scholarly journals The Dynamic Response and Failure Model of Thin Plate Rock Mass under Impact Load

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Feng Li ◽  
Xinhui Dong ◽  
Yue Wang ◽  
Hanwu Liu ◽  
Chuang Chen ◽  
...  
Keyword(s):  
Rock Mass ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Failure Mechanism ◽  
Thin Plate ◽  
Impact Load ◽  
Vibration Modes ◽  
Plate Model ◽  
Damage And Failure ◽  
Dynamic Disaster

The layered rock mass widely exists in mining, construction, transportation, and water conservancy projects, and the damage phenomena of plate crack and spalling often occurs in the process of coal and rock dynamic disaster in deep mining. Therefore, the rock mass nearby excavation surface is usually considered to be composed of layers of thin plate rock mass to reveal the damage and failure mechanism of rock mass. In the whole dynamic process of mining and coal and rock dynamic disaster, rock mass would bear the dynamic disturbance from mine earthquake, and at present, the mechanical characteristics of rock mass are mainly studied under static load, while dynamic mechanical response characteristics and the mechanisms of dynamic damage, failure, and disaster-causing are still unclear. This study mainly focused on the dynamic response characteristic and failure mechanism of rock mass based on a rectangular thin plate model. The frequency equations and deflection equations of the thin plate rock mass with different boundary conditions (S-F-S-F, S-C-S-C, and C-C-C-C) were established under free vibration by the thin plate model and the dual equation of the Hamilton system, and the deflection equations under impact load were derived based on the Duhamel integral. And then, the effective vibration modes of the thin plate rock mass with different boundary conditions and their natural frequencies were obtained by Newton’s iterative method. Based on the third-strength theory and the numerical simulation results by LS-DYNA, the maximum shear of the effective vibration modes and the processes of damage and failure under impact load were analyzed. The research results showed that the initial position of damage and failure may be determined by effective vibration mode with the lowest frequency; the develop tendency of which by the combined actions of other effective vibration modes and the effective vibration modes with lower frequency could have greater influence on the process of damage and failure of the thin plate rock mass, which are beneficial to revealing the mechanism of coal and rock dynamic disaster.

scholarly journals Bearing Seat Vibration Modes Undergoing Unbalanced Excitation of Multirotating Drums

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Yu Li ◽  
Zhong Tang ◽  
Xinzhong Wang ◽  
Hao Zhang ◽  
Yaoming Li
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Vibration Amplitude ◽  
Vibration Modes ◽  
Response Model ◽  
Response Characteristics ◽  
Transmission Modes ◽  
Combine Harvester ◽  
Seat Vibration ◽  
Poor Stability

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.

A New Method to the Elastodynamic Response of a Spherical Shell Under the Impact Load

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Shugen Xu ◽  
Yang Wei ◽  
Chong Wang ◽  
Weiqiang Wang
Keyword(s):  
Wave Equation ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Solution Structure ◽  
Structure Theorem ◽  
Impact Load ◽  
Structural Dynamic ◽  
Elastodynamic Response ◽  
The Impact

In this paper, a new methodology for solving response of a spherical shell based on developed solution structure theorem has been proposed. It can be used to solve the wave equation about the structural dynamic response of a spherical shell under the impact pressure. The proposed method can be used to solve a batch of partial differential equations having the similar governing equation with different initial and boundary conditions. A detailed solving procedure has been provided to show how to use this method correctly. Finally, a practical example is provided to show how to use the proposed method to solving the elastodynamic response of a spherical shell under inner impact load.

scholarly journals Dynamic Response and Failure Mechanism of Layered Thin Plate Rock Mass Under Sustained Dynamic Load

2021 ◽  
Author(s):  
Feng Li ◽  
Chuang Chen ◽  
Yue Zhang ◽  
Xin Zhao ◽  
Xinhui Dong ◽  
...  
Keyword(s):  
Rock Mass ◽  
Thin Plate ◽  
Dynamic Load ◽  
Failure Modes ◽  
Shear Failure ◽  
Maximum Shear Stress ◽  
Central Axis ◽  
Dynamic Loads ◽  
Vibration Modes ◽  
Short Side

Abstract Based on the dual equation of Hamilton system and Duhamel's integral, and the orthogonality of the deflection equations, the mechanical model of homogeneous rectangular thin plate rock mass was established. And the results showed that the effective vibration modes of thin plate granite with four sides fixed were the 1st, 5th and 6th orders under uniform dynamic load, and their vibration frequencies were 310rad/s, 975rad/s and 1309rad/s respectively. Under sustained dynamic load, moreover, the change of the vibration state of the 1st mode was the most sharp, and the positive and negative alternation of its amplitude was the most frequent in the whole period, which had the most obvious effect on the vibration of the thin plate rock mass. Based on the Fourier transform formula, the Fourier series expressions and waveforms of sustained dynamic loads which contained rectangular wave, triangular wave and impact wave were obtained. The vibration characteristics of thin plate rock mass under these three kinds of sustained dynamic loads, the dynamic distribution of deflection, stress and maximum shear stress, as well as the dynamic damage and failure modes were all obtained. The results showed that plate cracks occurred firstly in the middle of the four sides and these cracks would propagate rapidly along the boundary of the thin plate rock mass; and then, plate cracks occurred at the central of the thin plate and the main develop tendency of these cracks was outward along the long central axis, moreover, these cracks also tended to expand outward along the short side central axis. It could be concluded that the initial failure position of the thin plate rock mass could be determined by the 1st effective mode, and the development direction and trend of the damage could be determined by 5th and 6th effective vibration modes; under sustained dynamic load, tensile-shear failure occurred at four sides and shear failure at four corners; The tensile failure occurred in the central area of the thin plate, which developed into a main crack along the central long axis and a secondary crack along the short central axis, forming an " O-十" fracture pattern.

Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

2014 ◽  
Vol 21 (1) ◽  
pp. 405-415 ◽  
Author(s):  
Chao-jiao Zhai ◽  
Tang-dai Xia ◽  
Guo-qing Du ◽  
Zhi Ding
Keyword(s):  
Dynamic Response ◽  
Cylindrical Cavity ◽  
Analytical Approach ◽  
Impact Load

A Rapid Analysis Method for Microgyroscope Using System Vibration Modes

2009 ◽  
Vol 60-61 ◽  
pp. 353-356
Author(s):  
Guang Jun Liu ◽  
An Lin Wang ◽  
Zi Yi Yu ◽  
Xing Yang ◽  
Tao Jiang
Keyword(s):  
Performance Analysis ◽  
Dynamic Response ◽  
Computing Time ◽  
State Space Model ◽  
Rapid Analysis ◽  
Vibration Modes ◽  
Analysis Method ◽  
Space Model ◽  
System Equation ◽  
System Vibration

This paper proposes a rapid dynamic analysis method for microgyroscope using system vibration modes to solve the problems concerning to the computing time in the performance analysis of microgyroscope. The results of eigenvalue solution are employed to construct the state space model. The response of the microgyros cope can be reconstructed as a response superposition of the vibration modes, and then the system equation is decoupled into an uncoupled equation. The dynamic response of the microgyroscope can be calculated by a simple superposition.

scholarly journals Numerical solution of acoustic scattering by finite perforated elastic plates

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150767 ◽  
Author(s):  
A. V. G. Cavalieri ◽  
W. R. Wolf ◽  
J. W. Jaworski
Keyword(s):  
Boundary Conditions ◽  
Acoustic Scattering ◽  
Free Edge ◽  
Solution Procedure ◽  
Sound Level ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Beneficial Effects ◽  
Plate Length ◽  
Radiated Sound

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

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