Print Email Facebook Twitter Non-linear dynamic response of a beam using an impulse response method based on linear complex modes Title Non-linear dynamic response of a beam using an impulse response method based on linear complex modes Author Kok, Roy (TU Delft Civil Engineering and Geosciences) Contributor van Dalen, Karel (mentor) Metrikine, Andrei (graduation committee) van der Male, Pim (graduation committee) Degree granting institution Delft University of Technology Programme Civil Engineering Date 2019-07-25 Abstract The purpose of this thesis is to formulate and test a computational method, based on linear complex modes, to calculate the dynamic response of a beam with a boundary dashpot excited by a non-linear response-dependent dissipative force. This impulse response method is a time-stepping method which iteratively approximates the non-linear force by a sequence of short impulses and employs the response to a step force to calculate the response to each of them. The response to a step force consists of the summation of a particular and homogeneous solution of the governing partial differential equation, where the latter employs complex modes, and satisfies the initial conditions at the start of the time interval. To validate the impulse response method, it is compared to the classical modal reduction methods. Two modal reduction methods are distinguished, the first one employing real-valued modes (a) and the second employing complex modes (b), which in principle both violate the boundary conditions and result in an inaccurate response, especially at the boundary where the damping is located. The real-valued modes, corresponding to the undamped beam in free vibration, and the complex modes, corresponding to the beam with the boundary dashpot in damped free vibration, are determined to perform the methods. Elaboration of the impulse response method, and comparing it to the modal reduction method (a) leads to the general conclusion that the impulse response method is a suitable method to calculate the non-linear dynamic response of a cantilever beam with viscous damping at the top boundary. Three important requirements for the numerical procedure, (1) convergence, (2) stability and (3) accuracy, are met, under the assumption that the modal reduction method (a) approaches the exact solution. Increasing the influence of the viscous damping, and comparing the methods by the relative displacement difference, lead to results that are differently than expected, which makes it hard to state which method performs best. Subject Non-linearDynamic AnalysisEuler Bernoulli BeamModal AnalysisEigenvaluesDamping To reference this document use: http://resolver.tudelft.nl/uuid:99b63eca-b355-4893-8768-d5096c3cef4b Part of collection Student theses Document type master thesis Rights © 2019 Roy Kok Files PDF Non_linear_dynamic_respon ... _modes.pdf 2.98 MB Close viewer /islandora/object/uuid:99b63eca-b355-4893-8768-d5096c3cef4b/datastream/OBJ/view