An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators

Dongming  Tian; Zhuo Zhang; Yueqing  Yu; Xuping Zhang

doi:10.1109/ICARM.2017.8273206

An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators

Dongming Tian, Zhuo Zhang, Yueqing Yu, Xuping Zhang

Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

Abstract

This paper presents an equivalent analytical model for vibration analysis of the V-and Z-shaped electrothermal microactuators. Considering the geometric analogy between the line-shaped and V/Z-shaped beam, the analytical model for vibration of the line-shaped beam that characterize the V-and Z-shaped beams is established first. The line-shaped beam provides completely the same boundary conditions and geometric dimensions (beam span, width, thickness, and shuttle dimensions) as the V-and Z-shaped beams, except for the inclined angle and the middle step beam, namely the stiffness. By writing the frequency of the line-shaped beam as a product of its stiffness and the term determined by the boundary conditions, the first-order natural frequency of the V-and Z-shaped beams can be derived by substituting their stiffness into the frequency expression. As the movement of the shuttle (i.e., the stiffness) does not contribute higher order mode shapes, corresponding higher-order natural frequencies of the V-and Z-shaped beams can be predicted directly with the line-shaped beam model. Verification of the vibration model for the line-shaped beam as well as the equivalent approach to predicting the natural frequencies of the V-and Z-shaped beams was conducted by comparing the results with finite-element simulation data using ANSYS software. Results show that, apart from some inaccuracies in predicting the higher order frequencies for the Z-shaped beam, this equivalent approach is accurate for the first-order frequency of the V-and Z-shaped beam as well as the higher order frequencies for the V-shaped beam. With this simple equivalent model, it is possible to investigate the frequency characteristics of the two typical beams thus paving the way for control and improving the design of the V-and Z-shaped electrothermal microactuators.

Original language	English
Title of host publication	2017 2nd International Conference on Advanced Robotics and Mechatronics, ICARM 2017 : (ICARM)
Number of pages	6
Publisher	IEEE
Publication date	2017
Pages	456-461
ISBN (Print)	978-1-5386-3261-1
ISBN (Electronic)	978-1-5386-3260-4
DOIs	https://doi.org/10.1109/ICARM.2017.8273206
Publication status	Published - 2017
Event	IEEE International Conference on Advanced Robotics and Mechatronics - Hefei, China Duration: 29 Aug 2017 → 31 Aug 2017 http://www.ieee-arm.org/

Conference

Conference	IEEE International Conference on Advanced Robotics and Mechatronics
Country/Territory	China
City	Hefei
Period	29/08/2017 → 31/08/2017
Internet address	http://www.ieee-arm.org/

Keywords

Electrothermal Actuator
Natural Frequency
V-shaped beam
Vibration Analysis
Z-shaped beam

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10.1109/ICARM.2017.8273206

https://ieeexplore.ieee.org/document/8273206

Cite this

@inproceedings{85b2b48ff0b84c6aa37ece2b17dd2eb9,

title = "An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators",

abstract = "This paper presents an equivalent analytical model for vibration analysis of the V-and Z-shaped electrothermal microactuators. Considering the geometric analogy between the line-shaped and V/Z-shaped beam, the analytical model for vibration of the line-shaped beam that characterize the V-and Z-shaped beams is established first. The line-shaped beam provides completely the same boundary conditions and geometric dimensions (beam span, width, thickness, and shuttle dimensions) as the V-and Z-shaped beams, except for the inclined angle and the middle step beam, namely the stiffness. By writing the frequency of the line-shaped beam as a product of its stiffness and the term determined by the boundary conditions, the first-order natural frequency of the V-and Z-shaped beams can be derived by substituting their stiffness into the frequency expression. As the movement of the shuttle (i.e., the stiffness) does not contribute higher order mode shapes, corresponding higher-order natural frequencies of the V-and Z-shaped beams can be predicted directly with the line-shaped beam model. Verification of the vibration model for the line-shaped beam as well as the equivalent approach to predicting the natural frequencies of the V-and Z-shaped beams was conducted by comparing the results with finite-element simulation data using ANSYS software. Results show that, apart from some inaccuracies in predicting the higher order frequencies for the Z-shaped beam, this equivalent approach is accurate for the first-order frequency of the V-and Z-shaped beam as well as the higher order frequencies for the V-shaped beam. With this simple equivalent model, it is possible to investigate the frequency characteristics of the two typical beams thus paving the way for control and improving the design of the V-and Z-shaped electrothermal microactuators.",

keywords = "Electrothermal Actuator, Natural Frequency, V-shaped beam, Vibration Analysis, Z-shaped beam",

author = "Dongming Tian and Zhuo Zhang and Yueqing Yu and Xuping Zhang",

year = "2017",

doi = "10.1109/ICARM.2017.8273206",

language = "English",

isbn = "978-1-5386-3261-1 ",

pages = "456--461",

booktitle = "2017 2nd International Conference on Advanced Robotics and Mechatronics, ICARM 2017",

publisher = "IEEE",

note = "IEEE International Conference on Advanced Robotics and Mechatronics ; Conference date: 29-08-2017 Through 31-08-2017",

url = "http://www.ieee-arm.org/",

}

Tian, D, Zhang, Z, Yu, Y & Zhang, X 2017, An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators. in 2017 2nd International Conference on Advanced Robotics and Mechatronics, ICARM 2017: (ICARM). IEEE, pp. 456-461, IEEE International Conference on Advanced Robotics and Mechatronics, Hefei, China, 29/08/2017. https://doi.org/10.1109/ICARM.2017.8273206

An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators. / Tian, Dongming ; Zhang, Zhuo; Yu, Yueqing et al.
2017 2nd International Conference on Advanced Robotics and Mechatronics, ICARM 2017: (ICARM). IEEE, 2017. p. 456-461.

Research output: Contribution to book/anthology/report/proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators

AU - Tian, Dongming

AU - Zhang, Zhuo

AU - Yu, Yueqing

AU - Zhang, Xuping

PY - 2017

Y1 - 2017

N2 - This paper presents an equivalent analytical model for vibration analysis of the V-and Z-shaped electrothermal microactuators. Considering the geometric analogy between the line-shaped and V/Z-shaped beam, the analytical model for vibration of the line-shaped beam that characterize the V-and Z-shaped beams is established first. The line-shaped beam provides completely the same boundary conditions and geometric dimensions (beam span, width, thickness, and shuttle dimensions) as the V-and Z-shaped beams, except for the inclined angle and the middle step beam, namely the stiffness. By writing the frequency of the line-shaped beam as a product of its stiffness and the term determined by the boundary conditions, the first-order natural frequency of the V-and Z-shaped beams can be derived by substituting their stiffness into the frequency expression. As the movement of the shuttle (i.e., the stiffness) does not contribute higher order mode shapes, corresponding higher-order natural frequencies of the V-and Z-shaped beams can be predicted directly with the line-shaped beam model. Verification of the vibration model for the line-shaped beam as well as the equivalent approach to predicting the natural frequencies of the V-and Z-shaped beams was conducted by comparing the results with finite-element simulation data using ANSYS software. Results show that, apart from some inaccuracies in predicting the higher order frequencies for the Z-shaped beam, this equivalent approach is accurate for the first-order frequency of the V-and Z-shaped beam as well as the higher order frequencies for the V-shaped beam. With this simple equivalent model, it is possible to investigate the frequency characteristics of the two typical beams thus paving the way for control and improving the design of the V-and Z-shaped electrothermal microactuators.

AB - This paper presents an equivalent analytical model for vibration analysis of the V-and Z-shaped electrothermal microactuators. Considering the geometric analogy between the line-shaped and V/Z-shaped beam, the analytical model for vibration of the line-shaped beam that characterize the V-and Z-shaped beams is established first. The line-shaped beam provides completely the same boundary conditions and geometric dimensions (beam span, width, thickness, and shuttle dimensions) as the V-and Z-shaped beams, except for the inclined angle and the middle step beam, namely the stiffness. By writing the frequency of the line-shaped beam as a product of its stiffness and the term determined by the boundary conditions, the first-order natural frequency of the V-and Z-shaped beams can be derived by substituting their stiffness into the frequency expression. As the movement of the shuttle (i.e., the stiffness) does not contribute higher order mode shapes, corresponding higher-order natural frequencies of the V-and Z-shaped beams can be predicted directly with the line-shaped beam model. Verification of the vibration model for the line-shaped beam as well as the equivalent approach to predicting the natural frequencies of the V-and Z-shaped beams was conducted by comparing the results with finite-element simulation data using ANSYS software. Results show that, apart from some inaccuracies in predicting the higher order frequencies for the Z-shaped beam, this equivalent approach is accurate for the first-order frequency of the V-and Z-shaped beam as well as the higher order frequencies for the V-shaped beam. With this simple equivalent model, it is possible to investigate the frequency characteristics of the two typical beams thus paving the way for control and improving the design of the V-and Z-shaped electrothermal microactuators.

KW - Electrothermal Actuator

KW - Natural Frequency

KW - V-shaped beam

KW - Vibration Analysis

KW - Z-shaped beam

UR - http://www.scopus.com/inward/record.url?scp=85050812819&partnerID=8YFLogxK

U2 - 10.1109/ICARM.2017.8273206

DO - 10.1109/ICARM.2017.8273206

M3 - Article in proceedings

SN - 978-1-5386-3261-1

SP - 456

EP - 461

BT - 2017 2nd International Conference on Advanced Robotics and Mechatronics, ICARM 2017

PB - IEEE

T2 - IEEE International Conference on Advanced Robotics and Mechatronics

Y2 - 29 August 2017 through 31 August 2017

ER -

An Equivalent Line-beam Vibration Model for Frequency Analysis of the V- and Z-shaped Electrothermal Microactuators

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