The new stochastic linearization technique is employed to investigate the nonlinear mean square response of a beam with artitrary boundary conditions under time-dependent stationary random ...excitation. To demonstrate the accuracy of this new method, mean square response is obtained through both the new and conventional versions of the stochastic linearization technique. An example of a beam with both ends simply supported is presented for the case of white noise excitation to illustrate the present method. Numerical simulations are performed to check the accuracy of the modified technique. It is shown that the modified version can yield more accurate results for the mean square response of the beam than the conventional stochastic linearization technique, especially when there exists a large nonlinearity.
We study the global solvability of a nonlinear Cauchy problem, which arises in the theory of oscillations in elastic bodies. We show that the linearized problem defines a contraction semigroup, which ...is then used to transform the Cauchy problem into an integral equation. Finally, it is shown that the corresponding integral operator has a unique fixed point, which gives rise to a global solution of the original nonlinear problem.
Slow wave structure employed in a wide-band helix traveling wave tube (TWT) always support backward waves. A backward wave space harmonic of a signal at a harmonic of the drive signal can effectively ...interact with slow space-charge wave of an electron beam. The minus first space harmonic is in synchronism with the beam at some frequencies. As a consequence, the backward wave can compete with the forward wave and it results in the backward wave oscillation (BWO) power holes under large signal conditions. In this talk, we reported a study of BWO power holes in both simulations and experiments, and developed a step helix pitch method to suppress the BWO power hole.
In the previous papers, the relationship between the stress rate and the tangent stiffness was derived using the special orthogonal group SO (3) in the finite element formulation. The stress rates ...used are the Truesdell stress rate, the Jaumann stress rate, the Neo-Green stress rate and the Ishihara stress rate. In that work, the stiffness elements of the tangent stiffnesses of beam elements with SO (3) were given. Those elements include material stiffness ΔδΠm, geometric stiffness of rigid rotation ΔδΠ, geometric stiffness of stretch to stress direction ΔδΠ, geometric stiffness of stretch perpendicular to area ΔδΠ and geometric stiffness of stretch to deformation rate ΔδΠ. In this paper, post-buckling analyses are made using the beam element of Ishihara stress rate. It is shown that the results are almost the same as the results of both 2-dimensional and 3-dimensional analyses of elastica, because the beam element has only geometric stiffness of rigid rotation as geometric stiffness and it can exactly show the nonlinearity of rigid rotation. It is also shown that the beam element without SO (3) can't be used for 3-dimensional large rotation analysis.
A system of nonlinear, coupled, second-order differential equations describing the oscillations of a cantilever beam has been considered and solved. The multiple-time scale perturbation technique ...(MSPT) has been applied to solve those differential equations up to the fourth approximation. The obtained solutions are presented as the response of the system's different modes. The theoretical resonance conditions of the system (three different modes) have been obtained from the third and fourth approximations. Some of these resonance conditions have been confirmed applying well-known numerical techniques.
Schematic-based lumped parameterized behavioral modeling and simulation methodologies have become available since the emergence of analog HDLs. They greatly ease iterative hierarchical multi-domain ...simulation, which is critical to the design of MEMS. NODAS is one of such tools, with models written in VerilogA and simulation performed within the Cadence framework.This paper focuses on several key modeling issues in NODAS, including schematic representation, element communication, linear, nonlinear and multi-domain modeling, and extensibility to new physical effects, processes and physical domains. A nonlinear beam model and an electrostatic gap model are discussed as examples. Simulation comparison to finite element analyses and experimental data verifies the accuracy of the models and validates the simulation methodology.
The present state and future of “nonlinear dynamics” is explained in this review. First, chaotic vibrations of nonlinear beams are used as a material to demonstrate our present understanding of ...chaos, compared with the situation of the early stage of its research. Second, two topics, microcantilever dynamics of tapping-mode atomic force microscopy and design of Earth to the Moon transfer trajectories of spacecrafts, are chosen for describing the importance and usefulness of “nonlinear dynamics” in new technologies. Moreover, two applications of “nonlinear dynamics” to biped walking robots and nonlinear optimal control are briefly addressed.
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