Thermal Effects on Internal and External Resonances of a Nonlinear Timoshenko Beam

2014 ◽  
Author(s):  
Anna Warminska ◽  
Jerzy Warminski ◽  
Emil Manoach
Keyword(s):  
Timoshenko Beam ◽  
Thermal Effects ◽  
Internal Resonance ◽  
Structural Parameters ◽  
Effect Of Temperature ◽  
Simply Supported ◽  
Thermal Fields ◽  
Large Amplitude Vibrations ◽  
The Galerkin Method ◽  
The Mathematical Model

Large amplitude vibrations of a Timoshenko beam under an influence of thermal and mechanical loadings are studied in the paper. The structural parameters of the beam are considered enabling internal resonance conditions. Moreover, it is assumed that the beam gets instantly temperature which is distributed along its length and thickness. The mathematical model represented by a set of partial differential equations takes into account coupled mechanical and thermal fields. The problem is transformed to a set of ODEs by the Galerkin method and three modes of a simply supported beam at both ends are studied. The effect of temperature on internal and external resonances is analysed on the basis of the proposed reduced model.

Temperature Influence on Nonlinear Responses of Timoshenko Beam

2013 ◽  
Author(s):  
Anna Warminska ◽  
Jerzy Warminski ◽  
Emil Manoach
Keyword(s):  
Elevated Temperature ◽  
Timoshenko Beam ◽  
Nonlinear Oscillations ◽  
Multiple Time ◽  
Vibration Modes ◽  
Nonlinear Responses ◽  
Large Amplitude Vibrations ◽  
The Galerkin Method ◽  
The Mathematical Model ◽  
Multiple Time Scale Method

The goal of this paper is to study large amplitude vibrations of a Timoshenko beam under an influence of the elevated temperature. It is assumed that the beam gets the elevated temperature instantly and the temperature is uniformly distributed along the beam’s length and cross-section. The mathematical model represented by a set of partial differential equations is derived taking into account boundary conditions for a simply supported beam in the both ends. Next, the problem is reduced by the Galerkin method by means of free vibration modes. The influence of the temperature on a resonance localisation and nonlinear oscillations is studied numerically and analytically by the multiple time scale method.

scholarly journals On using the rotor acceleration mode to increase the accuracy of a two-stage gyrocompass

2020 ◽  
pp. 5-13
Author(s):  
Volodymyr Fedorov ◽  
Vladislav Kikot ◽  
Nataliya Shtefan
Keyword(s):  
Mathematical Model ◽  
Initial Position ◽  
Effect Of Temperature ◽  
Two Stage ◽  
Best Estimate ◽  
Torsion Suspension ◽  
Measured Angle ◽  
State Position ◽  
Acceleration Mode ◽  
The Mathematical Model

The article considers a two-stage gyrocompass with a rigid torsion suspension of the moving part. The principle of its action is based on balancing the elastic moment of the torsion bars with the gyroscopic moment. When this condition is met, the azimuth of the steady-state position of the rotor axis is calculated from the known kinetic moment , latitude and angular rigidity of the torsion bars, and the measured angle of rotation of the moving part of the gyroscope relative to its initial position. The “aging of the material” of the torsion bars, the effect of temperature on them, etc., leads to an uncontrolled change in the angular stiffness of the torsion bars, which, in turn, leads to an error in determining the position of the meridian. A method is proposed for determining the position of the meridian under conditions when the angular stiffness of the torsion is unknown. The method involves observing the motion of the gyroscope in a mode where the kinetic momentum changes linearly (the rotor accelerates). This movement is associated with the movement of the mathematical model of a two-stage gyrocompass in the same mode in the form of a differential equation of motion or in the form of its solution. As a result of minimizing the discrepancy between the real movement of the gyrocompass and the movement of its mathematical model, the “best estimate” of the parameter characterizing the position of the meridian and the “best estimate” of the angular stiffness of the torsion bars in this dimension are found. The results of modeling the corresponding information processing algorithms are considered. The advantages of the proposed method compared with traditional methods are indicated .

scholarly journals The Vibration of Simply Supported Non-Uniform Cross Sectional Pipe Conveying Fluid Resting on Viscoelastic Foundation

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Bernoulli Model ◽  
Viscoelastic Foundation ◽  
Cross Sectional ◽  
Flowing Fluid ◽  
Simply Supported ◽  
Critical Velocities ◽  
Stiffness And Damping ◽  
The Mathematical Model

The induced flexural vibration of slender pipe systems with continuous non uniform cross sectional area containing laminar flowing fluid lying on extended Winkler viscoelastic foundation is considered. The Euler Bernoulli model of the pipe has hinged ends. The inlet flow is considered constant steady that interacts with the wall of the pipe. The mathematical model is developed and its corresponding solution is obtained. The influence of the combination of variation of cross section, foundation stiffness and damping on the critical velocities, complex natural frequencies and stabilization of the system is presented.

SIZE-INDUCED EFFECTS IN NANOSTRUCTURED NiFe2O4

2010 ◽  
Vol 24 (30) ◽  
pp. 5973-5985
Author(s):  
M. GUNES ◽  
H. GENCER ◽  
T. IZGI ◽  
V. S. KOLAT ◽  
S. ATALAY
Keyword(s):  
Electron Microscopy ◽  
Annealing Temperature ◽  
Structural Parameters ◽  
Hydrothermal Process ◽  
Lattice Parameter ◽  
Effect Of Temperature ◽  
Vibrating Sample Magnetometer ◽  
X Ray Diffraction ◽  
X Ray ◽  
Scanning Electron

NiFe 2 O 4 nanoparticles were successfully prepared by a hydrothermal process, and the effect of temperature on them was studied. The particles were annealed at various temperatures ranging from 413 to 1473 K. Studies were carried out using powder X-ray diffraction, scanning electron microscopy, infrared spectroscopy, differential thermal analysis, thermogravimetric analysis and a vibrating sample magnetometer. The annealing temperature had a significant effect on the magnetic and structural parameters, such as the crystallite size, lattice parameter, magnetization and coercivity.

Response of a Simply Supported Timoshenko Beam to a Purely Random Gaussian Process

1958 ◽  
Vol 25 (4) ◽  
pp. 496-500
Author(s):  
J. C. Samuels ◽  
A. C. Eringen
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Equation ◽  
Mean Square ◽  
Bending Stress ◽  
Random Loading ◽  
Simply Supported ◽  
The Mean ◽  
Timoshenko Beam Equation ◽  
Classical Beam Theory

Abstract The generalized Fourier analysis is applied to the damped Timoshenko beam equation to calculate the mean-square values of displacements and bending stress, resulting from purely random loading. Compared with the calculations, based on the classical beam theory, it was found that the displacement correlations of both theories were in excellent agreement. Moreover, the mean square of the bending stress, contrary to the results of the classical beam theory, was found to be convergent. Computations carried out with a digital computer are plotted for both theories.

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

2021 ◽  
Author(s):  
Yu Xue ◽  
Jinqiang Li ◽  
Yu Wang ◽  
Fengming Li
Keyword(s):  
Band Gap ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
Structural Parameters ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Response Analysis ◽  
Working Mechanism ◽  
Frequency Wave ◽  
The Galerkin Method

Abstract This paper aims to explore the actual working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring (MBS) resonators for low-frequency wave absorption. The nonlinear MBS resonator consists of a mass, a cantilever beam and a spring that can provide negative stiffness in the transverse vibration of the resonator, and its stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate and the band-gap bounds related to the amplitude of resonator is derived by dispersion analysis. For the finite sized sandwich-like meta-plate with the fully free boundary condition subjected to external excitations, its dynamic equation is also established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by the numerical simulation, whose band-gap range demonstrates good agreement with the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by the design of the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite sized meta-plate, it can be observed that the nonlinearity of resonators can widen the wave attenuation range of meta-plate.

A Mathematical Calculation Method for Hysteresis Characteristics Analysis of Arc-Shaped Finger Seal

2020 ◽  
Author(s):  
Chun-Hua Du ◽  
Yan-Chao Zhang ◽  
Ya-Hui Cui ◽  
Shu-Na Dong ◽  
Hong-Hu Ji ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Structural Parameters ◽  
Maximum Error ◽  
Calculation Model ◽  
Correction Coefficient ◽  
Research Results ◽  
Characteristics Analysis ◽  
Leakage Characteristics ◽  
The Mathematical Model ◽  
Hysteresis Characteristics

Abstract In order to accurately predict the hysteresis characteristics of finger seal, the minimum hysteresis which can directly reflect the hysteresis of finger seal is proposed to characterize the hysteresis of finger seal. The mathematical model for calculating the minimum hysteresis of finger seal is established, the correction coefficient in the mathematical model is determined, and the mathematical model is verified by experiments. The influence of the structure and working condition parameters of finger laminates on the hysteresis characteristics is studied based on the modified calculation model, and the rule of influence is obtained in the end. Research results show that the maximum error between the leakage characteristics numerical calculation of finger seal base on modified calculation model and the experiment results is 7.64%, and the mathematical model of the minimum hysteresis is reasonable and reliable. The descending order of influence degree of structural parameters on the hysteresis characteristics of finger seal is: thickness of each finger laminate, finger repeat angle, arc radius of the finger beam arcs‘ centers, diameter of the finger base circle, width of the interstice between fingers, arc radius of finger beam. The research results provide a theoretical basis for further research on the influence of hysteresis on the finger seal leakage characteristics and the optimal design of finger seal structure.

The Effect of Temperature and Composition on Spinel Concentration and Crystal Size in High-Level Waste Glass

2001 ◽  
Author(s):  
Martin Mika ◽  
Milan Patek ◽  
Jaroslav Maixner ◽  
Simona Randakova ◽  
Pavel Hrma
Keyword(s):  
Crystal Size ◽  
Equilibrium Concentration ◽  
Effect Of Temperature ◽  
High Level Waste ◽  
Huge Number ◽  
Aluminoborosilicate Glass ◽  
High Level ◽  
The Cost ◽  
Different Content ◽  
The Mathematical Model

Abstract High-level radioactive wastes can be safely immobilized in alkali-aluminoborosilicate glass. To reduce the cost of the vitrification process, the waste loading should be maximized. This can be done by optimizing the process using mathematical modeling. The main objective of our work was to determine one of the necessary inputs for the mathematical model, which is the effect of temperature and composition on the concentration of spinel crystals and their size. We prepared six glasses with a different content of Li+, Na+, Mg2+, Ni2+, Cr3+, and SiIV and studied the effect of composition on the temperature dependence of spinel equilibrium concentration in glass by X-ray powder diffraction. The size of crystals was determined using optical microscopy. It was found that the temperature effect on spinel concentration significantly increased as the content of Ni2+ or Mg2+ in glass increased and slightly decreased as the content of Cr3+ increased and Li+ and Na+ content decreased. Both Ni2+ and Cr3+ acted as nucleating agents, producing a huge number of tiny spinel crystals (∼2 μm). In particular, Ni2+ seems to very significantly facilitate spinel crystallization.

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