Active vibration control of a shaft bracket-plate coupled system

Active vibration control of a shaft bracket-plate coupled system is investigated. The vibration of the plate is controlled with electromagnetic vibration absorbers (EVAs), which are mounted around the feet of the shaft bracket to impede the transmission of vibration from the bracket apex to the plate. A dynamic model is established on the Timoshenko beam theory and the Kirchhoff thin plate theory to reveal the mechanism of vibration transmission. It is exhibited that all the induced forces and moments at the coupling points contribute much to the transverse responses of the plate. The feasibility of active control with the EVAs is evaluated numerically based on the controllability of the plate vibration. It is demonstrated that the two-point in-plane control is able to attenuate the plate vibration under the excitation of in-plane disturbance forces, while the multi-point control is effective in reducing the plate vibration regardless of the directions of disturbance forces. An experimental system is built to verify the performance of the two-point in-plane control. The results have shown that with the help of adaptive control, the two-point in-plane control is capable of suppressing the vibration of the foundation induced by the in-plane forces acting on the shaft bracket.

Semi-analytical static analysis of nonlocal strain gradient laminated composite nanoplates in hygrothermal environment

In this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory is based on the classical laminated thin plate theory with strain gradient effect to take into account the nonlocality present in the nanostructures. The equilibrium equations have been carried out by using the principle of virtual works and a system of partial differential equations of the sixth order has been carried out, in contrast to the classical thin plate theory system of the fourth order. The solution has been obtained using a trigonometric expansion (e.g., Navier method) which is applicable to simply supported boundary conditions and limited lamination schemes. The solution is exact for sinusoidal loads; nevertheless, convergence has to be proved for other load types such as the uniform one. Both the effect of the hygrothermal loads and lamination schemes (cross-ply and angle-ply nanoplates) on the bending behavior of thin nanoplates are studied. Results are reported in dimensionless form and validity of the present methodology has been proven, when possible, by comparing the results to the ones from the literature (available only for cross-ply laminates). Novel applications are shown both for cross- and angle-ply laminated which can be considered for further developments in the same topic.

Study on Instability Mechanism of Extraction Structure under Undercut Space Based on Thin Plate Theory in Block Caving Method

The instability of extraction structure under the undercut space in the block caving stope presents specific characteristics: rib spalling and floor heave in ore-loading roadway and collapse of major apexes. In order to study the stress and displacement evolution law of extraction structure under undercut space and reveal the instability mechanism of extraction structure, the numerical simulation model of block caving stope was established using the finite difference software FLAC3D. According to the postundercutting strategy in Tongkuangyu Mine in China, extraction structure was formed first in the simulation process, and then the undercut level was divided into eight units for excavation step by step. The stress and displacement of extraction structure after each step of undercutting were monitored and analyzed. Based on the thin plate theory, the mechanism of stress change and deflection deformation of extraction structure was revealed. The research results show that, under the action of high horizontal tectonic stress and vertical stress, the extraction structure under undercut space produces vertical upward bending deformation after undercutting during the block caving. The tension stress concentration gradually appears in the side wall of the ore-loading roadway and the tip of the major apexes; with the increase of the undercutting area, the degree of tensile stress concentration gradually becomes strong; when the tensile strength of the rock mass in extraction structure is exceeded, extraction structure presents instability. It is necessary to make the overlying ore collapse on extraction structure as soon as possible after undercutting, which is beneficial to release the tension stress in the extraction structure under undercutting space.

A Method for Determining the Thicknesses of the Reserved Protective Layers in Complex Goafs Using a Joint-Modeling Method of GTS and Flac3D

In this study, a C-ALS underground cavity scanner was used to detect the shapes of mining goafs. In addition, GTS software was adopted to establish a three-dimensional geological model based on the status of the stopes, geological data, and mechanical parameters of each rock mass and to analyze the roof areas of the goafs. In regard to the morphology of the study area, based on a thin plate theory and the obtained field sampling data, a formula was established for the thicknesses of the reserved protective layers in the goafs. In addition, a formula for the thicknesses of the protective layers in the curved gobs was obtained. The thickness formula of the protective layers was then successfully verified. The detection results showed that the roof shapes of the goafs in the Yuanjiacun Iron Mine were mainly arc-shaped, and the spans of the goafs were generally less than 20 m. The stability of the arc-shaped roofs was found to be greater than that of the plate-shaped roofs. Therefore, by reducing the thicknesses of the protective layers in mining goafs, the ore recovery rates can be increased on the basis of safe production conditions. The formula of the thickness of the security layers obtained through the thin plate theory was revised based on the statistical results of the roof shapes of the goafs and then combined using GTS and FLAC3D. The modeling method successfully verified the stability of the mined-out areas. It was found that the verification results were good, and the revised formula was able to improve the recovery rate of the ore under the conditions of meeting safe production standards. Also, it was found that the revised formula could be used in the present situation. At the same time, it was also determined that the complexity of the rock masses obstructed the full identification of the joints and fissures in the present orebodies. Therefore, it is necessary to incorporate C-ALS underground cavity scanners to regularly observe the shapes of the goafs in order to ensure that stability and safety standards are maintained.

Fracture criterion of basic roof deformation in fully mechanized mining with large dip angle

To explore the structure evolution of overlying strata and pressure characteristics of coal mining with large dip angle, the basic roof mechanical model was established that based on the thin plate theory and the development characteristics of 1212 (3) working face of Panbei Mine. The formula was deduced that used for calculating the basic roof stress distribution in large dip angle coal seam. It revealed the mechanism evolution of mining stress and its influence on overburden deformation. Furthermore, it was also discussed that the effect of false roof on the failure of the basic roof. It showed that the false roof increases the differentiation of gangue’s filling rate in goaf and improves the evolution rate of basic roof fracture. It is the main influencing factor that the large dip angle leads to the “scoop” distribution of the stress and deformation in basic roof. It dominates the evolution of overburden fractures and the regional instability. The maximum deformation of the basic roof is located in the middle and upper part of the working face. This theoretical model is verified by means of numerical simulation and field monitoring.

A Linearised Hybrid FE-SEA Method for Nonlinear Dynamic Systems Excited by Random and Harmonic Loadings

The present paper proposes a linearised hybrid finite element-statistical energy analysis (FE-SEA) formulation for built-up systems with nonlinear joints and excited by random, as well as harmonic, loadings. The new formulation was validated via an ad-hoc developed stochastic benchmark model. The latter was derived through the combination of the Lagrange-Rayleigh-Ritz method (LRRM) and the Monte Carlo simulation (MCS). Within the build-up plate systems, each plate component was modelled by using the classical Kirchhoff’s thin-plate theory. The linearisation processes were carried out according to the loading-type. In the case of random loading, the statistical linearisation (SL) was employed, while, in the case of harmonic loading, the method of harmonic balance (MHB) was used. To demonstrate the effectiveness of the proposed hybrid FE-SEA formulation, three different case studies, made-up of built-up systems with localized cubic nonlinearities, were considered. Both translational and torsional springs, as joint components, were employed. Four different types of loadings were taken into account: harmonic/random point and distributed loadings. The response of the dynamic systems was investigated in terms of ensemble average of the time-averaged energy.

Vibration of a U-shaped steel–concrete composite hollow waffle floor under human-induced excitations

The U-shaped steel–concrete composite hollow waffle floor is an innovative slender large-span floor system, where severe vibration may occur under human-induced excitations. In this research, a theoretical analysis and experimental testing are performed to explore the vibration behaviour of the composite hollow waffle floor. First, the natural frequency formula is proposed based on orthotropic thin plate theory, and the main rigidity calculation for the composite hollow waffle floor is given. Second, the mode shape, frequency and damping ratio of the composite hollow waffle floor are captured by on-site tests and validated by analytical and numerical methods, indicating that the floor has a low-frequency with a low damping ratio. Third, the vibration response of the composite hollow waffle floor is obtained by walking and running tests considering the influence of the frequency, spatial position, group size and route; in addition, the relationships between the values involved in the vibration evaluation are discussed. Finally, the composite hollow waffle floor presents satisfactory vibration performance evaluated by the threshold values among the current codes.

Nonlinear Pull-in Instability of Rectangular Nanoplates Based on the Positive and Negative Second-Order Strain Gradient Theories with Various Edge Supports

Based on the positive and negative second-order strain gradient theories along with Kirchhoff thin plate theory and von Kármán hypothesis, the pull-in instability of rectangular nanoplate is analytically investigated in the present article. For this purpose, governing models are extracted under intermolecular, electrostatic, hydrostatic, and thermal forces. The Galerkin method is formally exerted for converting the governing equation into an ordinary differential equation. Then, the homotopy analysis method is implemented as a well-designed technique to acquire the analytical approximations for analyzing the effects of disparate parameters on the nonlinear pull-in behavior. As an outcome, the impacts of nonlinear forces on nondimensional fundamental frequency, the voltage of pull-in, and softening and hardening effects are examined comparatively.

Design and Analysis of Capacitive Micromachined Ultrasonic Transducer

Background:Objective:To simulate a Micromechanical systems (MEMS) based CMUT working as a transmitter with the existing design and provide comparison within the possible architectural geometries.Methods:FEM simulation software COMSOL is used to simulate the 3D model of the transducer radiating in the air. The classical thin-plate theory is employed to solve for CMUT with a circular shape which is sufficient when the ratio of the diameter to thickness of the plate is very large, an aspect common in CMUTs. The Galerkin-weighted residual technique is used to get a solution for thin plate equation with the presumption that the deflections are small in comparison to the thickness of the plate.Results:The resonant frequency of CMUT with different geometries have been calculated. The deflection of membrane with applied DC bias is shown along with collapse voltage calculation. The generated ultrasound is shown with the AC bias superimposed on the DC bias. The capacitance change with the increasing DC voltage is discussed. The deflection of membrane is maximum as the resonance frequency is proved.Conclusion:The review of Capacitive Micromachined Ultrasonic Transducer architectures with different shapes is highlighted. The working behavior of CMUT with suitable dimension is simulated in 3D providing researcher data to wisely choose the CMUT prior to the fabrication. The CMUT is prioritized on various characteristics like wafer area utilization, deflection percentage within the cavity and durability of the transducer.

Nonlinear Parametric Vibration and Chaotic Behaviors of an Axially Accelerating Moving Membrane

Nonlinear vibration characteristics of a moving membrane with variable velocity have been examined. The velocity is presumed as harmonic change that takes place over uniform average speed, and the nonlinear vibration equation of the axially moving membrane is inferred according to the D’Alembert principle and the von Kármán nonlinear thin plate theory. The Galerkin method is employed for discretizing the vibration partial differential equations. However, the solutions concerning to differential equations are determined through the 4th order Runge–Kutta technique. The results of mean velocity, velocity variation amplitude, and aspect ratio on nonlinear vibration of moving membranes are emphasized. The phase-plane diagrams, time histories, bifurcation graphs, and Poincaré maps are obtained; besides that, the stability regions and chaotic regions of membranes are also obtained. This paper gives a theoretical foundation for enhancing the dynamic behavior and stability of moving membranes.