A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation

1996 ◽  
Vol 118 (3) ◽  
pp. 313-317 ◽  
Author(s):  
D. J. Segalman ◽  
C. R. Dohrmann
Keyword(s):  
Natural Frequency ◽  
Configuration Space ◽  
Flexible Structures ◽  
Second Order ◽  
General Linear ◽  
New Approach ◽  
Kinematic Constraints ◽  
Rotation Rates ◽  
Deformation Modes

The problem of calculating the vibrations of rotating structures has challenged analysts since it was observed that the use of traditional modal approaches may incorrectly lead to the prediction of infinite deformation when rotation rates exceed the first natural frequency. Much recently published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but only simple structures such as individual beams and plates are addressed. The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes. This technique, tentatively named a Method of Quadratic Components, utilizes a nonlinear configuration space in which all kinematic constraints are satisfied up to second order.

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 2: Example Calculations

1996 ◽  
Vol 118 (3) ◽  
pp. 318-322 ◽  
Author(s):  
D. J. Segalman ◽  
C. R. Dohrmann ◽  
A. M. Slavin
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Membrane Structure ◽  
Flexible Structures ◽  
Preceding Paper ◽  
General Linear ◽  
Rotation Rates ◽  
Deformation Modes ◽  
Modal Coordinates

The problem of calculating the vibrations of rotating structures has challenged analysts since the observation that use of traditional modal coordinates in such problems leads to the prediction of instability involving infinite deformation when rotation rates exceed the first natural frequency. A method using a system of nonlinearly coupled deformation modes to analyze rotating general, linear (unjointed) structures that addresses the problem of erroneously predicting infinite deformations has been presented in a preceding paper (Segalman and Dohrmann, 1995). This technique is employed to address several types of problems ranging from simple beams to an inflated membrane structure. Some of the details of exploiting existing finite element codes to evaluate the relevant matrices are also developed.

scholarly journals Improved image-based deformation measurement for geotechnical applications

2016 ◽  
Vol 53 (5) ◽  
pp. 727-739 ◽  
Author(s):  
S.A. Stanier ◽  
J. Blaber ◽  
W.A. Take ◽  
D.J. White
Keyword(s):  
Measurement Precision ◽  
Deformation Measurement ◽  
Centrifuge Model Test ◽  
Displacement Fields ◽  
New Approach ◽  
Performance Benchmarking ◽  
Image Velocimetry ◽  
Spatially Varying ◽  
Deformation Modes ◽  
Sand Plug

This paper describes and benchmarks a new implementation of image-based deformation measurement for geotechnical applications. The updated approach combines a range of advances in image analysis algorithms and techniques best suited to geotechnical applications. Performance benchmarking of the new approach has used a series of artificial images subjected to prescribed spatially varying displacement fields. An improvement by at least a factor of 10 in measurement precision is achieved relative to the most commonly used particle image velocimetry (PIV) approach for all deformation modes, including rigid-body displacements, rotations, and strains (compressive and shear). Lastly, an example analysis of a centrifuge model test is used to demonstrate the capabilities of the new approach. The strain field generated by penetration of a flat footing and an entrapped sand plug into an underlying clay layer is computed and compared for both the current and updated algorithms. This analysis demonstrates that the enhanced measurement precision improves the clarity of the interpretation.

Fundamentals concerning wave loading on offshore structures

1986 ◽  
Vol 173 ◽  
pp. 667-681 ◽  
Author(s):  
James Lighthill
Keyword(s):  
Fluid Mechanics ◽  
Natural Frequency ◽  
Potential Flow ◽  
Vortex Flow ◽  
Offshore Structures ◽  
Second Order ◽  
Mechanics Of Solids ◽  
Wave Loading ◽  
Velocity Fluctuations ◽  
Substantial Body

This article is aimed at relating a certain substantial body of established material concerning wave loading on offshore structures to fundamental principles of mechanics of solids and of fluids and to important results by G. I. Taylor (1928a,b). The object is to make some key parts within a rather specialised field accessible to the general fluid-mechanics reader.The article is concerned primarily to develop the ideas which validate a separation of hydrodynamic loadings into vortex-flow forces and potential-flow forces; and to clarify, as Taylor (1928b) first did, the major role played by components of the potential-flow forces which are of the second order in the amplitude of ambient velocity fluctuations. Recent methods for calculating these forces have proved increasingly important for modes of motion of structures (such as tension-leg platforms) of very low natural frequency.

scholarly journals ANALYSIS OF THE GLOBAL AND LOCAL IMPERFECTION OF STRUCTURAL MEMBERS AND FRAMES

2019 ◽  
Vol 25 (8) ◽  
pp. 805-818 ◽  
Author(s):  
Charlotte Mercier ◽  
Abdelouahab Khelil ◽  
Ali Khamisi ◽  
Firas Al Mahmoud ◽  
Rémi Boissiere ◽  
...  
Keyword(s):  
Second Order ◽  
Structural Defects ◽  
Order Effects ◽  
Structural Members ◽  
Buckling Mode ◽  
New Approach ◽  
Order Analysis ◽  
Main Challenge ◽  
Buckling Failure ◽  
Global And Local

Stresses of a structure are determined with a first or a second order analysis. The choice of the method is guided by the potential influence of the structure’s deformation. In general, considering their low rigidity with regard to those of buildings, scaffolding and shoring structures quickly reach buckling failure. Imperfections, such as structural defects or residual stresses, generate significant second order effects which have to be taken into account. The main challenge is to define these imperfections and to include them appropriately in the calculations. The present study suggests a new approach to define all the structure’s imperfections as a unique imperfection, based on the shape of elastic critical buckling mode of the structure. This study proposes a method allowing to determine the equation of the elastic critical buckling mode from the eigenvectors of the second order analysis of the structure. Subsequently, a comparative study of bending moments of different structures calculated according to current Eurocode 3 or 9 methods or according to the new method is performed. The obtained results prove the performance of the proposed method.

First- and Second-Order Kinematics-Based Constraint System Analysis and Reconfiguration Identification for the Queer-Square Mechanism

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xi Kang ◽  
Xinsheng Zhang ◽  
Jian S. Dai
Keyword(s):  
Configuration Space ◽  
Bilinear Form ◽  
System Analysis ◽  
Kinematic Model ◽  
Second Order ◽  
Constraint System ◽  
Lie Bracket ◽  
Geometric Conditions ◽  
Reconfigurable Mechanisms ◽  
Order Constraints

Reconfiguration identification of a mechanism is essential in design and analysis of reconfigurable mechanisms. However, reconfiguration identification of a multiloop reconfigurable mechanism is still a challenge. This paper establishes the first- and second-order kinematic model in the queer-square mechanism to obtain the constraint system by using the sequential operation of the Lie bracket in a bilinear form. Introducing a bilinear form to reduce the complexity of first- and second-order constraints, the constraint system with first- and second-order kinematics of the queer-square mechanism is attained in a simplified form. By obtaining the solutions of the constraint system, six motion branches of the queer-square mechanism are identified and their corresponding geometric conditions are presented. Moreover, the initial configuration space of the mechanism is obtained.

Reduction approach to second order perturbed state-dependent sweeping process

2019 ◽  
Vol 28 (2) ◽  
Author(s):  
MUSTAPHA FATEH YAROU
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sweeping Process ◽  
New Approach ◽  
Standard Methods ◽  
First Order ◽  
Finite Dimensional ◽  
Perturbed State ◽  
State Dependent

In this paper, we present a new approach to solving second order nonconvex perturbed sweeping process in finite dimensional setting. It consists in a reduction of the problem to a first order one without use of the standard methods of fixed point theory. The perturbation, that is the external force applied on the system is not necessary with bounded values.

Vibration Reduction of Flexible Structures Using Extended Input Shaper and Smart Materials

2001 ◽  
Author(s):  
G. Song ◽  
B. Kotejoshyer ◽  
J. Fei
Keyword(s):  
Smart Materials ◽  
Vibration Suppression ◽  
Flexible Structures ◽  
Flexible Beam ◽  
Smart Sensor ◽  
New Approach ◽  
Active Vibration Suppression ◽  
Command Input ◽  
Active Vibration ◽  
Smart Actuator

Abstract This paper presents a new approach of integrating the method of command input shaping and the technique of active vibration suppression for vibration reduction of flexible structures during slew operations. The control object is a flexible composite beam driven by a high torque DC motor with the presence of nonlinearities such as backlash and stick-slip type of friction. Two piezoelectric patches are bonded on the surface of the flexible beam near its cantilevered end and are used as the smart actuator and the smart sensor respectively. In this new approach, the method of command input shaping is used to modify the existing command so that less vibration will be caused by the command itself. To overcome the nonlinearities associated with the DC motor, an extended shaper is designed. The technique of active vibration suppression using smart materials is used to actively control the vibration during and after the slew. With this pair of smart actuator and smart sensor, a strain rate feedback (SRF) controller is designed for active vibration suppression. With the extended Zero Vibration Derivative (ZVD) shaper and the SRF controller, the proposed new approach can effectively reduce the vibration of the flexible beam during slew operations.

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