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 ...

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.

Comparison of 1719 differential GPS measurements with a 1 m LiDAR DEM covering West Seattle shows that DEM elevation errors range from –4.88 m to +3.32 m. The errors are spatially correlated with a semivariogram range of 125 m, an unclustered mean of –0.11 m, and an unclustered standard deviation of ±0.75 m. Although there are statistically significant correlations between elevation error and e...

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 ...

Isogeometric Analysis (IGA) is used in combination with proper orthogonal decomposition (POD) for model order reduction of the time parameterized acoustic wave equations. We propose a fully discrete IGA-Newmark-POD approximation and we analyze the associated numerical error, which features three components due to spatial discretization by IGA, time discretization with the Newmark scheme, and mo...

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...

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...

The von-K arm an non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-b time marching scheme in time. In the Newmark-b scheme, a non-linear fixed point iteration algorithm is employed. We monitor both temporal and spatial discretization errors based on derived analytical solutions, demonstrating...