Discussion: “On interactive buckling in a sandwich structure” by C. D. Coman

A recent article by Coman (Z Angew Math Phys 2009) on the response of compression sandwich struts made some claims on the quality of the simplified version of the interactive buckling model presented in Hunt and Wadee (Proc R Soc A 454(1972):1197–1216, 1998). Some of these claims are examined in detail herein; it is concluded that great care must be exercised when performing parametric studies with equations that have been derived from simplifying a mechanical model. This is because the resulting system of equations does not necessarily describe the original mechanical system in full, since the key assumptions necessarily change.     

Mobility and reactivity of lattice oxygen in Gd-doped ceria promoted by Pt

Summary For samples of the Ce_1-xGd_xO_2-y system prepared by the Pechini route and promoted with Pt, the mobility and reactivity of lattice oxygen were found to correlate with the density of surface and bulk anion vacancies.     

Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency–energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. PACS numbers: 05.45.Xt, 02.30.Hq     

Broadband energy exchanges between a dissipative elastic rod and a multi-degree-of-freedom dissipative essentially non-linear attachment

We analyze complex, multi-frequency, non-linear modal interactions in the damped dynamics of a viscously damped dispersive finite rod coupled to a multi-degree-of-freedom essentially non-linear attachment. We perform a parametric study to show that the attachment can be an effective broadband energy absorber and dissipater of shock energy from the rod. It is shown that strong targeted energy transfer from the rod to the attachment occurs when there is strong stiffness asymmetry in the attachment. For weak viscous dissipation, a clear understanding of dynamical transitions in the integrated rod-non-linear attachment system can be gained by wavelet transforming the time series and superimposing the resulting wavelet spectra in the frequency-energy plot (FEP) of the periodic orbits of the underlying Hamiltonian system. Two distinct NES configurations are analyzed in detail, and their damped responses are analyzed by the Hilbert-Huang transform (HHT). We show that the HHT is capable of analyzing even complex non-linear damped transitions, by providing the dominant frequency components (or equivalently, time scales) at which the non-linear phenomena take place, and clarifying the series of non-linear resonance captures between the rod and attachment dynamics that are responsible for the broadband energy exchanges in this system.     

Interconnect and lumped elements modeling in interior penalty discontinuous Galerkin time-domain methods

In this paper, we present an approach on how to incorporate passive lumped elements such as resistors, capacitors and inductors in DGTD methods and their application to interconnect modeling. Starting from the voltage and current relationships, we derive the equivalent relationships that describe each of the R, L, C in terms of the electric and magnetic fields. Next, these field expressions are weakly enforced through the Interior Penalty (IP) DG formulation. The proposed method is explicit and conditionally stable. Additionally, a local time-stepping strategy is applied to increase efficiency and reduce the computational time. Finally, a numerical example is presented to validate the proposed approach.     

Einige Resultate über die III-Hauptflächen eines Strahlensystems

Stephanidis has introduced the third quadratic differential form III of a rectilinear congruence S in the real 3-dimensional Euclidean space [6]. In the present paper we prove that the form III can be expressed in terms of the first and the second quadratic form of the congruence S and of the second fundamental form of the middle enveloppe M(u,v) of S. Further, we study the congruences, for which the III-principle surfaces coincide with some well-known ruled surfaces of the congruence S.

---

---

Herrn Professor Dr. Walter Benz zum 60. Geburtstag gewidmet     

Über eine von J. Hoschek erzeugte Klasse von Strahlensystemen

Hoschek has in [2] defined a class H(S) of congruences which are derived by suitable linear transformations from a given congruence S. In this paper we present a detailed study of the number of existing isotropic congruences in the class H(S) which has already been supplied with the structure of a vector space. Finally, using two subspaces of H(S), we derive conditions so that the congruence S is isotropic.     

On the singular set,the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces

Consider a finite volume hyperbolic surface. Under perturbation the spectrum of the Laplace operator is unstable but the singular set is stable. We characterize the singular set in terms of the resolvent of the Laplace operator and extend Fermi's Golden Rule to the case of multiple eigenvalues. the date of receipt and acceptance should be inserted later     

A molecular mechanics force field for lignin

A CHARMM molecular mechanics force field for lignin is derived. Parameterization is based on reproducing quantum mechanical data of model compounds. Partial atomic charges are derived using the RESP electrostatic potential fitting method supplemented by the examination of methoxybenzene:water interactions. Dihedral parameters are optimized by fitting to critical rotational potentials and bonded parameters are obtained by optimizing vibrational frequencies and normal modes. Finally, the force field is validated by performing a molecular dynamics simulation of a crystal of a lignin fragment molecule and comparing simulation-derived structural features with experimental results. Together with the existing force field for polysaccharides, this lignin force field will enable full simulations of lignocellulose.