Incipient deformation mechanisms of a semi-circular cantilever beam subjected to an out-of-plane step-loading

1996 ◽  
Vol 18 (7-8) ◽  
pp. 829-848 ◽  
Author(s):  
T.X. Yu ◽  
Y.L. Hua ◽  
S.R. Reid
Keyword(s):  
Cantilever Beam ◽  
Deformation Mechanisms ◽  
Out Of Plane ◽  
Plane Step ◽  
Step Loading

Interfacial Sliding in Back-End Interconnect Structures in Microelectronic Devices

2002 ◽  
Vol 716 ◽  
Author(s):  
K.A. Peterson ◽  
C. Park ◽  
I. Dutta
Keyword(s):  
Dielectric Material ◽  
Single Layer ◽  
Component Reliability ◽  
Force Microscopy ◽  
Interfacial Sliding ◽  
Microelectronic Devices ◽  
Atomic Force ◽  
Layer Structures ◽  
Out Of Plane ◽  
Plane Step

AbstractDeformation of interconnect structures at the back-end of microelectronic devices during processing or service can have a pronounced effect on component reliability. Here, we use atomic force microscopy (AFM) to study plastic deformation and interfacial sliding of Cu interconnects lines on Si. The behavior of both stand-alone Cu lines and lines embedded in a low K dielectric was studied. Following thermal cycling, changes were observed in the in-plane Cu line dimensions, as well as the out-of plane step height between Cu and dielectric in single layer structures. These were attributed to differential deformation of the Cu/Si and Cu/dielectric material pairs due to thermal expansion mismatch, accommodated by interfacial creep. These results are discussed in light of previous work on the mechanism of interfacial creep. Some preliminary results on the distortion of Cu lines due to package-level stresses are also presented.

Transient Response of a Right-Angled Bent Cantilever Subjected to Out-of Plane Tip Loading

1997 ◽  
Author(s):  
B. Wang ◽  
Z. M. Xiao ◽  
G. Lu
Keyword(s):  
Cantilever Beam ◽  
Transient Response ◽  
Response Mode ◽  
Phase Response ◽  
Applied Force ◽  
Constant Force ◽  
Input Energy ◽  
Transient Behaviour ◽  
Finite Duration ◽  
Out Of Plane

This paper provides an analysis of the transient behaviour of a right-angled bent cantilever beam subjected to a suddenly applied force at its tip perpendicular to its plane. A double-hinge mechanism is required to complete the possible deformation under a rectangular force pulse (constant force applied for a finite duration) with a four-phase response mode. The kinematics of the various response phases are described and the partitioning of the input energy at the plastic hinges during the motion is evaluated.

The Udwadia–Kalaba Trajectory Control Applied to a Cantilever Beam—Experimental Results

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Raphael Pereira Spada ◽  
Rodrigo Nicoletti
Keyword(s):  
Cantilever Beam ◽  
Tracking Control ◽  
Equations Of Motion ◽  
Constrained Systems ◽  
Mode Shapes ◽  
Laser Vibrometer ◽  
Successful Implementation ◽  
Out Of Plane ◽  
Control Forces

The Udwadia–Kalaba methodology is a possible way of explicitly obtaining the equations of motion of constrained systems. From these equations of motion, one can estimate the necessary forces in the constraint to keep the system in a given motion. Hence, the Udwadia–Kalaba methodology can also apply to active tracking control of subsystems or the control of points of a structure. In this work, one investigates experimentally the benefits and drawbacks of such control strategy by applying it to the control of out-of-plane vibrations of a cantilever beam. The beam is excited by a shaker mounted near the clamped end of the beam. A second shaker applies the control forces in the free end of the beam, where an accelerometer is used for feedback. The vibration behavior of the beam under excitation/control is measured by a laser vibrometer. Results show that the methodology changes the dynamic behavior of the structure by changing its boundary conditions at the point of control, thus shifting natural frequencies and mode shapes. Results also show that the successful implementation of the method experimentally is sensitive to the quality of modeling of the structure.

Dynamic profilometry without out-of-plane conversion to measure vibration frequency of a cantilever beam

2009 ◽  
Vol 11 (8) ◽  
pp. 085409 ◽  
Author(s):  
C Meneses-Fabian ◽  
G Rodriguez-Zurita ◽  
R Rodriguez-Vera ◽  
F Mendoza-Santoyo ◽  
Amalia Martinez
Keyword(s):  
Cantilever Beam ◽  
Vibration Frequency ◽  
Out Of Plane

Out-of-Plane Impact at the Tip of a Right-Angled Bent Cantilever Beam

1995 ◽  
Vol 62 (4) ◽  
pp. 887-892 ◽  
Author(s):  
B. Wang ◽  
T. X. Yu ◽  
S. R. Reid
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Bending Moment ◽  
Pure Bending ◽  
Concentrated Mass ◽  
Impulsive Load ◽  
Out Of Plane ◽  
History Of ◽  
The Cross

The present paper provides an analysis of the response of a right-angled bent cantilever beam subjected to an out-of-plane impulsive load (i.e., suddenly imposed velocity) applied to concentrated mass at its tip. If T0 and M0 are the fully plastic torque and bending moment, respectively, of the cross section, it is shown that for the case T0/M0 < 1, a double hinge mechanism is required, with a pure bending hinge in the first segment of the beam and a combined bending-torsion hinge in the second segment. The history of deformation is described following impartation of the load.

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