Modeling Quantitative Acoustic Microscopy for Layered Coatings

Multilayered ceramic and metallic coatings are receiving much attention for applications to improve the resistance to wear of surfaces. To assure the integrity of such coatings, quantitative nondestructive techniques are needed to determine the properties of coating materials and to evaluate the bonding quality of the interface between the coating and the substrate

Nonlinear problems of complex natural systems: Sun and climate dynamics

Universal role of the nonlinear one-third subharmonic resonance mechanism in generation of the strong fluctuations in such complex natural dynamical systems as global climate and global solar activity is discussed using wavelet regression detrended data. Role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Nino phenomenon have been discussed in detail. The large fluctuations of the reconstructed temperature on the millennial time-scales (Antarctic ice cores data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to Earth precession effect on the energy that the intertropical regions receive from the Sun. Effects of Galactic turbulence on the temperature fluctuations are discussed in this content. It is also shown that the one-third subharmonic resonance can be considered as a background for the 11-years solar cycle, and again the global (solar) rotation and chaotic propagating waves play significant role in this phenomenon. Finally, a multidecadal chaotic coherence between the detrended solar activity and global temperature has been briefly discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1002.1024, arXiv:1004.4639, arXiv:1006.4591, arXiv:1003.294

Extending the functionality of a symbolic computational dynamic solver by using a novel term-tracking method

Symbolic computational dynamic solvers are currently under development in order to provide new and powerful tools for modelling nonlinear dynamical systems. Such solvers consist of two parts; the core solver, which comprises an approximate analytical method based on perturbation, averaging, or harmonic balance, and a specialised term-tracker. A term-tracking approach has been introduced to provide a powerful new feature into computational approximate analytical solutions by highlighting the many mathematical connections that exist, but which are invariably lost through processing, between the physical model of the system, the solution procedure itself, and the final result which is usually expressed in equation form. This is achieved by a highly robust process of term-tracking, recording, and identification of all the symbolic mathematical information within the problem. In this paper, the novel source and evolution encoding method is introduced for the first time and an implementation in Mathematica is described through the development of a specialised algorithm

Transient Response of a Laminated Composite Plate

Propagation of guided waves in a laminated plate is of interest for ultrasonic nondestructive evaluation of defects and for material characterization. There is a need for a thorough understanding of the wave propagation characteristics in such a plate in order to use ultrasonic means to determine the material properties, assess damage, and characterize defects. The problem is also of interest for study of acoustic emission

N-1 modal interactions of a three-degree-of-freedom system with cubic elastic nonlinearities

In this paper the (Formula presented.) nonlinear modal interactions that occur in a nonlinear three-degree-of-freedom lumped mass system, where (Formula presented.), are considered. The nonlinearity comes from springs with weakly nonlinear cubic terms. Here, the case where all the natural frequencies of the underlying linear system are close (i.e. (Formula presented.)) is considered. However, due to the symmetries of the system under consideration, only (Formula presented.) modes interact. Depending on the sign and magnitude of the nonlinear stiffness parameters, the subsequent responses can be classified using backbone curves that represent the resonances of the underlying undamped, unforced system. These backbone curves, which we estimate analytically, are then related to the forced response of the system around resonance in the frequency domain. The forced responses are computed using the continuation software AUTO-07p. A comparison of the results gives insights into the multi-modal interactions and shows how the frequency response of the system is related to those branches of the backbone curves that represent such interactions

Measurements of Elastic Constants of Thin Al2O3 and SiC/Al Composite using Coupled Ultrasonic Plate Modes

An ultrasonic technique utilizing coupled ultrasonic plate modes for the measurement of elastic constants has been suggested in our previous studies [1–3]. The technique is based on measurements of obliquely incident ultrasonic beam zero-transmission angles and reconstruction from these angles of the composite elastic constants. Such a technique is particularly useful for measuring elastic constants of anisotropic plates and it has a unique capacity to measure in-plane elastic constants of thin anisotropic plates

Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators

In this paper, we describe a direct normal form decomposition for systems of coupled nonlinear oscillators. We demonstrate how the order of the system can be reduced during this type of normal form transformation process. Two specific examples are considered to demonstrate particular challenges that can occur in this type of analysis. The first is a 2 d.f. system with both quadratic and cubic nonlinearities, where there is no internal resonance, but the nonlinear terms are not necessarily ε1-order small. To obtain an accurate solution, the direct normal form expansion is extended to ε2-order to capture the nonlinear dynamic behaviour, while simultaneously reducing the order of the system from 2 to 1 d.f. The second example is a thin plate with nonlinearities that are ε1-order small, but with an internal resonance in the set of ordinary differential equations used to model the low-frequency vibration response of the system. In this case, we show how a direct normal form transformation can be applied to further reduce the order of the system while simultaneously obtaining the normal form, which is used as a model for the internal resonance. The results are verified by comparison with numerically computed results using a continuation software

Out-of-unison resonance in weakly nonlinear coupled oscillators

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems

Coherent Signal Amplification in Bistable Nanomechanical Oscillators by Stochastic Resonance

Stochastic resonance is a counter-intuitive concept[1,2], ; the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers[3], SQUIDs[4,5], magnetoelastic ribbons[6], and neurophysiological systems such as the receptors in crickets[7] and crayfish[8]. Although it is fundamentally important as a mechanism of coherent signal amplification, stochastic resonance is yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators, which can play an important role in the realization of controllable high-speed nanomechanical memory cells. Our nanomechanical systems were excited into a dynamic bistable state and modulated in order to induce controllable switching; the addition of white noise showed a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems paves the way for exploring macroscopic quantum coherence and tunneling, and controlling nanoscale quantum systems for their eventual use as robust quantum logic devices.Comment: 18 pages, 4 figure