Responses of Stochastic Shell Structures to Non-Gaussian Random Excitations

2008 ◽  
Author(s):  
Cho W. S. To
Keyword(s):  
Finite Elements ◽  
Acoustic Radiation ◽  
Random Excitation ◽  
Ease Of Use ◽  
Shell Structures ◽  
Central Difference ◽  
Spherical Cap ◽  
Relative Ease ◽  
Central Difference Method ◽  
Non Gaussian

An approach dealing with the responses of and acoustic radiation from temporally and spatially stochastic shell structures to non-Gaussian random excitations is presented in this paper. It employs the stochastic central difference method developed earlier by the author and his associate. The emphasis of the presentation is, however, on the responses of stochastic shell structures with large spatial variations and under non-Gaussian nonstationary random excitations. The shell structures are discretized by the mixed formulation, lower order triangular shell finite elements developed by the author and his associate in 1994. As a demonstration of the relative ease of use of the approach, computed results for a temporally and spatially stochastic, clamped spherical cap subjected to a central point force treated as a non-Gaussian nonstationary random excitation are included. It is concluded that a simple and relatively very efficient approach is available for analysis of responses of temporally and spatially stochastic shell structures perturbed by non-Gaussian nonstationary random excitations.

Large Nonlinear Responses of Spatially Nonhomogeneous Stochastic Shell Structures Under Nonstationary Random Excitations

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Shell Structures ◽  
Random Disturbance ◽  
Hybrid Strain ◽  
Central Difference ◽  
Spherical Cap ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Novel Approach ◽  
Random Disturbances

A novel approach for determining large nonlinear responses of spatially homogeneous and nonhomogeneous stochastic shell structures under intensive transient excitations is presented. The intensive transient excitations are modeled as combinations of deterministic and nonstationary random excitations. The emphases are on (i) spatially nonhomogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, (iii) intensive deterministic and nonstationary random disturbances, and (iv) the large responses of a specific spherical cap under intensive apex nonstationary random disturbance. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The novel approach consists of the stochastic central difference method, time coordinate transformation, and modified adaptive time schemes. Computed results of a temporally and spatially stochastic shell structure are presented. Computationally, the procedure is very efficient compared with those entirely or partially based on the Monte Carlo simulation, and it is free from the limitations associated with those employing the perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method. The computed results obtained and those presented demonstrate that the approach is simple and easy to apply.

Large Nonlinear Random Responses of Spatially Non-Homogeneous Stochastic Shell Structures

2006 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element ◽  
Random Excitation ◽  
Shell Structures ◽  
Response Analysis ◽  
Hybrid Strain ◽  
Central Difference ◽  
Approximation Techniques ◽  
Nonlinear Responses ◽  
Random Disturbances ◽  
Excitation Processes

This paper is concerned with large nonlinear random response analysis of spatially non-homogeneous stochastic shell structures under transient excitations. The latter are treated as nonstationary random excitation processes. The emphases are on (i) spatially non-homogeneous and homogeneous stochastic shell structures with large spatial variations, (ii) large nonlinear responses with finite strains and finite rotations, and (iii) intensive nonstationary random disturbances. The shell structures are approximated by the lower order mixed or hybrid strain based triangular shell finite elements developed earlier by the author and his associate. The nonstationary random nonlinear responses are evaluated by a procedure that consists of the stochastic central difference method, time co-ordinate transformation, and modified adaptive time scheme. Computationally, the procedure is very efficient compared with those entirely and partially based on Monte Carlo simulation, and is free from the limitations associated with those employing perturbation approximation techniques, such as the so-called stochastic finite element or probabilistic finite element method.

Nonstationary Random Response Analysis of Spatially Stochastic Structures Without Applying Probabilistic Finite Elements

2000 ◽  
Author(s):  
C. W. S. To
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Response Analysis ◽  
Structural Systems ◽  
Random Response ◽  
Central Difference ◽  
Central Difference Method ◽  
Random Responses ◽  
First Time

Abstract A procedure based on the stochastic central difference method that was presented earlier by the author has been extended to cases involving with spatially and temporally stochastic structural systems that are approximated by the versatile finite element method. It is believed that for the first time nonstationary random responses of this class of systems are considered. The procedure eliminates the limitations associated with those employing the so-called stochastic or probabilistic finite element methods. Owing to its simplicity, the proposed method can easily be incorporated into many commercially available finite element packages.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

Structural Modal Multifurcation With Internal Resonance: Part 2—Stochastic Approach

1993 ◽  
Vol 115 (2) ◽  
pp. 193-201 ◽  
Author(s):  
R. A. Ibrahim ◽  
B. H. Lee ◽  
A. A. Afaneh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Axial Load ◽  
Random Excitation ◽  
Stochastic Bifurcation ◽  
Density Level ◽  
Analytical Treatment ◽  
Asymmetric Mode ◽  
Non Gaussian ◽  
Gaussian Closure

Stochastic bifurcation in moments of a clamped-clamped beam response to a wide band random excitation is investigated analytically, numerically, and experimentally. The nonlinear response is represented by the first three normal modes. The response statistics are examined in the neighborhood of a critical static axial load where the normal mode frequencies are commensurable. The analytical treatment includes Gaussian and non-Gaussian closures. The Gaussian closure fails to predict bifurcation of asymmetric modes. Both non-Gaussian closure and numerical simulation yield bifurcation boundaries in terms of the axial load, excitation spectral density level, and damping ratios. The results of both methods are in good agreement only for symmetric response characteristics. In the neighborhood of the critical bifurcation parameter the Monte Carlo simulation yields strong nonstationary mean square response for the asymmetric mode which is not directly excited. Experimental and Monte Carlo simulation exhibit nonlinear features including a shift of the resonance peak in the response spectra as the excitation level increases. The observed shift is associated with a widening effect in the response bandwidth.

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