scholarly journals Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method

2021 ◽  
Vol 2 (1) ◽  
pp. 41-50
Author(s):  
Masoud Goharimanesh ◽  
◽  
Ali Koochi ◽  
Keyword(s):  
Energy Balance ◽  
Closed Form ◽  
Nonlocal Elasticity ◽  
Casimir Force ◽  
Nonlocal Parameter ◽  
Closed Form Solution ◽  
Form Solution ◽  
Balance Method ◽  
Energy Balance Method ◽  
The Impact

This paper deals with investigating the nonlinear oscillation of carbon nanotube manufactured nano-resonator. The governing equation of the nano-resonator is extracted in the context of the nonlocal elasticity. The impact of the Casimir force is also incorporated in the developed model. A closed-form solution based on the energy balance method is presented for investigating the oscillations of the nano-resonator. The proposed closed-form solution is compared with the numerical solution. The impact of influential parameters including applied voltage, Casimir force, geometrical and nonlocal parameters on the nano resonator’s vibration and frequency are investigated. The obtained results demonstrated that the Casimir force reduces the nano-resonator frequency. However, the nonlocal parameter has a hardening effect and enhances the system’s frequency.

scholarly journals On the impact of antenna diversity in IEEE 802.11b DCF with capture

2004 ◽  
Vol 17 (1) ◽  
pp. 41-52
Author(s):  
Zoran Velkov-Hadzi ◽  
Boris Spasenovski
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Access Point ◽  
Form Solution ◽  
Capture Probability ◽  
Antenna Diversity ◽  
Ieee 802.11B ◽  
Selection Diversity ◽  
Maximum Selection ◽  
The Impact

In this paper, we examined the influence of capture effect with L-fold antenna diversity at the Access Point over IEEE 802.11b DCF. We obtained an exact closed-form solution for the conditional capture probability in case of ideal selection diversity, and an approximate closed-form solution for the conditional capture probability in case of maximum selection diversity in a Rayleigh-faded channel. Obtained analytical expressions have general significance and can be applied for any other multiple access wireless network. We also analytically evaluated saturation throughput increase of the IEEE 802.11b DCF protocol exposed to capture.

A closed-form solution to eye-to-hand calibration towards visual grasping

2014 ◽  
Vol 41 (6) ◽  
pp. 567-574 ◽  
Author(s):  
Hui Pan ◽  
Na Li Wang ◽  
Yin Shi Qin
Keyword(s):  
Closed Form ◽  
Design Methodology ◽  
Closed Form Solution ◽  
Form Solution ◽  
Content Type ◽  
The Impact ◽  
Calibration Plane

Purpose – The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration. Design/methodology/approach – The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration. Findings – Simulation and actual experiments confirm that the accuracy of calibration is obviously improved. Originality/value – Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

2019 ◽  
Keyword(s):  
Closed Form ◽  
Recursive Algorithm ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Problem Solution ◽  
Underlying Asset ◽  
Quadratic Hedging ◽  
Hedging Problem ◽  
The Impact

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.

scholarly journals CESSATION OF FREE VIBRATIONS OF A NONLINEAR ELASTIC SYSTEM DUE TO VISCOUS RESISTANCE

2021 ◽  
pp. 69-75
Author(s):  
Vasiliy Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Energy Balance ◽  
Finite Number ◽  
Power Law ◽  
Dry Friction ◽  
Free Vibrations ◽  
Balance Method ◽  
Viscous Resistance ◽  
Energy Balance Method ◽  
Number Of Cycles ◽  
The Impact

The paper deals with free vibrations of a system with power-law nonlinear elasticity subjected to power-law viscous resistance. The relation between the nonlinearity indices is determined when the impact of the viscous resistance force causes the vibrations to die away. In this case the vibrations are limited in time i.e. consist of a finite number of cycles analogous to a system with Coulomb dry friction. The research exploits the energy balance method. The periodic Ateb-functions are used to obtain an approximate formula for the work of dissipative force over a semi-cycle of vibrations. A recursive power-law equation for the vibration swings is derived from the condition of equality of the work to the potential energy change. By analyzing the change of the coefficient in the equation, which is related to the change of the semi-cycle number as well as the vibration swings, the condition for the equation to have no positive root is determined, which means that the vibrations die away. The condition is formulated in the form of an inequality. It is shown to generalize the results previously known. The theoretical inferences are verified by numerical integration of the nonlinear differential equation of motion. It is shown that under the conditions proposed in the paper the free vibrations consist of a finite number of cycles even if dry friction is absent from the system. Special cases are highlighted, when the approximate energy balance method results into exact computational formulae. The length of the cycles increases during the motion since it depends on the swing of damped vibrations in the essentially nonlinear system with rigid force characteristics considered.

An Analytical Study of Skull Deformation During Head Impacts

2013 ◽  
Author(s):  
Shahab Mansoor-Baghaei ◽  
Ali M. Sadegh
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Realistic Model ◽  
Form Solution ◽  
Ellipsoidal Shell ◽  
Complex Differential Equation ◽  
Head Impacts ◽  
The Difference ◽  
The Impact ◽  
Skull Deformation

Spherical shells have been employed to model impacts to human heads; however, an ellipsoidal shell is that is more realistic model of the head has not fully investigated. In this paper, impact of an elastic ellipsoidal shell with an elastic flat half space is analytically analyzed and a closed-form solution is derived which led to a complex differential equation. Due to the complexity of the impact equation it could not be solved by standard solutions. Therefore, the Newtonian method and a linearization scheme are employed to simplify this equation in order to obtain the response of the impact problem and the closed-form solution. The analytical solutions are validated by finite element method. Good agreement between the closed form solution and the FE results is observed. To show the difference, the ellipsoidal solutions are also compared to the spherical solutions. To the best of our knowledge, this method and its closed-form solution have not been addressed in the literature. It is concluded that the closed-form solution is trustworthy and can be used to investigate the impact of the skull (as an elastic ellipsoidal shell) with a rigid or elastic plate, including the skull deformation and parametric studies. This solution could be expanded to include the brain materials inside the ellipsoidal shell.

The Impact of Arbitrary Oriented Ellipsoidal Shell With a Barrier: Analytical Study

2015 ◽  
Vol 82 (4) ◽  
Author(s):  
Shahab Mansoor-Baghaei ◽  
Ali M. Sadegh
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Linearization Method ◽  
Form Solution ◽  
Ellipsoidal Shell ◽  
Explicit Finite Element ◽  
Closed Form Solutions ◽  
Transmitted Force ◽  
The Impact

In this paper, a closed form solution of an arbitrary oriented hollow elastic ellipsoidal shell impacting with an elastic flat barrier is presented. It is assumed that the shell is thin under the low speed impact. Due to the arbitrary orientation of the shell, while the pre-impact having a linear speed, the postimpact involves rotational and translational speed. Analytical solution for this problem is based on Hertzian theory (Johnson, W., 1972, Impact Strength of Materials, University of Manchester Institute of Science and Technology, Edward Arnold Publication, London) and the Vella’s analysis (Vella et al., 2012, “Indentation of Ellipsoidal and Cylindrical Elastic Shells,” Phys. Rev. Lett., 109, p. 144302) in conjunction with Newtonian method. Due to the nonlinearity and complexity of the impact equation, classical numerical solutions cannot be employed. Therefore, a linearization method is proposed and a closed form solution for this problem is accomplished. The closed form solution facilitates a parametric study of this type of problems. The closed form solution was validated by an explicit finite element method (FEM). Good agreement between the closed form solution and the FE results is observed. Based on the analytical method the maximum total deformation of the shell, the maximum transmitted force, the duration of the contact, and the rotation of the shell after the impact were determined. Finally, it was concluded that the closed form solutions were trustworthy and appropriate to investigate the impact of inclined elastic ellipsoidal shells with an elastic barrier.

Simplified Approach to Design of Crushable Material due to Dynamic Load

2012 ◽  
Author(s):  
Sivadol Vongmongkol ◽  
Asgar Faal-Amiri ◽  
Hari M. Srivastava
Keyword(s):  
Closed Form ◽  
Energy Absorption ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Closed Form Solution ◽  
High Energy ◽  
Form Solution ◽  
Piping System ◽  
The Impact

Crushable material has widely been used as an engineering solution for energy absorption devices among many industries. Abnormal and severe accident loads in the design of nuclear power plants are required to be addressed in order to comply with Nuclear Regulatory Commission (NRC) requirements which makes the crushable material more suitable in its highly dynamic application. One of the severe loads is from a postulated high energy piping system rupture. Its effects are required to be mitigated so that the proper operation of safety related systems, structures and components (SSC) of these facilities is assured. The postulated pipe rupture loads are among the highest loads that need to be addressed in the design process of nuclear power plants. The impact forces produced by the postulated pipe rupture are typically being absorbed by energy absorption devices called “Pipe Whip Restraints” in which the restraints can minimize the loads affecting the SSCs to within an acceptable limit. This paper provides a simplified closed-form solution to determine the energy absorbing characteristic that will help to design these devices. This paper will also provide a comparison between results of the proposed simplified closed-form solution equations to the experimental test results and the calculated results using finite element analysis.

Nonlinear Oscillations Analysis of the Elevator Cable in a Drum Drive Elevator System

2015 ◽  
Vol 7 (1) ◽  
pp. 43-57 ◽  
Author(s):  
H. Askari ◽  
D. Younesian ◽  
Z. Saadatnia
Keyword(s):  
Energy Balance ◽  
Closed Form ◽  
Natural Frequency ◽  
Governing Equation ◽  
Nonlinear Oscillations ◽  
Quadratic Function ◽  
Balance Method ◽  
Closed Form Expression ◽  
Energy Balance Method ◽  
Elevator Cable

AbstractThis paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive. The governing equation of motion of the objective system is developed by virtue of Lagrangian’s method. A complicated term is broached in the governing equation of the motion of the system owing to existence of multiplication of a quadratic function of velocity with a sinusoidal function of displacement in the kinetic energy of the system. The obtained equation is an example of a well-known category of nonlinear oscillators, namely, non-natural systems. Due to the complex terms in the governing equation, perturbation methods cannot directly extract any closed form expressions for the natural frequency. Unavoidably, different non-perturbative approaches are employed to solve the problem and to elicit a closed-form expression for the natural frequency. Energy balance method, modified energy balance method and variational approach are utilized for frequency analyzing of the system. Frequency-amplitude relationships are analytically obtained for nonlinear vibration of the elevator’s drum. In order to examine accuracy of the obtained results, exact solutions are numerically obtained and then compared with those obtained from approximate closed-form solutions for several cases. In a parametric study for different nonlinear parameters, variation of the natural frequencies against the initial amplitude is investigated. Accuracy of the three different approaches is then discussed for both small and large amplitudes of the oscillations.

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