Rocking Response of the Rigid Block Under Rectangular Pulse Excitation: A Comparison between ODE and Optimization-Based Solvers

## Keywords

Rocking
Rigid block
ODE solver
Mathematical programming
Differential equation of motion

## How to Cite

Gagliardo, R. ., Portioli, F. ., Cascini , L. ., & Landolfo, R. . (2022). Rocking Response of the Rigid Block Under Rectangular Pulse Excitation: A Comparison between ODE and Optimization-Based Solvers. Journal of Advances in Applied & Computational Mathematics, 8, 109–116. https://doi.org/10.15377/2409-5761.2021.08.8

## Abstract

In this paper, the response of the rigid block under rectangular pulse excitation is investigated using two different modeling approaches and solvers. The first approach relies on the numerical integration of the differential equation of motion. The second approach is based on the formulation of the dynamic problem in terms of a special class of mathematical programming problem that is the linear complementarity problem. A validation study is carried out comparing the solutions given by the proposed formulation with the ones given by the numerical integration of the differential equation of motion obtained from ODE solvers available in MATLAB®. Potentialities and limitations of the mathematical programming formulation are discussed in terms of energy dissipation and restitution coefficient at impacts and in terms of solution times.

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