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Many engineering problems can be solved using a linear approximation. In the Finite Element Analysis (FEA) the set of equations, describing the structural behaviour is then linear K d = F (1.1) In this matrix equation, K is the stiffness matrix of the structure, d is the nodal displacements vector and F is the external nodal force vector. Characteristics of linear problems is that the displacements are proportional to the loads, the stiffness of the structure is independent on the value of the load level. Though behaviour of real structures is nonlinear, e.g. displacements are not proportional to the loads; nonlinearities are usually unimportant and may be neglected in most practical problems.
Dynamic tests were conducted utilizing clamped aluminum and composite beams and plates excited by shakers and acoustic progressive wave tubes. The total strains and the components, bending and axial and the displacements were measured with increasing levels of excitation. Bistable behaviour is observed with sinusoidal excitation for both the beams and plates. The beams randomly excited exhibit a slight frequency shift and peak broadening, which can be attributed to an increased stiffening or hard spring geometric nonlinearity. The plates randomly excited exhibit a greater frequency shift and peak broadening than the beams. The implications of nonlinear behaviour of beams and plates relative to fatigue lives are studied. The Miles single mode model is modified to account for multimodal response. Trends in the strain peek probability densities at low level and high levels of excitation are analyzed to determine the effects of axial strain on their shape. An effective multimodal cyclic frequency model is developed. A method to incorporate the effects of multimodal response of simple structures is presented with fatigue life estimates.
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"The vibration of a highly flexible cantilever beam is investigated. The order three equations of motion, developed by Crespo da Silva and Glyn (1978), for the nonlinear flexural-flexural-torsional vibration of inextensional beams, are used to investigate the time response of the beam subjected to harmonic excitation at the base. The equation for the planar flexural vibration of the beam is solved using the finite element method. The finite element model developed in this work employs Galerkin's weighted residuals method, combined with the Newmark technique, and an iterative process. This finite element model is implemented in the program NLB1, which is used to calculate the steady state and transient responses of the beam. The steady state response obtained with NLB is compared to the experimental response obtained by Malatkar (2003). Some disagreement is observed between the numerical and experimental steady state responses, due to the presence of numerical error in the calculation of the nonlinear inertia term in the former. The transient response obtained with NLB reasonably agrees with the response calculated with ANSYS®."--Abstract.
Nonlinear Dynamics, Volume 1: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear System Identification Nonlinear Modeling & Simulation Nonlinear Reduced-order Modeling Nonlinearity in PracticeNonlinearity in Aerospace Systems Nonlinearity in Multi-Physics Systems Nonlinear Modes and Modal Interactions Experimental Nonlinear Dynamics
* Explains the physical meaning of linear and nonlinear structural mechanics. * Shows how to perform nonlinear structural analysis. * Points out important nonlinear structural dynamics behaviors. * Provides ready-to-use governing equations.