1. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Analytical model of the air spring Figure Legend:

2. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Calculation results of the pressure in the tanks and the flow rate in the circular tube (y a = 0.1 mm, V b = 546 mL) Figure Legend:

3. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Vibration model of a body supported by an air spring Figure Legend:

4. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Experimental setup Figure Legend:

5. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Comparison between experimental and theoretical values for various pipe lengths (d = 4.0 mm, X 0 = 0.1 mm, V b = 546 mL) Figure Legend:

6. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Comparison between experimental and theoretical values for various input amplitude (d = 4.0 mm, L = 1.0 m, V b = 546 mL) Figure Legend:

7. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Critical oscillation amplitude for laminar flow versus Reynolds number Re ω (Zhao and Cheng [17]) Figure Legend:

8. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Vibration response of supported mass and fluid in the pipe (d = 4.0 mm, X 0 = 0.1 mm, V b = 546 mL) Figure Legend:

9. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 A vibration model of the air spring Figure Legend:

10. Date of download: 7/8/2016 Copyright © ASME. All rights reserved. From: An Approximate Formula to Calculate the Restoring and Damping Forces of an Air Spring With a Small Pipe J. Vib. Acoust. 2013;135(5):051029-051029-9. doi:10.1115/1.4023820 Pascal's principle Figure Legend: