Space–time finite element approach to general description of a moving inertial load

The paper deals with the vibrations of structures subjected to a moving inertial load. Classical description of the moving mass particle based on the Hermitian shape functions fails in the case of wave equations of motion. Especially for hyperbolic equations solutions diverge. The velocity approach to the space–time finite element method has been used. Continuous Galerkin method for solving differential equations of motion was applied. Comprehensive moving mass matrices and elemental matrices for the case of a string, the Euler beam, and the Timoshenko beam have been derived. The numerical results are compared with the literature semi-analytical solutions. These numerical algorithms can be applied in transport engineering, manufacturing, and robotics.

► Space–time general matrices for moving inertial load are given for the first time.
► Characteristic matrices can be applied directly to almost all types of structures.
► Comparison with semi-analytical results exhibits excellent accuracy.