TAILIEUCHUNG - AA242B: MECHANICAL VIBRATIONS

A rough assessment of the importance of engineering activities that are not covered by R&D expenditure, as collected by the OECD, can be derived from Figure . Among the services supplied to clients there are two groups: technical counselling and the development of software. These tasks are not classified as R&D. However, they contribute to product innovation and comprise activities in the case of counselling necessary to initiate engineering based on the final specifications of a client’s procurement contract. The development of software comprises minor adjustments of programmes to clients’ permanently changing needs as part of after-sales services. | AA242B MECHANICAL VIBRATIONS AA242B MECHANICAL VIBRATIONS Direct Time-Integration Methods These slides are based on the recommended textbook M. Géradin and D. Rixen Mechanical Vibrations Theory and Applications to Structural Dynamics Second Edition Wiley John Sons Incorporated ISBN-13 9780471975465 AA242B MECHANICAL VIBRATIONS AA242B MECHANICAL VIBRATIONS Outline Q Stability and Accuracy of Time-Integration Operators z Newmark s Family of Methods Explicit Time Integration Using the Central Difference Algorithm AA242B MECHANICAL VIBRATIONS AA242B MECHANICAL VIBRATIONS Stability and Accuracy of Time-Integration Operators Multistep Time-Integration Methods Lagrange s equations of dynamic equilibrium p t 0 Mq Cq Kq 0 q 0 qo q 0 qo First-order form CM M0 K0 0 -M AB -AA 0 0 - 0 u Au where A Ag1AA q q q q U i Direct time-integration Ỡ AA242B MECHANICAL .

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