A simple mass oscillator metasurface design with linear phase shift

In this paper, a simple mass oscillator metasurface is designed, which can regulate the phase shift of flexural wave covering 0-2π by adjusting the number of mass oscillators on the connecting bar. Based on the forced vibration theory, there is a simple approximately linear relationship between the number and phase shift of mass oscillators, which can more intuitively and accurately predict the phase of different number of mass oscillators, and then realize the metasurface design of mass oscillators with different requirements. Therefore, arbitrary regulation of flexural waves, such as abnormal refraction, beam focusing, and self-acceleration, can be realized by reasonably arranging the number of mass oscillators. The results show that the proposed metasurface can be greatly simplified both in the establishment of phase shift relation and in the fabrication of structure configuration, and will have broad application potential in the engineering field.

Study of flexural wave propagation through a cable stayed beam subjected to a moving load

A physical perspective of the propagation and attenuation of flexural waves is presented in this paper for the dynamic behaviors of cable stayed beams subjected to a moving load. Based on the method of reverberation-ray matrix (MRRM), the waveform solutions of the wave equations of a simplified beam-cable system subjected to a moving load (hereinafter referred to as a beam-cable system) are given, and the theory is verified by a numerical example. The dynamic response of cable stayed beams is decomposed into nine kinds of flexural waves, including traveling waves, near-field waves, and nondispersive waves, according to the wavenumber characteristics. Numerical examples are analyzed to demonstrate the propagation characteristics of flexural waves through cable stayed beams. Numerical results show that the flexural waves in the cable stayed beams are mainly low-frequency waves whose frequencies are less than 3 times the structural fundamental frequency, which can be used to further improve the computational efficiency of response analysis method based on MRRM, and the proportion of high-frequency components increases gradually with increasing structural stiffness. The near-field wave can be transformed into a traveling shear wave when its frequency is larger than the critical frequency, which decreases with increasing radius of gyration and decreasing elastic modulus of the beam. With the increase in the radius of gyration and the elastic modulus of the beam, the attenuation effect of the near-field wave weakens. The wave velocity and the wave dispersion effect have a positive correlation with the stiffness-related parameters of the beam-cable system. The study of the effect of the beam-cable system parameters on flexural wave propagation characteristics can be applied to achieve a better dynamic design for engineering structures.

Refraction of Flexural Waves by Ultra-broadband Achromatic Meta-slab with Wavelength-dependent Phase Shifts

Great progress has been made in modulating flexural waves by elastic metasurfaces. Most of the proposed elastic metasurfaces suffer from chromatic aberration, limited in a narrow bandwidth around the designed frequency. In this paper, overcoming the chromatic aberration, an ultra-broadband achromatic meta-slab (UAM) with subunits of gradient thickness is proposed to realize the refraction angle unchanged with the incident frequency. Based on the phase compensation principle, wavelength-dependent phase shifts for the UAM that realize achromaticity are obtained. In order to verify the effectiveness of the theoretical design, the transmitted wavefields are solved according to the phased array theory, and the results correspond with those obtained by the finite element (FE) simulations and experiments, which show that the refraction angle is unchanged for incident frequencies from 2 kHz to 8 kHz. Besides, the UAM is extended into a periodic meta-slab, and multifrequency achromaticity is realized. Our designed meta-slabs overcome the chromatic aberration by simple configurations, which have significance in the applications of vibration control, vibrational energy harvesting, and health monitoring.

Airborne noise calculation for single-layer partitions with the concentrated parameters method

The article considers an approach to the calculation of sound insulation for building partitions with the method of concentrated parameters at the standard frequency range, which is specified in regulatory documents. The concepts of “reduced” and “concentrated” masses are introduced for objects that are sound conductors. It is noted that the physical model of sound insulation in the three conditionally allocated frequency ranges of the standard spectrum has differences. The calculated equations of sound insulation for three frequency ranges are given. Systems of equations for obtaining the calculation formulas at the first and the second frequency ranges are used. The systems consist of equations for the conservation of the amount of motion and the conservation of kinetic energy. The influence of the damping effect of air and resonant phenomena in the plate on the final value of sound insulation is described. The nature of sound propagation in the third frequency range is considered, in which, unlike the first two sections of the frequency spectrum, where the propagation of flexural waves is mainly recorded in the plate, shear and dilatational vibrations have a predominant influence on the sound insulation level. Examples of graphs for massive partitions obtained by the considered method are given. The accuracy of the proposed method is evaluated in comparison with the normative code’s method and the method based on the theory of self-matching of sound fields. A general algorithm for calculating sound insulation in the entire standard frequency range is presented.

Energy spreading, equipartition and chaos in lattices with non-central forces

We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quadratic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quadratic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.

Enhanced Energy Harvesting of Flexural Waves in Elastic Beams by Bending Mode of Graded Resonators

We show efficient elastic energy transfer and wave confinement through a graded array of resonators attached to an elastic beam. Experiments demonstrate that flexural resonators of increasing lengths allow to reduce wave scattering and to achieve the rainbow effect with local wavefield amplifications. We show that the definition of a monotonically decreasing distribution of the natural frequencies of the resonators along the wave propagation direction, is the preferable choice to increase the energy efficiency of the system. The proposed configuration is suitable for micro-fabrication, envisaging practical applications for micro-scale vibration energy harvesting.