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See detailFirst Integrals and Solutions of Duffing-Van der Pol Type Equations
Udwadia, Firdaus; Cho, Hancheol ULg

in Journal of Applied Mechanics (2014), 81(3), 034501-1-034501-4

A simple transformation is used to obtain the first integrals and the solutions of the Duffing–van der Pol type equation under certain conditions. It is shown that the system can be totally integrable and ... [more ▼]

A simple transformation is used to obtain the first integrals and the solutions of the Duffing–van der Pol type equation under certain conditions. It is shown that the system can be totally integrable and this total integrability admits new solutions. The new solutions require weaker conditions on the system’s parameters than hereto known. [less ▲]

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See detailLagrangians for Damped Linear Multi-Degree-of-Freedom Systems
Udwadia, Firdaus; Cho, Hancheol ULg

in Journal of Applied Mechanics (2013), 80(4), 041023-1041023-10

This paper deals with finding Lagrangians for damped, linear multi-degree-of-freedom systems. New results for such systems are obtained using extensions of the results for single and two degree-of-freedom ... [more ▼]

This paper deals with finding Lagrangians for damped, linear multi-degree-of-freedom systems. New results for such systems are obtained using extensions of the results for single and two degree-of-freedom systems. The solution to the inverse problem for an n-degree-of-freedom linear gyroscopic system is obtained as a special case. Multi-degree-of-freedom systems that commonly arise in linear vibration theory with symmetric mass, damping, and stiffness matrices are similarly handled in a simple manner. Conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained and several examples are provided. [less ▲]

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See detailSome Further Remarks on Hamilton's Principle
Udwadia, Firdaus; Leitmann, George; Cho, Hancheol ULg

in Journal of Applied Mechanics (2011), 78(1), 011014-1011014-4

This paper deals with the inverse problem of finding a suitable integrand so that upon the use of the calculus of variations, one obtains the equations of motion for systems in which the forces are ... [more ▼]

This paper deals with the inverse problem of finding a suitable integrand so that upon the use of the calculus of variations, one obtains the equations of motion for systems in which the forces are nonpotential. New extensions and generalizations of previous results are obtained. [less ▲]

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See detailAlternative approaches for the derivation of discontinuous Galerkin methods for nonlinear mechanics
Noels, Ludovic ULg; Radovitzky, Raúl

in Journal of Applied Mechanics (2007), 74

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element ... [more ▼]

Discontinuous Galerkin methods are commonly derived by seeking a weak statement of the governing differential equations via a weighted-average approach allowing for discontinuous fields at the element interfaces of the discretization. In order to ensure consistency and stability of the formulation, this approach requires the definition of a numerical flux and a stabilization term. Discontinuous Galerkin methods may also be formulated from a linear combination of the governing and compatibility equations weighted by suitable operators. A third approach based on a variational statement of a generalized energy functional has been proposed recently for finite elasticity. This alternative approach naturally leads to an expression of the numerical flux and the stabilization terms in the context of large deformation mechanics problems. This paper compares these three approaches and establishes the conditions under which identical formulations are obtained. [less ▲]

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See detailFluid-structure interaction effects in the dynamic response of free-standing plates to uniform shock loading
Kambouchev, Nayden; Radovitzky, Raúl; Noels, Ludovic ULg

in Journal of Applied Mechanics (2007), 74

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and ... [more ▼]

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid–structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylor’s FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter. [less ▲]

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