scholarly journals Analytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force

2018 ◽  
Vol 5 (7) ◽  
pp. 180639
Author(s):  
A. Le Bot ◽  
G. Duval ◽  
P. Klein ◽  
J. Lelong
Keyword(s):  
Analytical Solution ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Varying ◽  
Bending Vibration ◽  
Simply Supported ◽  
Random Forces ◽  
Walled Cylinder

This paper presents the analytical solution of radial vibration of a rolling cylinder submitted to a time-varying point force. In the simplest situation of simply supported edges and zero in-plane vibration, the cylinder is equivalent to an orthotropic pre-stressed plate resting on a visco-elastic foundation. We give the closed-form solution of vibration as a series of normal modes whose coefficients are explicitly calculated. Cases of both deterministic and random forces are examined. We analyse the effect of rolling speed on merging of vibrational energy induced by Doppler's effect for the example of rolling tyre.

An analytical solution for jointed tunnel linings in elastic soil or rock

2008 ◽  
Vol 45 (11) ◽  
pp. 1572-1593 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Segmental Lining ◽  
Sophisticated Method ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for tunnel linings that can be idealized as an inner jointed segmental lining and an outer thick-walled cylinder embedded in a homogeneous infinite elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground and lining–lining interfaces. In addition, the closed-form solution is verified by comparing it with finite element results where it is shown to agree well with this more sophisticated method of analysis.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

scholarly journals Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
R. T. Al-Khairy ◽  
Z. M. AL-Ofey
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Closed Form Solution ◽  
Infinite Medium ◽  
Form Solution ◽  
Time Dependent ◽  
Hyperbolic Heat Conduction ◽  
Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.

Analysis of Simply-Supported Orthotropic Cylindrical Shells Subject to Lateral Impact Loads

1990 ◽  
Vol 57 (2) ◽  
pp. 376-382 ◽  
Author(s):  
A. P. Christoforou ◽  
S. R. Swanson
Keyword(s):  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Double Fourier Series ◽  
Form Solution ◽  
Lateral Impact ◽  
Simply Supported ◽  
Response Characteristics ◽  
Simple Support ◽  
The Impact ◽  
Approximate Procedure

An analytic solution is given for the problem of simply-supported orthotropic cylindrical shells subject to impact loading. The closed-form solution has not been obtained previously. The analysis is based on an expansion of the loads, displacements, and rotations in a double Fourier series which satisfies the end boundary conditions of simple support. Each expansion is assumed to be separable into a function of time and a function of position. By neglecting in-plane and rotary inertia the problem becomes a second-order ordinary differential equation in time for the Fourier coefficients of the radial deflection. For a given loading impulse the solution can be found by invoking the convolution integral. The results show that for impact by a heavy mass, the solution is equivalent to that obtained by an approximate procedure of neglecting the mass of the shell, which leads to a simple simple-degree-of-freedom analysis. For problems of impact by smaller masses, the higher response frequencies of the cylinder become important. The results show the importance of dynamic effects in the predicted impact duration, peak force, and peak deflection relative to the quasi-static response. The results show that the response amplitude varies linearly with the impact velocity, but the response characteristics depend on the mass of the impactor and the mass and stiffness of the cylinder.

The Bauschinger and Hardening Effect on Residual Stresses in an Autofrettaged Thick-Walled Cylinder

1986 ◽  
Vol 108 (1) ◽  
pp. 108-112 ◽  
Author(s):  
P. C. T. Chen
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Closed Form Solution ◽  
High Strength ◽  
Form Solution ◽  
Residual Stress Distribution ◽  
Hardening Effect ◽  
Reverse Yielding ◽  
Walled Cylinder ◽  
Elastic Unloading

Most of the earlier solutions for residual stresses were based on the assumption of elastic unloading and only a few considered reverse yielding. In this paper a new theoretical model for a high strength steel is proposed and a closed-form solution of residual stresses in autofrettaged tubes has been obtained. The new results indicate that the influence of the combined Bauschinger and hardening effect on the residual stress distribution is significant.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

scholarly journals Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge Condition

2009 ◽  
Vol 57 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Rajeev Bansal ◽  
Samir Das
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Stream Water ◽  
Closed Form Solution ◽  
Hydraulic Head ◽  
Flow Equation ◽  
Form Solution ◽  
Positive Zero ◽  
Rain Infiltration ◽  
Analytical Result

Analytical Solution for Transient Hydraulic Head, Flow Rate and Volumetric Exchange in an Aquifer Under Recharge ConditionThis paper presents closed form solution for unsteady flow equation corresponding to the transient hydraulic head, flow rate and volumetric exchange of a confined aquifer which is in contact with a constant piezometric head at one end and a stream whose water level is rising at a constant rate at the other end. The aquifer is also subjected to receive constant inflow due to rain infiltration. The unsteady groundwater flow equation is solved using Laplace transform to get analytical expressions for the transient hydraulic head and flow rate at the left and right interfaces and the net volumetric exchange of water at the aquifer-stream interface. The analytical results presented here show the effect of recharge due to rain infiltration on the net volumetric exchange and reveal the conditions for which net inflow in the aquifer could be positive, negative or zero. The results obtained have the capability to determine transient hydraulic head for two extreme scenarios: (i) very slow rise and (ii) very fast rise in the stream water. Analytical result show that the net volumetric exchange could be positive, zero or negative depending on the surface infiltration and stream water rise rate.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

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