1,720,976 research outputs found
Nonlinear dynamics of a beam on elastic foundation
No full textThe nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations
Applicability conditions of a Nonlinear Superposition Technique
No full textThe analytical conditions for the applicability of a Non!linear Superposition Technique"NST# are established by using the Normal Form Method "NFM#[ The superpositiontechnique represents the extension of modal analysis to weakly non!linear vibrationsystems[ In this paper it is shown that the NST leads to a non!uniform perturbationexpansion for the solution of dynamical systems when some special non!linear terms arepresent in the dynamical system[ An analytical proof for general dynamical systems anda numerical application to a simple mechanical system is included in the paper
Study of Reduced-Order Models for Gust-Response Analysis of Flexible Wings
No full textThree types of aeroelastic reduced-order models (ROMs) for flutter and gust-response analyses are examined, one of which is introduced here. One is based on the finite-state description of unsteady aerodynamics obtained through a rational-matrix approximation of the frequency-domain transcendental aerodynamic operator. Coupling this with the equations of the structural dynamics yields the aeroelastic ROM. The drawback of this approach is
that some aerodynamic states have to be added to the structural states in the state-space format description of the aeroelastic system. The second model that is discussed yields directly the finite-state description of the aeroelastic operator without altering the dimensions of the state space. This model is iterative in nature, in that it requires an estimate of aeroelastic eigenvalues and eigenvectors from the original eigenproblem. Finally, an alternate ROM
formulation for the gust-response problem is proposed. It combines good level of accuracy with reduction of additional aerodynamic states and thus can be conveniently used in preliminary design process and control-law synthesis
Modal Analysis of Aeroelastic Response of a Hovering Rotor -- The Impact of the Mode Choice
No full text
- …
