Meta-models of repeated dissipative joints for damping design phase

Developing tools to predict dissipation in mechanical assemblies starting from the design process is a subject of increasing interest. Design phases imply numerous computations resulting from the use of families of models with varying properties. Model reduction is thus a critical tool to make such design studies affordable. Existing model reduction methods make computation of models with detailed non-linear parts accessible although costly although allowing the generation of a small size model for the linear part. One is, thus, interested in introducing meta-models of the behavior in the non-linear part by determining a basis of principal joint deformations. In this work, one seeks to validate the ability to predict macro-forces associated with the principal deformation shapes. Taking the case of aeronautic structures as cylindrical ones with multiple joints, one seeks to validate the construction of a meta-model associated to the joint. The ability to use such a meta-model to predict damping associated with viscoelastic behavior in a specifically designed bolted joint will be illustrated

Reduced-order modeling and dynamics of nonlinear acoustic waves in a combustion chamber

For understanding the fundamental properties of unsteady motions in combustion chambers, and for applications of active feedback control, reduced-order models occupy a uniquely important position. A framework exists for transforming the representation of general behavior by a set of infinite-dimensional partial differential equations to a finite set of nonlinear second-order ordinary differential equations in time. The procedure rests on an expansion of the pressure and velocity fields in modal or basis functions, followed by spatial averaging to give the set of second-order equations in time. Nonlinear gasdynamics is accounted for explicitly, but all other contributing processes require modeling. Reduced-order models of the global behavior of the chamber dynamics, most importantly of the pressure, are obtained simply by truncating the modal expansion to the desired number of terms. Central to the procedures is a criterion for deciding how many modes must be retained to give accurate results. Addressing that problem is the principal purpose of this paper. Our analysis shows that, in case of longitudinal modes, a first mode instability problem requires a minimum of four modes in the modal truncation whereas, for a second mode instability, one needs to retain at least the first eight modes. A second important problem concerns the conditions under which a linearly stable system becomes unstable to sufficiently large disturbances. Previous work has given a partial answer, suggesting that nonlinear gasdynamics alone cannot produce pulsed or 'triggered' true nonlinear instabilities; that suggestion is now theoretically established. Also, a certain form of the nonlinear energy addition by combustion processes is known to lead to stable limit cycles in a linearly stable system. A second form of nonlinear combustion dynamics with a new velocity coupling function that naturally displays a threshold character is shown here also to produce triggered limit cycle behavior

Controlling crystal symmetries in phase-field crystal models

We investigate the possibility to control the symmetry of ordered states in phase-field crystal models by tuning nonlinear resonances. In two dimensions, we find that a state of square symmetry as well as coexistence between squares and hexagons can be easily obtained. In contrast, it is delicate to obtain coexistence of squares and liquid. We develop a general method for constructing free energy functionals that exhibit solid-liquid coexistence with desired crystal symmetries. As an example, we develop a free energy functional for square-liquid coexistence in two dimensions. A systematic analysis for determining the parameters of the necessary nonlinear terms is provided. The implications of our findings for simulations of materials with simple cubic symmetry are discussed.Comment: 19 pages, 6 figure

Nonlinear spinor field in Bianchi type-I Universe filled with viscous fluid: numerical solutions

We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $\lambda F$, with $\lambda$ being a self-coupling constant and $F$ being a function of the invariants $I$ an $J$ constructed from bilinear spinor forms $S$ and $P$. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of $\tau$, where $\tau$ is the volume scale of BI universe. System of equations for $\tau$ and \ve, where \ve is the energy of the viscous fluid, is deduced. This system is solved numerically for some special cases.Comment: 15 pages, 4 figure