It is often prohibitively expensive to integrate the response of a high order nonlinear system, such as a finite element model of a nonlinear structure, so a set of linear eigenvectors is often used as a basis in order to create a reduced order model (ROM). By augmenting the linear basis with a small set of discontinuous basis functions, ROMs of systems with local nonlinearities have been shown to compare well with the corresponding full order models.When evaluating the quality of a ROM, it is common to compare the time response of the model to that of the full order system, but the time response is a complicated function that depends on a predetermined set of initial conditions or external force. This is difficult to use as a metric to measure convergence of a ROM, particularly for systems with strong, non-smooth nonlinearities, for two reasons: (1) the accuracy of the response depends directly on the amplitude of the load/initial conditions, and (2) small differences between two signals can become large over time. Here, a validation metric is proposed that is based solely on the ROM’s equations of motion. The nonlinear normalmodes (NNMs) of the ROMs are computed and tracked as modes are added to the basis set. The NNMs are expected to converge to the true NNMs of the full order system with a sufficient set of basis vectors. This comparison captures the effect of the nonlinearity through a range of amplitudes of the system, and is akin to comparing natural frequencies and mode shapes for a linear structure. In this research, the convergencemetric is evaluated on a simply supported beam with a contacting nonlinearity modeled as a unilateral piecewise-linear function. Various time responses are compared to show that the NNMs provide a good measure of the accuracy of the ROM. The results suggest the feasibility of using NNMs as a convergencemetric for reduced order modeling of systems with various types of nonlinearities.
The reflection of an optical wave from metal, arising from strong interactions between the optical electric field and the free carriers of the metal, is accompanied by a phase reversal of the reflected electric field. A far less common route to achieving high reflectivity exploits strong interactions between the material and the optical magnetic field to produce a “magnetic mirror” that does not reverse the phase of the reflected electric field. At optical frequencies, the magnetic properties required for strong interaction can be achieved only by using artificially tailored materials. Here, we experimentally demonstrate, for the first time to the best of our knowledge, the magnetic mirror behavior of a low-loss all-dielectric metasurface at infrared optical frequencies through direct measurements of the phase and amplitude of the reflected optical wave. The enhanced absorption and emission of transverse-electric dipoles placed close to magnetic mirrors can lead to exciting new advances in sensors, photodetectors, and light sources.
The voltage on a single-turn loop inside an enclosure characterizes the enclosure shielding effectiveness against a lightning insult. In this paper, the maximum induced voltage on a single-turn loop inside an enclosure from lightning coupling to a metal enclosure wall is expressed in terms of two multiplicative factors: (A) the normalized enclosure wall peak penetration ratio (i.e., ratio of the peak interior electric field multiplied by the sheet conductance to the exterior magnetic field) and (B) the DC voltage on an ideal optimum coupling loop assuming the ideal penetration ratio of one. As a result of the decomposition, the variation of the peak penetration ratio (A) for different coupling mechanisms is found to be small; the difference in the maximum voltage hence arises from the DC voltage on the optimum coupling loop (B). Maximum voltages on an optimum coupling loop inside a finite cylinder enclosure for direct attachment and a lightning line source at different distances from the enclosure are given in Table 3.
This study details a methodology for quantification of errors and uncertainties of a finite element heat transfer model applied to a Ruggedized Instrumentation Package (RIP). The proposed verification and validation (V&V) process includes solution verification to examine errors associated with the code's solution techniques, and model validation to assess the model's predictive capability for quantities of interest. The model was subjected to mesh resolution and numerical parameters sensitivity studies to determine reasonable parameter values and to understand how they change the overall model response and performance criteria. To facilitate quantification of the uncertainty associated with the mesh, automatic meshing and mesh refining/coarsening algorithms were created and implemented on the complex geometry of the RIP. Automated software to vary model inputs was also developed to determine the solution’s sensitivity to numerical and physical parameters. The model was compared with an experiment to demonstrate its accuracy and determine the importance of both modelled and unmodelled physics in quantifying the results' uncertainty. An emphasis is placed on automating the V&V process to enable uncertainty quantification within tight development schedules.
Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416-422]. Given mth-order, n-dimensional realvalued symmetric tensors A and B, the goal is to find λ ε ℝ and x ε ℝn, x ≠= 0 such that Axm-1 = λBxm-1. Different choices for B yield different versions of the tensor eigenvalue problem. We present our generalized eigenproblem adaptive power (GEAP) method for solving the problem, which is an extension of the shifted symmetric higher-order power method (SS-HOPM) for finding Z-eigenpairs. A major drawback of SS-HOPM is that its performance depended on choosing an appropriate shift, but our GEAP method also includes an adaptive method for choosing the shift automatically.
During an environment, it is desirable to know the forces or inputs on the system of interest. With the inputs, one can directly use a finite element or experimental model to predict responses not measured in a field test. One can attempt to measure point forces using force gauges, however, these gauges are insufficient due to the inability to place a gauge at a forcing interface or to measure a force applied over an area. SWAT (Sum of weighted acceleration technique) is a method that uses mode shapes as a modal filter with measured accelerations and to solve the inverse problem and calculate the forces and moments on the system. This paper will examine an application where the use of a force gauge is impossible due to the external forces being applied over an area. The paper will calculate the sum of the forces and moments imparted on the system and will use a finite element model to check the plausibility of the calculated forces.
Scanning electron microscopes (SEMs) are used in neuroscience and materials science to image square centimeters of sample area at nanometer scales. Since imaging rates are in large part SNR-limited. imaging time is proportional to the number of measurements taken of each sample; in a traditional SEM. large collections can lead to weeks of around-the-clock imaging time. We previously reported a single-beam sparse sampling approach that we have demonstrated on an operational SEM for collecting "smooth" images. In this paper, we analyze how measurements from a hypothetical multi-beam system would compare to the single-beam approach in a compressed sensing framework. To that end. multi-beam measurements are synthesized on a single-beam SEM. and fidelity of reconstructed images are compared to the previously demonstrated approach. Since taking fewer measurements comes at the cost of reduced SNR, image fidelity as a function of undersampling ratio is reported.
We have demonstrated single-mode lasing in a single gallium nitride nanowire using distributed feedback by external coupling to a dielectric grating. By adjusting the nanowire grating alignment we achieved a mode suppression ratio of 17dB.