This paper presents a counterexample to the conjecture that the semi-explicit Lie-Newmark algorithm is variational. As a consequence the Lie-Newmark method is not well-suited for long-time simulation of rigid body-type mechanical systems. The counterexample consists of a rigid body in a static potential field.

Variational methods are a class of symplectic-momentum integrators for ODEs. Using these schemes, it is shown that the classical Newmark algorithm is structure preserving in a non-obvious way, thus explaining the observed numerical behavior. Modifications to variational methods to include forcing and dissipation are also proposed, extending the advantages of structure preserving integrators to ...

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC...

In this study, A finite element model based on the third order theory is presented for the active vibration control of composite beams with distributed piezoelectric sensors and actuators. For calculating the total charge on the sensor, the direct piezoelectric equation is used and the actuators provide a damping effect on the composite beam by coupling a negative velocity feedback control algo...

The paper considers an improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatiotemporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up no now, the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the ...

CALIBRATION AND RANKING OF COARSE-GRAINED MODELS IN MOLECULAR SIMULATIONS USING BAYESIAN FORMALISM Hadi Meidani,1,∗ Justin B. Hooper,2 Dmitry Bedrov,2 & Robert M. Kirby3 1Department of Civil and Environmental Engineering, 1211 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61822, USA 2Department of Materials Science & Engineering, 206 Civil and Mate...

The Newmark method is an effective method for numerical time integration in dynamic problems. The results of Newmark method are function of its parameters (β, γ and ∆t). In this paper, a stationary mode I dynamic crack problem is coded in extended finite element method )XFEM( framework in Matlab software and results are verified with analytical solution. This paper focuses on effects of main pa...