Maximum entropy approach for modeling random uncertainties in transient elastodynamics.
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Citations
Stochastic finite element method for vibroacoustic loads prediction.
Data-driven modal surrogate model for frequency response uncertainty propagation
Multilevel solvers for stochastic fluid flows
Meso‐ to Macro‐scale Probability Aspects for Size Effects and Heterogenous Materials Failure
Random dynamical response of a multibody system with uncertain rigid bodies
References
Information Theory and Statistical Mechanics. II
Non-Uniform Random Variate Generation.
Simulation and the Monte Carlo Method.
On fluctuations of eigenvalues of random Hermitian matrices
Random field finite elements
Related Papers (5)
Frequently Asked Questions (15)
Q2. What have the authors stated for future works in "Maximum entropy approach for modeling random uncertainties in transient elastodynamics" ?
1. Nevertheless, experiments are in progress to study the correlation which could exist between the dispersion of the random responses and parameters δM, δD and δK associated with the random generalized matrices.
Q3. What are the advantages of parametric approaches?
The parametric approaches existing in literature are very useful when the number of uncertain parameters is small and when the probabilistic model can be constructed for the set of parameters considered.
Q4. What is the dynamic magnification factor of the mean model?
The dynamic magnification factor increases when the random uncertainties increase, and is greater than the deterministic dynamic amplification factor of the mean model.
Q5. What is the definition of the variational formulation of the mean boundary value problem?
The variational formulation of the mean boundary value problem defined by Eqs. (1)-(3) consists in finding a function t 7→ u(t) with values in such thatm(ü, v) + d(u̇, v) + k(u, v) = g(v ; t) , ∀v ∈ , ∀t ∈ [0, T ] , (12) with the initial conditions defined by Eq. (4).
Q6. What is the generalized damping matrix of the mean reduced matrix model?
The generalized damping matrix [ Dn] of the mean reduced matrix model, defined by Eq. (29), is written as [ Dn] = 2 ξ Ωref[ Mn] in which [ Mn] is the generalized mass matrix of the mean reduced matrix model, defined by Eq. (29), and where Ωref = 2 π × 200 rad/s.
Q7. What is the method for calculating the variance of a random matrices?
In addition, the authors have to calculate multiple integrals in a higher dimension (see Eq. (85)) for which a well suited method consists in using a Monte Carlo calculation with or without variance reduction procedures49−55.
Q8. What is the eigenfunction of the mean reduced matrix model?
The mean reduced matrix model is obtained using the Ritz-Galerkin projection of the variational formulation of the mean boundary value problem on the subspace n of spanned by the structural modes {1 , . . . , n } of the mean structural model, which correspond to the n lowest eigenfrequen-cies {ω1, . . . , ωn}.
Q9. What is the convergent model of the Monte Carlo numerical method?
For nS sufficiently high (nS ≥ 300) the Monte Carlo numerical method is reasonably converged and it can be seen that the nonparametric model proposed is convergent with respect to dimension n of the random reduced matrix model (see Section VI.D).
Q10. What is the way to predict the transient response of a complex structure?
For a complex structure, such a mean boundary value problem defined by Eqs. (1)-(3) is not able to predict the transient response due to impulsive loads whose energy is distributed over a very broad frequency band, i.e. over the low-, medium- and high-frequency ranges (for instance, if there is energy in the medium-frequency range, more advanced probabilistic mechanical models such as the fuzzy structure theory have to be used to take into account the role played by the structural complexity8); the most that this kind of deterministic mean boundary value problem is able to predict is the transient response due to impulsive loads whose energy is mainly distributed over a broad lowfrequency range for which the mean reduced matrix model defined by Eqs. (25)-(27) is suitable andJ. Acoust.
Q11. what is the hn(t) function of the linear filter associated with second-order?
Fn(τ) dτ , (84)in which t 7→ [hn(t)] is the matrix-valued impulse response function of the linear filter associated with second-order differential Eq. (81).
Q12. What is the variational form of the themean boundary value problem?
The variational formulation of themean boundary value problem is absolutely necessary to construct the mean reduced matrix model in the general case.
Q13. How many timesteps per period is the mean reduced matrix model?
This time-step corresponds to 10 timesteps per period for the structural mode of the mean model whose eigenfrequency is ν61 = 402.24 Hz.
Q14. What is the probability density function of random matrix?
Let us consider ν random matrices [A1n], . . . , [A ν n] with values in +n (!) such that for each j in {1, . . . , ν}, the probability density function of random matrix [Ajn] satisfies Eqs. (47)-(49).
Q15. What is the way to describe the probability model?
An explicit construction and representation of the probability model have been obtained and are very well suited to algebraic calculus and to Monte Carlo numerical simulation.