In this paper the response of the rigid block under rectangular pulse excitation is investigated using two different modelling 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 limitation of the mathematical programming formulation are discussed in terms of energy dissipation and restitution coefficient at impacts and in terms of solution times.

Rocking Response of the Rigid Block Under Rectangular Pulse Excitation: A Comparison between ODE and Optimization-Based Solvers / Gagliardo, R.; Portioli, F. P. A.; Cascini, L.; Landolfo, R.. - In: JOURNAL OF ADVANCES IN APPLIED & COMPUTATIONAL MATHEMATICS. - ISSN 2409-5761. - 8:(2022), pp. 109-116. [10.15377/2409-5761.2021.08.8]

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

#### Abstract

In this paper the response of the rigid block under rectangular pulse excitation is investigated using two different modelling 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 limitation 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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2022
Rocking Response of the Rigid Block Under Rectangular Pulse Excitation: A Comparison between ODE and Optimization-Based Solvers / Gagliardo, R.; Portioli, F. P. A.; Cascini, L.; Landolfo, R.. - In: JOURNAL OF ADVANCES IN APPLIED & COMPUTATIONAL MATHEMATICS. - ISSN 2409-5761. - 8:(2022), pp. 109-116. [10.15377/2409-5761.2021.08.8]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/922358`
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