Study of Non-Linear Theory of Vertical Impact Damping System

2011 ◽  
Vol 66-68 ◽  
pp. 119-124
Author(s):  
Jian Sheng Zhang
Keyword(s):  
Transfer Function ◽  
Analytical Solution ◽  
Linear Theory ◽  
Piecewise Linear ◽  
Dynamical Response ◽  
Compatibility Conditions ◽  
Mechanics Model ◽  
Theory Research ◽  
Vertical Impact ◽  
Impact Damping

A mechanics model of vertical impact damping system was founded based on the experimental device introduced in [1], and interrelated theory research was made on the mechanics model. The analytical solution of system dynamical response was gained using transfer function combining with the system’s neighboring boundary compatibility conditions in the fact of the piecewise linear characteristics of the system.

Two‐step, piecewise‐linear SAR ADC with programmable transfer function

2019 ◽  
Vol 55 (8) ◽  
pp. 444-446
Author(s):  
S. Sengupta ◽  
M.L. Johnston
Keyword(s):  
Transfer Function ◽  
Piecewise Linear ◽  
Sar Adc

scholarly journals Path-following analysis of the dynamical response of a piecewise-linear capsule system

2016 ◽  
Vol 37 ◽  
pp. 102-114 ◽  
Author(s):  
Joseph Páez Chávez ◽  
Yang Liu ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch
Keyword(s):  
Piecewise Linear ◽  
Path Following ◽  
Dynamical Response

An analytical solution to contaminant diffusion in semi-infinite clayey soils with piecewise linear adsorption

Chemosphere ◽  
2011 ◽  
Vol 85 (8) ◽  
pp. 1248-1255 ◽  
Author(s):  
Haijian Xie ◽  
Yunmin Chen ◽  
Zhanghua Lou ◽  
Liangtong Zhan ◽  
Han Ke ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Piecewise Linear ◽  
Clayey Soils ◽  
Contaminant Diffusion

scholarly journals Modeling of stress states in intact layered rock massifs

2021 ◽  
pp. 14-25
Author(s):  
Юрий Владимирович Немировский ◽  
Александр Александрович Тырымов
Keyword(s):  
Analytical Solution ◽  
Anisotropic Medium ◽  
Structural Model ◽  
Piecewise Linear ◽  
Field Observations ◽  
Layered Rock ◽  
Geological Factors ◽  
Stress States ◽  
Distribution Of Stresses ◽  
Linear Nature

Предложена структурная модель анизотропной среды для расчета напряженнодеформированного состояния в нетронутых массивах горных пород, которая учитывает ряд горнотехнических и горно-геологических факторов. Результаты аналитического решения позволили объяснить известные из практики натурных наблюдений факты (возможность превосходства горизонтальных напряжений над вертикальными, кусочно-линейный характер напряжений и т.д.), которые находились в противоречии с широко распространенными гипотезами о распределении напряжений в породных массивах. A structural model of an anisotropic medium is proposed for calculating the stressstrain state in intact rock massifs, which takes into account a number of mining and geological factors. The results of the analytical solution allowed us to explain the facts known from the practice of field observations (the possibility of the superiority of horizontal stresses over vertical ones, the piecewise linear nature of stresses, etc.), which were in contradiction with the widespread hypotheses about the distribution of stresses in rock massifs.

scholarly journals Dynamic properties of piecewise linear systems with fractional time-delay feedback

2021 ◽  
pp. 146134842110076
Author(s):  
Jianchao Zhang ◽  
Jun Wang ◽  
Jiangchuan Niu ◽  
Yufei Hu
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Analytical Solution ◽  
Goodness Of Fit ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
State Solution ◽  
Comparison Results

The forced vibration of a single-degree-of-freedom piecewise linear system containing fractional time-delay feedback was investigated. The approximate analytical solution of the system was obtained by employing an averaging method. A frequency response equation containing time delay was obtained by studying a steady-state solution. The stability conditions of the steady-state solution, the amplitude–frequency results, and the numerical solutions of the system under different time-delay parameters were compared. Comparison results indicated a favorable goodness of fit between the two parameters and revealed the correctness of the analytical solution. The effects of the time-delay and fractional parameters, piecewise stiffness, and piecewise gap on the principal resonance and bifurcation of the system were emphasized. Results showed that fractional time delay occurring in the form of equivalent linear dampness and stiffness under periodic variations in the system and influenced the vibration characteristic of the system. Moreover, piecewise stiffness and gap induced the nonlinear characteristic of the system under certain parameters.

scholarly journals Transfer Matrix Method for Natural Vibration Analysis of Tree System

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Bin He ◽  
Xiaoting Rui ◽  
Huiling Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Damage Identification ◽  
Continuous System ◽  
Dynamical Response ◽  
Transfer Matrices ◽  
Chain System ◽  
Mechanics Model

The application of Transfer matrix method (TMM) ranges from linear/nonlinear vibration, composite structure, and multibody system to calculating static deformation, natural vibration, dynamical response, and damage identification. Generally TMM has two characteristics: (1) the TMM formulae share similarity to the chain mechanics model in terms of topology structure; then TMM often is selected as a powerful tool to analyze the chain system. (2) TMM is adopted to deal with the problems of the discrete system, continuous system, and especial discrete/continuous coupling system with the uniform matrix form. In this investigation, a novel TMM is proposed to analyze the natural vibration of the tree system. In order to make the TMM of the tree system have the two above advantages of the TMM of the chain system, the suitable state vectors and transfer matrices of the typical components of the tree system are constructed. Then the topology comparability between the mechanics model and its corresponding formulae of TMM can be adopted to assembling the transfer matrices and transfer equations of the global tree system. Two examples of natural vibration problems validating the method are given. The formulation of the proposed TMM is mathematically intuitive and can be held and applied by the engineers easily.

scholarly journals Analytical Solutions for Unsteady Groundwater Flow in an Unconfined Aquifer under Complex Boundary Conditions

Water ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 75
Author(s):  
Yawen Xin ◽  
Zhifang Zhou ◽  
Mingwei Li ◽  
Chao Zhuang
Keyword(s):  
Analytical Solution ◽  
Groundwater Flow ◽  
Piecewise Linear ◽  
Unconfined Aquifer ◽  
Piecewise Linear Approximation ◽  
Level Fluctuation ◽  
Level Variation ◽  
Groundwater Dynamics ◽  
River Level ◽  
Complex Boundary

The response laws of groundwater dynamics on the riverbank to river level variations are highly dependent on the river level fluctuation process. Analytical solutions are widely used to infer the groundwater flow behavior. In analytical calculations, the river level variation is usually generalized as instantaneous uplift or stepped, and then the analytical solution of the unsteady groundwater flow in the aquifer is derived. However, the river level generally presents a complex, non-linear, continuous change, which is different from the commonly used assumptions in groundwater theoretical calculations. In this article, we propose a piecewise-linear approximation to describe the river level fluctuation. Based on the conceptual model of the riverbank aquifer system, an analytical solution of unsteady groundwater flow in an unconfined aquifer under complex boundary conditions is derived. Taking the Xiluodu Hydropower Station as an example, firstly, the monitoring data of the river level during the period of non-impoundment in the study area are used to predict the groundwater dynamics with piecewise-linear and piecewise-constant step approximations, respectively, and the long-term observation data are used to verify the calculation accuracy for the different mathematical models mentioned above. During the reservoir impoundment period, the piecewise-linear approximation is applied to represent the reservoir water level variation, and to predict the groundwater dynamics of the reservoir bank.

Sign in / Sign up

Export Citation Format

Share Document