scholarly journals Dynamic Analysis of an Infinitely Long Beam Resting on a Kelvin Foundation under Moving Random Loads

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Y. Zhao ◽  
L. T. Si ◽  
H. Ouyang
Keyword(s):  
Fourier Transform ◽  
Random Vibration ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Integration Scheme ◽  
Random Loads ◽  
Numerical Integration Scheme ◽  
Vibration Responses ◽  
The Fourier Transform

Nonstationary random vibration analysis of an infinitely long beam resting on a Kelvin foundation subjected to moving random loads is studied in this paper. Based on the pseudo excitation method (PEM) combined with the Fourier transform (FT), a closed-form solution of the power spectral responses of the nonstationary random vibration of the system is derived in the frequency-wavenumber domain. On the numerical integration scheme a fast Fourier transform is developed for moving load problems through a parameter substitution, which is found to be superior to Simpson’s rule. The results obtained by using the PEM-FT method are verified using Monte Carlo method and good agreement between these two sets of results is achieved. Special attention is paid to investigation of the effects of the moving load velocity, a few key system parameters, and coherence of loads on the random vibration responses. The relationship between the critical speed and resonance is also explored.

scholarly journals FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250037 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Fourier Transform ◽  
Regime Switching ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
Finite State ◽  
Jump Diffusion Model ◽  
Log Price ◽  
The Fourier Transform

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

scholarly journals A New Approach on the Response of Non-Uniform Prestressed Timoshenko Beams on Elastic Foundation Subjected to Harmonic Loads

2021 ◽  
Vol 4 (2) ◽  
pp. 66-87
Author(s):  
O.K. Ogunbamike
Keyword(s):  
Elastic Foundation ◽  
Moving Load ◽  
Closed Form Solution ◽  
Complete Information ◽  
Form Solution ◽  
Mode Shapes ◽  
Accurate Information ◽  
Timoshenko Beams ◽  
Beams On Elastic Foundation ◽  
Vibration Responses

The dynamic response of the Timoshenko beam resting on an elastic foundation subjected to harmonic moving load using modal analysis (MA) was investigated. The method of MA was employed to obtain a closed form solution to this class of dynamical systems. In order to use MA, accurate information is needed on the natural frequencies, mode shapes and orthogonality of the mode shapes. A thorough literature survey reveals that the method has not been reported in existing literature to solve non-prestressed Timoshenko beams. Thus, we present complete information on how to use MA to derive the forced vibration responses of a simply thick beam subjected to harmonic moving loads. The effects of axial force and foundation parameters on the dynamic characteristics of the beams are studied and described in detail. In order to validate the accuracy of this method, we compare the frequency parameter with the existing literature which appears to compare favorably.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

The Axially Loaded Circular Cylinder

1962 ◽  
Vol 29 (2) ◽  
pp. 318-320
Author(s):  
H. D. Conway
Keyword(s):  
Exact Solution ◽  
Fourier Transform ◽  
Circular Cylinder ◽  
Closed Form ◽  
Cross Sections ◽  
Closed Form Solution ◽  
Form Solution ◽  
Concentrated Force ◽  
Transform Method ◽  
Fourier Transform Method

Commencing with Kelvin’s closed-form solution to the problem of a concentrated force acting at a given point in an indefinitely extended solid, a Fourier transform method is used to obtain an exact solution for the case when the force acts along the axis of a circular cylinder. Numerical values are obtained for the maximum direct stress on cross sections at various distances from the force. These are then compared with the corresponding stresses from the solution for an infinitely long strip, and in both cases it is observed that the stresses are practically uniform on cross sections greater than a diameter or width from the point of application of the load.

Dynamic Parameters Estimation and Fault Identification From Random Response of Rolling Element Bearing in a Rotor Bearing System

2019 ◽  
Author(s):  
Pankaj Kumar ◽  
S. Narayanan ◽  
Sayan Gupta
Keyword(s):  
Random Vibration ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parameters Estimation ◽  
Rolling Element Bearing ◽  
Vibration Signals ◽  
Rolling Element ◽  
Rotor Bearing ◽  
Element Bearing ◽  
Bearing System

Abstract This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently the response statistics of experimentally obtained random vibration signal are processed through the closed form solution of the FP equation as the inverse process of parameters estimation from the measured response. Further, the dynamic behavior of rigid rotor-bearing system is investigated under combined excitation of white noise and harmonic forces arising due to rotor unbalance force. The effect of system nonlinearities, stiffness, damping and unbalanced excitation force on the dynamic response are investigated using the bifurcation plot. For assessment of structural degradation of bearings, a novel entropy based approach is developed. Experimental studies on roller bearing are carried out to demonstrate the effectiveness of the proposed approach.

Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

Exact closed-form solutions for Lamb’s problem—II: a moving point load

2020 ◽  
Vol 223 (2) ◽  
pp. 1446-1459
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Point Source ◽  
Closed Form ◽  
High Speed ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
High Speed Rail ◽  
Lamb’S Problem ◽  
Homogeneous Half Space

SUMMARY In this paper, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb’s problem. Starting with the integral solutions of Bakker et al., we followed the method developed by Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker et al., which confirms the correctness of our formulae. The solution obtained in this paper may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.

Response of a bridge to a moving vehicle load

2006 ◽  
Vol 33 (1) ◽  
pp. 49-57 ◽  
Author(s):  
J H Lin
Keyword(s):  
Standard Deviation ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Statistical Characteristics ◽  
Roughness Coefficient ◽  
Vehicle Speed ◽  
Moving Vehicle ◽  
Bridge Span ◽  
Pavement Roughness

The determination of the statistical characteristics of bridge deflections due to a load of a vehicle moving across the span of a bridge is frequently a problem of great interest for bridge engineers. Developed herein is a spectral approach for evaluating the variation of bridge deflections due to a vehicle moving at constant speed along a rough bridge surface. Based on the above-mentioned approach, this study presents a closed-form solution for variances of bridge deflections. An example of application of the solution to the estimation of variances of bridge deflections is also presented. The effects of pavement type, vehicle speed, and bridge span on standard deviation of bridge deflections are investigated. The results of numerical examples show that if the effect of engine motions on vehicle vibrations is disregarded, the standard deviation of bridge deflections is proportional to the square root of the pavement roughness coefficient a for a specified vehicle speed.Key words: moving load, bridge deflection, pavement roughness.

Sign in / Sign up

Export Citation Format

Share Document