Closed-form Approximations and Series Representations for Partially Saturated Ocean Acoustic Processes
نویسندگان
چکیده
An approximate, closed-form expression for the value of the integral encountered inthe calculation ofthe probability density function (PDF) of the envelope of a partially saturated ocean acoustic process i obtained. Furthermore, an expression of this PDF as a series of modified Bessel functions i presented. The results may also be directly applied to the evaluation of the PDF encountered in the structural reliability analysis of rotating machinery components. Numerical applications show that the closed-form expression is always within 1%-2% of the exact result. The required computational effort is substantially lower than that required by direct numerical integration.
منابع مشابه
Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations
An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...
متن کاملClassification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions
Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...
متن کاملNonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations
Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...
متن کاملConsolidation Around a Heat Source in an Isotropic Fully Saturated Rock with Porous Structure in Quasi-Static State
The titled problem of coupled thermoelasticity for porous structure has been solved with an instantaneous heat source acting on a plane area in an unbounded medium. The basic equations of thermoelasticity, after being converted into a one-dimensional form, have been written in the form of a vector-matrix differential equation and solved by the eigenvalue approach for the field variables in the ...
متن کاملAsymptotic Approximations to Truncation Errors of Series Representations for Special Functions
∞ ν=0 aν for special functions are constructed by solving a system of linear equations. The linear equations follow from an approximative solution of the inhomogeneous difference equation ∆rn = an+1. In the case of the remainder of the Dirichlet series for the Riemann zeta function, the linear equations can be solved in closed form, reproducing the corresponding Euler-Maclaurin formula. In the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004