Nonintrusive Nonlinear Reduced Order Models for Structures in Large Deformations: Validations to Atypical Structures and Basis Construction Aspects

The focus of this investigation is on reduced order models (ROMs) of the nonlinear geometric response of structures that are built nonintrusively, i.e., from standard outputs of commercial finite element codes. Several structures with atypical loading, boundary conditions, or geometry are considered to not only support the broad applicability of these ROMs but also to exemplify the different steps involved in determining an appropriate basis for the response. This basis is formed here as a combination of linear vibration modes and dual modes, and some of the steps involved follow prior work; others are novel aspects, all of which are covered in significant detail to minimize the expertise needed to develop these ROMs. The comparisons of the static and dynamic responses of these structures predicted by the ROMs and by the underlying finite element models demonstrate the high accuracy that can be achieved with the ROMs, even in the presence of significant nonlinearity.

An improved multi-mode seismic vibration control method using multiple tuned mass dampers

Multiple vibration modes of an engineering structure might be excited by earthquake ground motions. Multiple tuned mass dampers (MTMDs) are widely used to control these multi-mode vibrations. However, in the commonly used MTMD system, the mass element in each tuned mass damper (TMD) is normally assumed to be the same. To improve the performance of MTMDs for seismic-induced vibration control, non-uniform MTMD masses are adopted in the present study to improve the mass utilization of TMD, and a location factor is proposed to determine the best location of each TMD in the MTMD system. The effectiveness of the proposed method is validated through numerical study. The results show that the proposed method effectively reduces the seismic responses of the structure induced by multiple vibration modes.

In-plane selective excitation of arbitrary vibration modes using thickness-shear (d15) piezoelectric transducers

Experimental modal analysis (EMA) is of great importance for the dynamic characterization of structures. Existing methods typically employ out-of-plane forces for excitation and measure the acceleration or strain for modal analysis. However, these methods encountered difficulties in some cases. In this work, we proposed an in-plane excitation method based on thickness-shear (d15) piezoelectric transducers. Through the combination of distributed d15 PZT strips, arbitrary vibration modes can be selectively excited in a wide frequency range. Both simulations and experiments were conducted and the results validated the proposed method. Specifically, bending, torsional, and longitudinal vibration modes of a rectangular bar were selectively excited. Torsional modes of a shaft were excited without the aid of brackets and bending modes of a circular plate were excited with actuators placed at nodal lines. Furthermore, the electromechanical impedance of the PZT-structure system was measured from which the natural frequency and quality factor were directly extracted. Due to its simplicity and flexibility, the proposed vibration excitation method is expected to be widely used in near future.

Упругие свойства и ангармонизм твердых тел

The squares of the velocities of the longitudinal and transverse acoustic waves separately are practically not associated with anharmonicity, and their ratio (vL2 / vS2) turns out to be a linear function of the Grüneisen parameter γ - the measure of anharmonicity. The obtained dependence of (vL2 / vS2) on γ is in satisfactory agreement with the experimental data. The relationship between the quantity (vL2 / vS2) and anharmonicity is explained through its dependence on the ratio of the tangential and normal stiffness of the interatomic bond λ, which is a single-valued function of the Grüneisen parameter λ (γ). The relationship between Poisson's ratio μ and Grüneisen parameter γ, established by Belomestnykh and Tesleva, can be substantiated within the framework of Pineda's theory. Attention is drawn to the nature of the Leont'ev formula, derived directly from the definition of the Grüneisen parameter by averaging the frequency of normal lattice vibration modes. The connection between Grüneisen, Leontiev and Belomestnykh-Tesleva relations is considered. The possibility of a correlation between the harmonic and anharmonic characteristics of solids is discussed.

Mobile Interface CMS Method for Vibration Characteristics Prediction of Mistuned Bladed Disk with Different Coupling Degrees

The prediction of vibration characteristics was studied in the mistuned bladed disk by the mobile interface prestressed component mode synthesis (CMS) superelement method. When the strongly, generally, and weakly coupling in the mistuned bladed disk, according to the results of the direct FEM method, the prediction accuracy of this method was verified and compared with the fixed-interface CMS method by using the relative error of dynamic frequency, vibration mode matching function, and dimensionless root mean square error of vibration amplitudes. It is pointed that for mistuned bladed disk in the strong coupling, the prediction accuracy of dynamic frequency and vibration amplitudes are higher by the mobile interface CMS method and the vibration modes are matched with the direct method. In weak coupling, the results of dynamic frequency and vibration modes predicted by the mobile interface CMS method and the fixed-interface CMS method are consistent with the direct method, but the vibration amplitudes’ prediction error of the mobile interface CMS method is lower than that of the fixed-interface CMS method. In general coupling, the mobile interface CMS method has higher dynamic frequency prediction accuracy at low order, and the two methods have comparable dynamic frequency prediction accuracy at high order. The vibration modes predicted by the two methods are matched with the direct FEM method, and the prediction accuracy of vibration amplitude by the mobile interface CMS method is better than that of the fixed-interface CMS method. The results indicate that the mobile interface CMS method could more accurately predict vibration characteristics of the mistuned bladed disk with different coupling degrees and could be an effective measurement for studying the vibration characteristics of the mistuned bladed disk system.

Bearing Seat Vibration Modes Undergoing Unbalanced Excitation of Multirotating Drums

Transmission modes of multiple rotating parts on combine harvester are complex and diverse, which resulted in large vibration and poor stability when the entire machine is harvesting. Aiming at the complex vibration problem of the combine harvester threshing system, this paper established the dynamic response model of the multidrum parallel system under different transmission modes and solved the vibration characteristics of the system. An experiment on the axial unbalance response of the parallel drum system under different transmission modes was carried out. The results show that the internal units of the threshing system form a whole through the transmission system, which causes the unbalanced response of the system to be superimposed on parallel threshing drums, thereby increasing the vibration amplitude. In addition, the change of the transmission mode will cause the vibration transmission path in the system to change greatly, and the boundary conditions of the system will be changed at the same time, which will eventually lead to the change of the unbalanced response characteristics.

Ultra-Wide Bandgap in Two-Dimensional Metamaterial Embedded with Acoustic Black Hole Structures

This paper reports a type of metamaterial plate enabling in-plane ultra-wide vibration isolation in engineering equipment development. It is composed of periodic hexagonal lattice structures. The acoustic black hole (ABH) structures are embedded in each cell wall of the conventional hexagonal lattice, which results in the reduction of local stiffness in the cell wall and the local mass in the hexagonal corner. The lattice can be simplified as the form of lumped masses vibrating on springs, and two types of eigenstates can be obtained: the rotational eigenstates and the transverse eigenstates. The geometric nonlinearity of the ABH structure leads to unevenly distributed vibration modes, resulting in the ultra-wide bandgap. Experimental results prove the effective attenuation capacity. Compared with the traditional hexagonal lattice, the proposed design provides greater advantages in practical application.