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Research Papers

Predicting Changes in Vibration Behavior With Respect to Multiple Variables Using Empirical Sensitivity Functions

[+] Author and Article Information
Chulho Yang1

Mechanical Engineering Technology, Oklahoma State University, 385 Cordell South, Stillwater, OK 74078chulho.yang@okstate.edu

Douglas E. Adams

Mechanical Engineering, Purdue University, West Lafayette, IN 47907deadams@ecn.purdue.edu

1

Corresponding author.

J. Vib. Acoust 132(6), 061004 (Sep 16, 2010) (7 pages) doi:10.1115/1.4001843 History: Received August 18, 2009; Revised April 28, 2010; Published September 16, 2010; Online September 16, 2010

Engineers must routinely predict how structural systems will vibrate after design modifications are made to the mass, damping, or stiffness properties of the components. To reduce the cost of product development, sensitivity prediction methods are desired that can be applied using only empirical data from an initial prototype. Embedded sensitivity functions derived solely from empirical data have previously been applied (a) to identify optimal design modifications for reducing linear vibration resonance problems and (b) to predict the change in frequency response. In this previous work, predictive methods were developed that assumed that only one design parameter in the system was modified. In many applications, it is necessary to extend this approach to all major parameters for a more accurate prediction of the structural dynamic response. This paper utilizes a multivariable Taylor series to take into account multiple parameter changes that affect a broadband frequency range. The method is applied to a single degree of freedom analytical model to determine the accuracy of the predictions. Finite element analyses are then conducted on a three-story structure and an automotive vehicle component with modifications to the stiffness and mass distributions to demonstrate the feasibility of these predictions in applications to more complicated structural systems.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Single degree of freedom model: M1=1 kg, K1=5000 N/m, and C1=10 N s/m

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Figure 2

(a) Magnitude and (b) phase angle of the initial FRF with 5000 N/m stiffness (-), modified FRF with 7000 N/m stiffness (- -), and predicted FRF in 100 step iteration from the initial FRF (-.-.-)

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Figure 3

(a) Magnitude and (b) phase angle of the initial FRF with 5000 N/m stiffness (-), modified FRF with 7000 N/m stiffness and 1.2 kg mass (- -), and predicted FRF in 100 step iteration from the initial FRF (-.-.-) considering stiffness change only

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Figure 4

(a) Magnitude and (b) phase angle of the initial FRF with 5000 N/m stiffness (-), modified FRF with 7000 N/m stiffness and 1.2 kg mass (- -), and predicted FRF in 30 step iteration from the initial FRF (-.-.-) considering both stiffness and mass changes

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Figure 5

Transversal mode shapes of a three-story building model at 18, 51, and 74 Hz (from left to right)

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Figure 6

Comparison of FRFs (H31) before and after the modification in thickness of frames between the ground and the first floor with a predicted curve considering only a stiffness change: base line (-), modified (- -), and predicted (-.-.-)

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Figure 7

Comparison of FRFs (H31) before and after the modification in thickness of frames between the ground and the first floor with a predicted curve considering only mass change: base line (-), modified (- -), and predicted (-.-.-)

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Figure 8

Comparison of FRFs (H31) before and after the modification in thickness of frames between the ground and the first floor with a predicted curve considering both stiffness and mass changes: base line (-), modified (- -), and predicted (-.-.-)

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Figure 9

Comparison of FRFs (H21) before and after the modification in stiffness and mass between the ground and the first floor with a predicted curve considering only stiffness change: base line (-), modified (- -), and predicted (-.-.-)

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Figure 10

Comparison of FRFs (H21) before and after the modification in stiffness and mass between the ground and the first floor with a predicted curve considering mass change only: base line (-), modified (- -), and predicted (-.-.-)

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Figure 11

Comparison of FRFs (H21) before and after the modification in stiffness and mass between the ground and the first floor with a predicted curve considering both stiffness and mass changes: base line (-), modified (- -), and predicted (-.-.-)

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Figure 12

Meshed model of a part in a suspension system and the modified areas

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Figure 13

Magnitude of the initial FRF of the base line system (-), modified FRF with changes in stiffness by 25,329,238 N/m and mass by 1.46 kg (- -), and predicted FRF calculated considering the stiffness change only (-.-.-)

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Figure 14

Magnitude of the initial FRF of the base line system (-), modified FRF with changes in stiffness by 25,329,238 N/m and mass by 1.46 kg (- -), and predicted FRF calculated considering both changes (-.-.-)

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