The Generalized-α Scheme as a Linear Multistep Integrator: Towards a General Mechatronic Simulator

2007 ◽  
Author(s):  
Olivier Bru¨ls ◽  
Martin Arnold
Keyword(s):  
Mass Matrix ◽  
Time Integration ◽  
Theoretical Background ◽  
Integration Scheme ◽  
Variable Step Size ◽  
Step Size ◽  
Mechatronic Systems ◽  
Variable Step ◽  
Time Integration Scheme ◽  
Consistent Formulation

This paper presents a consistent formulation of the generalized-α time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a non-constant mass matrix, controller dynamics, and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulae, which leads to elegant results related with consistency, order conditions for constant and variable step-size methods, as well as global convergence. The algorithm is applied for the simulation of a vehicle semi-active suspension.

The Generalized-α Scheme as a Linear Multistep Integrator: Toward a General Mechatronic Simulator

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
Olivier Brüls ◽  
Martin Arnold
Keyword(s):  
Mass Matrix ◽  
Time Integration ◽  
Theoretical Background ◽  
Integration Scheme ◽  
Variable Step Size ◽  
Step Size ◽  
Mechatronic Systems ◽  
Mass System ◽  
Time Integration Scheme ◽  
Consistent Formulation

This paper presents a consistent formulation of the generalized-α time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a nonconstant mass matrix, controller dynamics, and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulas, which leads to elegant results related to consistency, order conditions for constant and variable step-size methods, as well as global convergence. Those results are illustrated for a controlled spring-mass system, and the method is also applied for the simulation of a vehicle semi-active suspension.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

Separate Time Integration Based on the Hilber, Hughes, Taylor Scheme for Flexible Bodies With a Large Number of Modes

2020 ◽  
Vol 15 (6) ◽  
Author(s):  
Wolfgang Witteveen ◽  
Florian Pichler
Keyword(s):  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Integration Scheme ◽  
Step Size ◽  
Body Contact ◽  
Time Integration Scheme ◽  
Core Idea ◽  
Numerical Time Integration ◽  
Taylor Scheme ◽  
Local Deformations

Abstract In the current development of flexible multibody dynamics, the efficient and accurate consideration of distributed and nonlinear forces is an active area of research. Examples are, forces due to body-body contact or due to elastohydrodynamics (EHD). This leads to many additional modes for representing the local deformations in the areas on which those forces act. Recent publications show that these can be several hundred to several thousand additional modes. A conventional, monolithic numerical time integration scheme would lead to unacceptable computing times. This paper presents a method for an efficient time integration of such systems. The core idea is to treat the equations associated with modes representing local deformations separately. Using the Newmark formulas, a fixed point iteration is proposed for these separated equations, which can always be stabilized with decreasing step size. The concluding examples underline this property, as well as the fact that the proposed method massively outperforms the conventional, monolithic time integration with increasing number of modes.

A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2021 ◽  
Author(s):  
Alberto Carini ◽  
Markus V. S. Lima ◽  
Hamed Yazdanpanah ◽  
Simone Orcioni ◽  
Stefania Cecchi
Keyword(s):  
Adaptive Filters ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step

Active control for vehicle interior noise using the improved iterative variable step-size and variable tap-length LMS algorithms

2019 ◽  
Vol 67 (6) ◽  
pp. 405-414 ◽  
Author(s):  
Ningning Liu ◽  
Yuedong Sun ◽  
Yansong Wang ◽  
Hui Guo ◽  
Bin Gao ◽  
...  
Keyword(s):  
Steady State ◽  
Noise Control ◽  
Convergence Speed ◽  
Interior Noise ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Vehicle Interior ◽  
Vehicle Interior Noise ◽  
Variable Step

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

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