance is usually specified as a nonlinear function to simulate elastic, perfectly plastic behavior of the structure. The ultimate resistance, (R ) is reached upon formation of a collapse mechanism in the member. When the resistance is nonlinear, the dynamic equilibrium equation becomes ... 

When simple graphical, closed form or empirical solution methods arc not appropriate or do not provide sufficient information, the numerical time integration method can be used. This method is also known as the time history method. Most texts on structural dynamics (Biggs 1964, Clough 1993, Paz 1991) provide extensive coverage on numerical solution methods for nonlinear, SDOF systems. 

This representation is also called normal form and it is graphically depicted in Figure 3. It can be seen that the normal form is composed of three parts respectively given by the subsystems (4a), (4b) and (4c). The first part presents a linear structure and it is given by a chain of r — 1 integrators, whereas the second part has a nonlinear structure, where the input-output relationship explicitly appears. Finally, the last part is conformed by the dynamics of the n — r complementary functions. This part is called internal dynamics because it cannot be seen from the input-output relationship (see Figure 3) and whose structure can be linear or nonlinear. 

In Chapter 1, Raicu et al. make a unique comparison of nonlinear optical spectroscopy and x-ray crystallography in terms of the fundamental understanding of the time-resolved structural dynamics of myoglobin. 

We have presented two types of nonlinear IR spectroscopic techniques sensitive to the structure and dynamics of peptides and proteins. While the 2D-IR spectra described in this section have been interpreted in terms of the static structure of the peptide, the first approach (i.e., the stimulated photon echo experiments of test molecules bound to enzymes) is less direct in that it measures the influence of the fluctuating surroundings (i.e., the peptide) on the vibrational frequency of a test molecule, rather than the fluctuations of the peptide backbone itself. Ultimately, one would like to combine both concepts and measure spectral diffusion processes of the amide I band directly. Since it is the geometry of the peptide groups with respect to each other that is responsible for the formation of the amide I excitation band, its spectral diffusion is directly related to structural fluctuations of the peptide backbone itself. A first step to measuring the structural dynamics of the peptide backbone is to measure stimulated photon echoes experiments on the amide I band (51). 

Analysis of this 7feff using the techniques of nonlinear classical dynamics reveals the structure of phase space (mapped as a continuous function of the conserved quantities E, Ka, and Kb) and the qualitative nature of the classical trajectory that corresponds to every eigenstate in every polyad. This analysis reveals qualitative changes, or bifurcations, in the dynamics, the onset of classical chaos, and the fraction of phase space associated with each qualitatively distinct class of regular (quasiperiodic) and chaotic trajectories. 

Computational fluid dynamics models were developed over the years that include the effects of leaflet motion and its interaction with the flowing blood (Bellhouse et al., 1973 Mazumdar, 1992). Several finite-element structural models for heart valves were also developed in which issues such as material and geometric nonlinearities, leaflet structural dynamics, stent deformation, and leaflet coaptation for closed valve configurations were effectively dealt with (Bluestein and Einav, 1993 1994). More recently, fluid-structure interaction models, based on the immersed boundary technique. 

To obtain the dynamic response (according to Sect. 8.3.3) of the structure, four different types of earthquakes (El Centro 1940, Parkfield 2004, Ulcinj 1979, Petrovac 1979) with a maximum input acceleration of 0.36g have been applied. This set of records was chosen in order to investigate nonlinear structural response to excitations with different frequency content and duration. The results (Tables 8.8 and 8.9) show that, under acceleration of 0.36, the structure behaves in accordance with the designed seismic safety criteria (Sect. 8.3.4). 

Various types of oscillating behaviors such as emergence of chemical waves, chaotic patterns, and a rich variety of spatiotemporal structures are investigated in oscillatory chemical reactions in association with nonlinear chemical dynamics [1-3]. In non-equilibrium condition, the characteristic dynamics of such chemically reacting systems are capable to self-organize into diverse kinds of assembly patterns. With the help of nonlinear chemical dynamics, the complexity and orderliness of those chemical processes can be explained properly. Various biological processes which exhibited very time-based flucmations especially when they are away from equilibrium have also been described by mechanistic considerations and theoretical techniques of nonlinear chemical dynamics [4-7]. 

Katafygiotis, L., Moan, T. 6c Cheung, S. 2007. Auxiliary domain method for solving multiobjective dynamic reliability problems for nonlinear structures. Structural Engineering Mechanics 25(3), 347-363. 

Spacone, E., Filippou, EC. Taucer, EE 1996. Fibre beam-column element for nonlinear analysis of R/C frames. Part I formulation. Earthquake Engineering and Structural Dynamics, 25(7), 711-725. 

Sivaselvan, M.V. Reinhorn, A.M. 2004. Nonlinear structural analysis towards collapse simulation - a dynamical systems approach. Technical Report, Multidisciplinary Center for Earthquake Engineering Research. 

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