Abstract: Prediction of emission by a source of sound and a propagation of the sound within a surrounding medium, over a frequency range is provided. A system including the source and the surrounding medium is represented by elements e. For each element e and each frequency fi, a parameter Pe,i is associated to the element. At frequency fi, a parameter Pe,max is calculated over the frequency range. For each element e, elementary matrices Ke,max and Me,max are determined using the parameter Pe,max. For each frequency fi and for each element e, parameter Pe,i is used to determine a polynomial degree used to approximate the sound field, elementary matrices Ke,i and Me,i are extracted out of the matrices Ke,max and Me,max and are assembled into global matrices Ki and Mi. A global matrix system Zi is established based on the global matrices Ki and Mi, and the global matrix system is solved.

Abstract: The durability performance of a structure is virtually predicted, enabling the optimization of the durability performance. In a first act, the structure is modeled by a series of calculation points. Then, for each point, the stresses and strains brought by load cycles and defining hysteresis branches are determined. Then, an accumulated damage due to the load cycles is predicted and stored. For the prediction, first, using a hysteresis operator, a change in the stress along a portion of a hysteresis branch is calculated as a function of a change in the load in time, and, second, using the change in the stress and the stored accumulated damage, a change in the damage is calculated. Hence, also a change in the properties, including the stiffness, of the structure is calculated. Then, a further change in the stresses and strains is calculated on the basis of the change in these properties to determine a new adapted hysteresis branch.

Abstract: Methods for performing a dynamic analysis of complex systems are described. The dynamic analysis of complex systems is performed by sub-structuring of the system into a plurality of sub-structures. The sub-structures and the interfaces between the sub-structures are modelled using a generalized eigenvector analysis of a discretized model of a full system or a subassembly thereof comprising at least two sub-structures. The sub-structures then are combined at the interfaces into a combined system. The combined system then is solved. Optionally, selected sub-structures may be reduced. Performing such a dynamic analysis allows studying characteristics such as e.g. vibration and/or acoustical effects in a computational efficient way. Such methods can be applied for optimizing designs of such complex systems.

Abstract: Methods for performing a dynamic analysis of complex systems are described. The dynamic analysis of complex systems is performed by sub-structuring of the system into a plurality of sub-structures. The sub-structures and the interfaces between the sub-structures are modelled using a generalised eigenvector analysis of a discretised model of a full system or a subassembly thereof comprising at least two sub-structures. The sub-structures then are combined at the interfaces into a combined system. The combined system then is solved. Optionally, selected sub-structures may be reduced. Performing such a dynamic analysis allows studying characteristics such as e.g. vibration and/or acoustical effects in a computational efficient way. Such methods can be applied for optimising designs of such complex systems.