Parameters optimization of series–parallel inerter system with negative stiffness in controlling a single–degree–of–freedom system under base excitation

This study proposes a series–parallel inerter system with negative stiffness for the passive vibration control of an undamped single–degree–of–freedom system under base excitation. The necessary and sufficient conditions for stability of series-parallel inerter system with negative stiffness are established by Routh–Hurwitz criterion, and the stability boundary is obtained. The tuning parameters of the series-parallel inerter system with negative stiffness are determined through fixed point theory, and a comparison between the vibration mitigation performance of series-parallel inerter system with negative stiffness, series–parallel inerter system (without negative stiffness), and tuned mass damper is presented considering both harmonic excitation, transient excitation, and random (white noise) excitation. The results of this study demonstrate that under base harmonic excitation, series-parallel inerter system with negative stiffness outperforms the series–parallel inerter system and tuned mass damper in terms of suppression bandwidth and reducing the peak vibration amplitude of the primary mass. In the case of base acceleration–excited primary structure, more than 49.84% and 67.53% improvement can be obtained from series-parallel inerter system with negative stiffness as compared with tuned mass damper in terms of suppression bandwidth and reducing the peak vibration amplitude, respectively. Whereas in the case of base displacement–excited primary structure, more than 78% and 80% improvement can be obtained from series-parallel inerter system with negative stiffness, respectively, following the same criteria. A slightly lower improvement has been obtained from series-parallel inerter system with negative stiffness as compared with series–parallel inerter system, which justified the superiority of series–parallel inerter system compared to tuned mass damper. The transient response investigation showed that series-parallel inerter system with negative stiffness outperforms the series–parallel inerter system and tuned mass damper in terms of much shorter stabilization times and lower peak amplitude of the primary mass. Finally, the further comparison among these devices (series-parallel inerter system with negative stiffness, series–parallel inerter system, and tuned mass damper) under white noise excitation also shows that series-parallel inerter system with negative stiffness is superior to series–parallel inerter system and tuned mass damper for a small inertance mass ratio. This result could provide a theoretical basis for the design of inerter-based isolators with negative stiffness.

Steady-State Dynamical Response of a Strongly Nonlinear System with Impact and Coulomb Friction Subjected to Gaussian White Noise Excitation

The paper is devoted to the steady-state dynamical response analysis of a strongly nonlinear system with impact and Coulomb friction subjected to Gaussian white noise excitation. The Zhuravlev nonsmooth transformation of the state variables combined with the Dirac delta function is utilized to simplify the original system to one without velocity jump. Then, the steady-state probability density functions of the transformed system are derived in terms of the stochastic averaging method of energy envelope. The effectiveness of the presented analytical procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different restitution coefficients, amplitudes of friction, and noise intensities on the steady-state dynamical responses are investigated in detail. Results show different intensities of Gaussian white noise can affect the peaks value of the probability density functions, whereas the variations of restitution coefficients and amplitudes of friction can induce the occurrence of stochastic P-bifurcation.

Stochastic excitation for high-resolution Atomic Force Acoustic Microscopy imaging: a system theory approach.

In this work, a high-resolution Atomic Force Acoustic Microscopy imaging technique is shown in order to obtain the local indentation modulus at nanoscale using a model which gives a quantitative relationship between a set of contact resonance frequencies and indentation modulus through a white-noise excitation. This technique is based on white-noise excitation for system identification due to non-linearities in the tip-sample interaction. During a conventional scanning, a Fast Fourier Transform is applied to the deflection signal which comes from the photo-diodes of the Atomic Force Microscopy (AFM) for each pixel, while the tip-sample interaction is excited by a white-noise signal. This approach allows the measurement of several vibrational modes in a single step with high frequency resolution, less computational data and at a faster speed than other similar techniques. This technique is referred to as Stochastic Atomic Force Acoustic Microscopy (S-AFAM), where the frequency shifts with respect to free resonance frequencies for an AFM cantilever can be used to determine the mechanical properties of a material. S-AFAM is implemented and compared to a conventional technique (Resonance Tracking-Atomic Force Microscopy, RT-AFAM), where a graphite film over a glass substrate sample is analyzed. S-AFAM can be implemented in any AFM system due to its reduced instrumentation compared to conventional techniques.