Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

Guthrie, Michael A.

doi:10.1115/1.4051279

Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

Journal Article · Mon Jun 07 00:00:00 EDT 2021 · Journal of Applied Mechanics

DOI:https://doi.org/10.1115/1.4051279· OSTI ID:1784863

Guthrie, Michael A. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1784863

Report Number(s):: SAND--2021-6144J; 696355

Journal Information:: Journal of Applied Mechanics, Journal Name: Journal of Applied Mechanics Journal Issue: 10 Vol. 88; ISSN 0021-8936

Publisher:: ASMECopyright Statement

Country of Publication:: United States

Language:: English

References (14)

Incremental dynamic analysis Vamvatsikos, Dimitrios; Cornell, C. Allin Earthquake Engineering & Structural Dynamics, Vol. 31, Issue 3 https://doi.org/10.1002/eqe.141	journal	January 2002
Response and failure of metal tanks from impulsive spot loading: Experiments and calculations Schwer, Leonard E.; Holmes, Bayard S.; Kirkpatrick, Steven W. International Journal of Solids and Structures, Vol. 24, Issue 8 https://doi.org/10.1016/0020-7683(88)90050-9	journal	January 1988
Some experimental observations of anomalous response of fully clamped beams Kolsky, H.; Rush, P.; Symonds, P. S. International Journal of Impact Engineering, Vol. 11, Issue 4 https://doi.org/10.1016/0734-743X(91)90012-5	journal	January 1991
Experimental results on the counter-intuitive behaviour of thin clamped beams subjected to projectile impact Li, Q. M.; Zhao, L. M.; Yang, G. T. International Journal of Impact Engineering, Vol. 11, Issue 3 https://doi.org/10.1016/0734-743X(91)90043-F	journal	January 1991
Seismic drift and ductility demands and their dependence on ground motions Krawinkler, H.; Medina, R.; Alavi, B. Engineering Structures, Vol. 25, Issue 5 https://doi.org/10.1016/S0141-0296(02)00174-8	journal	April 2003
Anomalous elastic–plastic responses to short pulse loading of circular plates Bassi, Andrea; Genna, Francesco; Symonds, P. S. International Journal of Impact Engineering, Vol. 28, Issue 1 https://doi.org/10.1016/S0734-743X(02)00036-2	journal	January 2003
A counterintuitive region of response for elastic-plastic rings loaded with axisymmetric pressure pulses Forrestal, M. J.; Tzout, D. Y.; Li, J. International Journal of Impact Engineering, Vol. 15, Issue 3 https://doi.org/10.1016/S0734-743X(05)80014-4	journal	January 1994
Distinctive features of counter-intuitive behavior of plates and shells after removal of impulse load Galiev, Sh. U. International Journal of Impact Engineering, Vol. 19, Issue 2 https://doi.org/10.1016/S0734-743X(96)00015-2	journal	February 1997
Experimental observations and discussion of counterintuitive behavior of plates and shallow shells subjected to blast loading Galiev, Sh. U. International Journal of Impact Engineering, Vol. 18, Issue 7-8 https://doi.org/10.1016/S0734-743X(96)00029-2	journal	October 1996
Influence of cavitation upon anomalous behaviour of a plate/liquid/underwater explosion system Galiev, Sh. U. International Journal of Impact Engineering, Vol. 19, Issue 4 https://doi.org/10.1016/S0734-743X(96)00040-1	journal	April 1997
Determining the effective level of outrigger in preventing collapse of tall buildings by IDA with an alternative damage measure Samadi, M.; Jahan, N. Engineering Structures, Vol. 191 https://doi.org/10.1016/j.engstruct.2019.03.095	journal	July 2019
Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics Symonds, P. S.; Yu, T. X. Journal of Applied Mechanics, Vol. 52, Issue 3 https://doi.org/10.1115/1.3169093	journal	September 1985
Seismic Performance of Jacket Type Offshore Platforms Through Incremental Dynamic Analysis Asgarian, Behrouz; Ajamy, Azadeh Journal of Offshore Mechanics and Arctic Engineering, Vol. 132, Issue 3 https://doi.org/10.1115/1.4000395	journal	March 2010
Applied Incremental Dynamic Analysis Vamvatsikos, Dimitrios; Cornell, C. Allin Earthquake Spectra, Vol. 20, Issue 2 https://doi.org/10.1193/1.1737737	journal	May 2004

Similar Records

Nonlinear valve train dynamics simulation with a distributed parameter model of valve springs

Journal Article · Tue Jul 01 00:00:00 EDT 1997 · Journal of Engineering for Gas Turbines and Power · OSTI ID:533052

Rotary spring energy storage

Technical Report · Wed Jul 01 00:00:00 EDT 1981 · OSTI ID:5631607

Binary peak power multiplier and its application to linear accelerator design

Journal Article · Wed Oct 01 00:00:00 EDT 1986 · IEEE Trans. Microwave Theory Tech.; (United States) · OSTI ID:5657354

Related Subjects

42 ENGINEERING
equations of motion
nonlinear dynamics
nonmonotonicity
plasticity
springs
structural dynamics
structures
vibration

Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

Citation Formats

References (14)

Similar Records

Related Subjects