Idealisation and Formulation in Structural Dynamics Using Modal Analysis

2011 ◽  
Vol 418-420 ◽  
pp. 1022-1025
Author(s):  
Muhammad Danish ◽  
Vinay Kumar Pingali ◽  
Somnath Chattopadhyaya ◽  
N.K. Singh ◽  
A.K. Ray
Keyword(s):  
Reference Frame ◽  
Structural Dynamics ◽  
Reference Frames ◽  
Dynamic Equilibrium ◽  
Equations Of Motion ◽  
Complex Structure ◽  
Complicated Structure ◽  
Multiple Reference Frames ◽  
Lumped Masses ◽  
Multiple Reference

The crux feature of this paper is the equations of motion in a structural dynamics with respect to single reference frame that can be easily derived, and the results are well defined and converged. However, problem occurs, when the analysis of any complex, complicated structure is considered and its equation of motion is extracted with respect to single reference frame. The results are indecipherable, ambiguous and less converged. Thus, for such a complex structure, the results obtain with respect to multiple reference frames. In present study, an approximated model with a set of lumped masses, properly interconnected, along with discrete spring and damper elements are in consideration for continuous vibrating system. This results in dynamic equilibrium, which in turn results in formulation and idealization. As, rightly said by scientist Steve Lacy- “To me, there is spirit in a reed. It is a living thing, a weed, really and it does not contain spirit of sort. It’s really an ancient vibration”

A Fully Coupled Flow and 6-DOF Motion Solver in Multiple Reference Frames

2015 ◽  
Author(s):  
Hua Shan ◽  
Sung-Eun Kim ◽  
Bong Rhee
Keyword(s):  
Reference Frames ◽  
Inertial Frame ◽  
Equations Of Motion ◽  
Body Motion ◽  
Governing Equations ◽  
Flow Equations ◽  
Fixed Frame ◽  
Actuator Disk ◽  
Multiple Reference Frames ◽  
Multiple Reference

In many computational fluid dynamics (CFD) applications involving a single rotating part, such as the flow through an open water propeller rotating at a constant rpm, it is convenient to formulate the governing equations in a non-inertial rotating frame. For flow problems consisting of both stationary and rotating parts, e.g. the stator and the rotor of a turbine, or the hull and propeller of a ship, the multiple reference frames (MRF) approach has been widely used. In most existing MRF models, the computation domain is divided into stationary and rotating zones. In the stationary zone, the flow equations are formulated in the inertial frame, while in the rotating zone, the equations are solved in the non-inertial rotating frame. Also, the flow is assumed to be steady in both zones and the flow solution in the rotating zone can be interpreted as the phase-locked time average result. Compared with other approaches, such as the actuator disk (body-force) model, the MRF approach is superior because it accounts for the actual geometry of the rotating part, e.g. propeller blades. A more complicated situation occurs when the flow solver is coupled to the six degrees of freedom (6-DOF) equations of rigid-body motion in predicting the maneuver of a self-propelled surface or underwater vehicle. In many applications, the propeller is replaced by the actuator disk model. The current work attempts to extend the MRF approach to the 6-DOF maneuvering problems. The governing equations for unsteady incompressible flow in a non-inertial frame have been extended to the flow equations in multiple reference frames: a hull-fixed frame that undergoes translation and rotation predicted by the 6-DOF equations of motion and a propeller-fixed frame in relative rotation with respect to the hull. Because of the large disparity between time scales in the 6-DOF rigid body motion of the hull and the relative rotational motion of the propeller, the phase-locked solution in the propeller MRF zone is considered a reasonable approximation for the actual flow around the propeller. The flow equations are coupled to the 6-DOF equations of motion using an iterative coupling algorithm. The coupled solver has been developed as part of NavyFOAM. The theoretical framework and the numerical implementation of the coupled solver are outlined in this paper. Some numerical test results are also presented.

scholarly journals Flexible coding of object motion in multiple reference frames by parietal cortex neurons

2020 ◽  
Vol 23 (8) ◽  
pp. 1004-1015 ◽  
Author(s):  
Ryo Sasaki ◽  
Akiyuki Anzai ◽  
Dora E. Angelaki ◽  
Gregory C. DeAngelis
Keyword(s):  
Parietal Cortex ◽  
Reference Frames ◽  
Object Motion ◽  
Multiple Reference Frames ◽  
Multiple Reference ◽  
Flexible Coding

Multisensory integration in multiple reference frames in the posterior parietal cortex

2004 ◽  
Vol 5 (3) ◽  
Author(s):  
Marie Avillac ◽  
Etienne Olivier ◽  
Sophie Den�ve ◽  
Suliann Ben Hamed ◽  
Jean-Ren� Duhamel
Keyword(s):  
Multisensory Integration ◽  
Parietal Cortex ◽  
Posterior Parietal Cortex ◽  
Reference Frames ◽  
Posterior Parietal ◽  
Multiple Reference Frames ◽  
Multiple Reference

Rotordynamic Analysis Using the Complex Transfer Matrix

2012 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Reference Frame ◽  
Transfer Matrix ◽  
Reference Frames ◽  
Detection System ◽  
Numerical Technique ◽  
External Support ◽  
Starting Point ◽  
Rotating Reference Frame ◽  
Rotating Reference Frames ◽  
Lumped Masses

The transfer matrix method is an expedient numerical technique for determining the dynamic behavior of a rotordynamic system (e.g., whirl frequencies, steady-state response to forcing). The typical 8 × 8 transfer matrix suffers from several deficiencies. First, for a system incorporating damping, the method generates a characteristic polynomial of degree 8N for a model of N lumped masses (degree 4N for an undamped model). The high degree of the polynomial results in lengthy computation times and decreased accuracy. Second, as discussed herein, the 8 × 8 formulation fails to distinguish between forward and backward whirl. These deficiencies are overcome by a novel complex-valued state variable redefinition resulting in a 4×4 transfer matrix including external support stiffness and damping. The complex transfer matrix is then modified to account for analysis within a rotating reference frame. Analysis in a rotating reference frame is a judicious means to determine unique system fault characteristics, which serve as a starting point for the development of an on-line fault detection system. Insights into using the complex transfer matrix in a rotating reference frame are discussed. Analytical results in both inertial and rotating reference frames for an overhung rotor model are provided.

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