SOFTENING BRANCHES OF A TWO-DEGREE-OF-FREEDOM SYSTEM INDUCED BY SPATIAL BUCKLING

2006 ◽  
Vol 06 (04) ◽  
pp. 493-512 ◽  
Author(s):  
NOËL CHALLAMEL
Keyword(s):  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Lateral Loading ◽  
Load Parameter ◽  
Imperfection Sensitivity ◽  
Softening Effect ◽  
Out Of Plane ◽  
Secondary Bifurcation ◽  
Two Degree Of Freedom

The aim of this paper is to show how geometrical non-linearity may induce equivalent softening in a simple two-degree-of-freedom spatial elastic system. The generic structural model studied is a generalization of Augusti's spatial model, incorporating lateral loading. This model could be used as a teaching model to understand the softening effect induced by out-of-plane buckling. The lateral loading in the plane of maximal stiffness is considered as the varying load parameter, whereas the vertical load is perceived as a constant parameter. It is shown that a bifurcation occurs at the critical horizontal load. The fundamental path becomes unstable, beyond this critical value. However, two symmetrical bifurcate solutions appear, whose stability depend on the structural parameters value. No secondary bifurcation is observed for this system. The presented system possesses imperfection sensitivity, and imperfection insensitivity, depending on the values of the structural parameters. In any case, for sufficiently large rotations, collapse occurs with unstable softening branches induced by spatial buckling.

Wavelet-Based Damage Detection of Multi-Degree-of-Freedom Structures

2004 ◽  
Author(s):  
Yuito Hashimoto ◽  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Wavelet Transform ◽  
Damage Detection ◽  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Space Representation ◽  
State Space Representation ◽  
Damage Location ◽  
Propagation Of Singularities ◽  
Structural Responses

In this paper, a method is proposed to identify the occurrence and the location of damage from the responses of multi-degree-of-freedom (MDOF) structures based on the wavelet transform, which has the capacity to detect discontinuities and singularities. First, the propagation of singularities in responses is investigated qualitatively in order to explain how the structural responses are influenced by sudden changes of structural parameters (stiffness) resulting from damages. Next, in order to confirm the proposed method for complicated models, we evaluate the influence of sudden changes of structural parameters on responses quantitatively, and the relations between the wavelet transform and the damage location by the aid of the state space representation of the MDOF structures. Finally, laboratory-scale experiments are carried out to verify the performance and detectability of the proposed methods in a fourth story structural model installed by additional stiffness members.

Analysis of out-of-plane motion of a disc brake system using a two-degree-of-freedom model with contact stiffness

2005 ◽  
Vol 219 (7) ◽  
pp. 869-879 ◽  
Author(s):  
J-E Oh ◽  
Y-G Joe ◽  
K Shin
Keyword(s):  
Friction Coefficient ◽  
Relative Velocity ◽  
Normal Force ◽  
Contact Stiffness ◽  
Plane Motion ◽  
Degree Of Freedom ◽  
Brake System ◽  
Disc Brake ◽  
Out Of Plane ◽  
Two Degree Of Freedom

A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamic interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. The dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffnesses of the pad and disc are equally important. Complex eigenvalue analysis is conducted for the case where the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of the friction coefficient with respect to the normal force makes the system more unstable. Non-linear analysis is also performed to demonstrate various responses. Comparing the responses with experimental data has shown that the proposed model may qualitatively well represent a certain type of brake noise.

Identification of Structural Parameters by Wavelet Transform of Acceleration Response

1999 ◽  
Author(s):  
Akira Sone ◽  
Ryutaro Segawa ◽  
Shizuo Yamamoto ◽  
Arata Masuda ◽  
Hiroaki Hata
Keyword(s):  
Wavelet Transform ◽  
Numerical Simulations ◽  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Acceleration Response ◽  
Single Degree Of Freedom ◽  
Displacement Response ◽  
Single Degree ◽  
Stiffness And Damping

Abstract The method to identify structural parameters of multi-degree of freedom structures by the wavelet transform of displacement response is previously proposed However, the vibration of structure is measured by the accelerometers. Therefore, if it is possible to identify structural parameters by the wavelet transform of only acceleration responses, it is very useful. In this paper, the method to identify structural parameters such as stiffness and damping by wavelet transform of acceleration responses is presented. To verify the applicability of the proposed method, numerical simulations using the single degree of freedom structure and the four-degree-of-freedom structure and the experiments using simple structural model are conducted. From both results, it has been clear that the proposed method can give the good estimation for the structural parameters.

scholarly journals Two Degree-of-Freedom Fiber-Coupled Heterodyne Grating Interferometer with Milli-Radian Operating Range of Rotation

Sensors ◽  
2019 ◽  
Vol 19 (14) ◽  
pp. 3219 ◽  
Author(s):  
Fuzhong Yang ◽  
Ming Zhang ◽  
Yu Zhu ◽  
Weinan Ye ◽  
Leijie Wang ◽  
...  
Keyword(s):  
Angular Displacement ◽  
Reference Beam ◽  
Angular Position ◽  
Degree Of Freedom ◽  
Displacement Measurement ◽  
Operating Range ◽  
Out Of Plane ◽  
Grating Interferometer ◽  
To Receive ◽  
Two Degree Of Freedom

In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

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