TY - JOUR

T1 - Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach

AU - Pirrotta, Antonina

AU - Pantelous, Athanasios A.

AU - Kougioumtzoglou, Ioannis A.

AU - Pirrotta, Antonina

AU - Antoniou, Efstathios N.

PY - 2017

Y1 - 2017

N2 - An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, based on the theoretical machinery of polynomial matrices, a closed form analytical solution is derived for the system response that involves non-singular matrices and relies on the use of a basis of the null space of the constraints matrix. Several structural/mechanical systems with singular matrices are included as examples for demonstrating the validity of the developed framework and for elucidating certain numerical aspects.

AB - An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, based on the theoretical machinery of polynomial matrices, a closed form analytical solution is derived for the system response that involves non-singular matrices and relies on the use of a basis of the null space of the constraints matrix. Several structural/mechanical systems with singular matrices are included as examples for demonstrating the validity of the developed framework and for elucidating certain numerical aspects.

KW - Applied Mathematics

KW - Closed form solution

KW - Linear constrained structural/mechanical systems

KW - Modeling and Simulation

KW - Multibody systems

KW - Polynomial matrix theory

KW - Singular matrix

KW - Applied Mathematics

KW - Closed form solution

KW - Linear constrained structural/mechanical systems

KW - Modeling and Simulation

KW - Multibody systems

KW - Polynomial matrix theory

KW - Singular matrix

UR - http://hdl.handle.net/10447/259301

UR - http://www.elsevier.com/inca/publications/store/5/2/4/9/9/8/

M3 - Article

VL - 42

SP - 423

EP - 440

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

ER -