scholarly journals On a remarkable geometric-mechanical synergism based on a novel linear eigenvalue problem

2021 ◽  
Author(s):  
Johannes Kalliauer ◽  
Michał Malendowski ◽  
Herbert A. Mang
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Load Level ◽  
Numerical Verification ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Linear Eigenvalue Problem ◽  
Dimensional Unit ◽  
Unit Hypersphere ◽  
The One

AbstractThe vertices of two specific eigenvectors, obtained from a novel linear eigenvalue problem, describe two curves on the surface of an N-dimensional unit hypersphere. N denotes the number of degrees of freedom in the framework of structural analysis by the Finite Element Method. The radii of curvature of these two curves are 0 and 1. They correlate with pure stretching and pure bending, respectively, of structures. The two coefficient matrices of the eigenvalue problem are the tangent stiffness matrix at the load level considered and the one at the onset of loading. The goals of this paper are to report on the numerical verification of the aforesaid geometric-mechanical synergism and to summarize current attempts of its extension to combinations of stretching and bending of structures.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

scholarly journals Study on the Leakage and Inter-Stage Pressure Drop Characteristics of Two-Stage Finger Seal

2021 ◽  
Vol 11 (5) ◽  
pp. 2239
Author(s):  
Hailin Zhao ◽  
Hua Su ◽  
Guoding Chen ◽  
Yanchao Zhang
Keyword(s):  
Pressure Drop ◽  
Pressure Difference ◽  
Radial Displacement ◽  
Mean Square ◽  
The Finite Element Method ◽  
Axial Pressure ◽  
Two Stage ◽  
One Stage ◽  
The One ◽  
Lower Contact

To solve the high leakage and high wear problems faced by sealing devices in aeroengines under the condition of high axial pressure difference, the two-stage finger seal is proposed in this paper. The finite element method and computational fluid dynamics (FEM/CFD) coupling iterative algorithm of the two-stage finger seal is developed and validated. Then the performance advantages of two-stage finger seal compared to the one-stage finger seal are studied, as well as the leakage and the inter-stage pressure drop characteristics of two-stage finger seal are investigated. Finally, the measure to improve the inter-stage imbalance of pressure drop of two-stage finger seal is proposed. The results show that the two-stage finger seal has lower leakage and lower contact pressure than the one-stage finger seal at high axial pressure difference, but there exists an inter-stage imbalance of pressure drop. Increasing the axial pressure difference and the root mean square (RMS) roughness of finger element can aggravate the imbalance of pressure drop, while the radial displacement excitation of rotor has little influence on it. The results also indicate that the inter-stage imbalance of pressure drop of the two-stage finger seal can be improved by increasing the number of finger elements of the 1st finger seal and decreasing the number of finger elements of the 2nd finger seal.

Development of Reformative Surgery Method Using Partial Freezing for the Liver

2006 ◽  
Vol 128 (6) ◽  
pp. 862-866
Author(s):  
M. Takahashi ◽  
S. Nomura ◽  
M. Jindai ◽  
S. Shibata ◽  
X. Zhu ◽  
...  
Keyword(s):  
Cooling Rate ◽  
Degrees Of Freedom ◽  
Operation Time ◽  
Basic Research ◽  
Freezing Temperature ◽  
The Finite Element Method ◽  
Porcine Liver ◽  
Liver Sample ◽  
Peltier Module ◽  
Increment Rate

To minimize surgical stresses including blood loss and operation time to the patients during hepatic resection, we studied the feasibility of a combination of a partial liver freezing technique and shape-memory alloy, which also enables a free-designed resection curve. In this surgical procedure, the region surrounding a tumor in the liver is frozen to excise and prevent hemorrhage. The liver was frozen by a Peltier module. The effects of cooling rate and freezing temperature on the excision force that arise between a scalpel and the liver are carried out experimentally as a basic research for partial freezing surgical procedures. A porcine liver was used as a liver sample. The physical properties were estimated by using the finite element method based on the heat transfer characteristics of the liver. Isolation of the liver was conducted using a scalpel attached to the end-effector of a 3 degrees of freedom robot. In the experiments, the minimum excision force was obtained at a temperature between 272K and 275K; therefore, it is preferable that the liver be excised within this temperature range. Lowering of the cooling rate decreases the excision force even if the temperature of the liver remains unchanged. The lower the temperature of the liver is, the larger the increment rate of excision force is with regard to the cooling rate.

scholarly journals Finite Element Analysis of Thermoelastic Contact Stability

1994 ◽  
Vol 61 (4) ◽  
pp. 919-922 ◽  
Author(s):  
Taein Yeo ◽  
J. R. Barber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Eigenvalue Problem ◽  
Linear Perturbation ◽  
Dimensional System ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Analysis by the mixed method of statically indeterminate frames with elements of increased rigidity and numerical verification of the calculation results using the finite element method

2021 ◽  
Vol 14 (2) ◽  
pp. 54-66
Author(s):  
Svetlana Sazonova ◽  
Viktor Asminin ◽  
Alla Zvyaginceva
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Initial Data ◽  
Mixed Method ◽  
Numerical Verification ◽  
Bending Moments ◽  
The Finite Element Method ◽  
Calculation Results ◽  
Internal Forces ◽  
Element Method

The sequence of application of the mixed method for calculating internal forces in statically indeterminate frames with elements of increased rigidity is given. The main system is chosen for the frame with one kinematic and one force unknown. The canonical equations of the mixed method are written, taking into account their meaning. Completed the construction of the final diagram of the bending moments and all the necessary calculations and checks. When calculating integrals, Vereshchagin's rule is applied. The solution of the problem is checked by performing the calculation using the computer program STAB12.EXE; the results of the calculations are numerically verified using the finite element method. An example of the formation of the initial data for the STAB12.EXE program and the subsequent processing of the calculation results, the rules for comparing the numerical results and the results obtained in the calculation of the frame by the mixed method are given.

The non-uniform stationary measure for discrete-time quantum walks in one dimension

2015 ◽  
Vol 15 (11&12) ◽  
pp. 1060-1075
Author(s):  
Norio Konno ◽  
Masato Takei
Keyword(s):  
Eigenvalue Problem ◽  
Discrete Time ◽  
Quantum Walks ◽  
Stationary Measure ◽  
Unitary Matrix ◽  
Uniform Measure ◽  
Simple Argument ◽  
Stationary Measures ◽  
Time Quantum ◽  
The One

We consider stationary measures of the one-dimensional discrete-time quantum walks (QWs) with two chiralities, which is defined by a 2 $\times$ 2 unitary matrix $U$. In our previous paper \cite{Konno2014}, we proved that any uniform measure becomes the stationary measure of the QW by solving the corresponding eigenvalue problem. This paper reports that non-uniform measures are also stationary measures of the QW except when $U$ is diagonal. For diagonal matrices, we show that any stationary measure is uniform. Moreover, we prove that any uniform measure becomes a stationary measure for more general QWs not by solving the eigenvalue problem but by a simple argument.

An appropriate biomechanical model of seated human subjects exposed to whole-body vibration

2021 ◽  
pp. 146441932110394
Author(s):  
Raj Desai ◽  
Anirban Guha ◽  
Pasumarthy Seshu
Keyword(s):  
Degrees Of Freedom ◽  
Human Subjects ◽  
Computational Cost ◽  
Biomechanical Model ◽  
Whole Body ◽  
Body Parts ◽  
Lumped Parameter ◽  
Long Duration ◽  
The One ◽  
The Right

Long duration automobile-induced vibration is the cause of many ailments to humans. Predicting and mitigating these vibrations through seat requires a good model of seated human body. A good model is the one that strikes the right balance between modelling difficulty and simulation results accuracy. Increasing the number of body parts which have been separately modelled and increasing the number of ways these parts are connected to each other increase the number of degrees of freedom of the entire model. A number of such models have been reported in the literature. These range from simple lumped parameter models with limited accuracy to advanced models with high computational cost. However, a systematic comparison of these models has not been reported till date. This work creates eight such models ranging from 8 to 26 degrees of freedom and tries to identify the model which strikes the right balance between modelling complexity and results accuracy. A comparison of the models’ prediction with experimental data published in the literature allows the identification of a 12 degree of freedom backrest supported model as optimum for modelling complexity and prediction accuracy.

scholarly journals Analysis of dynamic characteristics of viscoelastic frame structures

2019 ◽  
Vol 90 (1) ◽  
pp. 147-171
Author(s):  
Roman Lewandowski ◽  
Przemysław Wielentejczyk
Keyword(s):  
Eigenvalue Problem ◽  
Viscoelastic Material ◽  
Dynamic Characteristics ◽  
Nonlinear Eigenvalue Problem ◽  
Continuation Method ◽  
Frame Structures ◽  
Influence Of Temperature ◽  
Linear Eigenvalue Problem ◽  
Influence Of Temperature On ◽  
Parametric Analyses

Abstract Planar frame structures made of a viscoelastic material are considered in the paper. The technically very important structures made of a homogenous material are contemplated. A family of rheological models (classic and fractional) are used to describe the mechanical properties of the viscoelastic material. In particular, the dynamic characteristics of the structures are of interest. A numerically very efficient method is proposed to determine such characteristics. The method requires the solution to the linear eigenvalue problem for corresponding elastic structures and the solution to a nonlinear, algebraic equation. The presented method is much more efficient than other methods where, very often, the continuation method is used to solve the nonlinear eigenvalue problem. The influence of temperature changes on dynamic characteristics is analyzed using the frequency–temperature principle. The results of several parametric analyses are presented and discussed. For the first time, the influence of temperature on the dynamic characteristics of beams has been studied in detail.

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