Exact(2)
The analysis yields closed form expressions for the second order statistics of the response.
Expressions for the second and third order non-linear stiffness matrices of the empty shell are then determined through the finite element method.
Similar(58)
Based on the NI LW approximation, analytic expressions for the second-order difference-frequency seepage force by bichromatic incident waves are developed.
The expressions for the first and second moments have been obtained.
Approximate expressions for the first three spectral characteristics of the response are developed by neglecting small oscillatory terms.
We develop novel closed-form expressions for the fourth-order elasticity tensor (tangent moduli) in full generality.
The expressions for the first and second moments, for the components and for the waves, have been obtained by Laplace transformation and matrix diagonalization.
Using moment analysis and matrix diagonalization, expressions for the first and second chromatographic moments of components and waves, written in matrix form, are derived.
Approximate expressions for the fourth order moment of a wave propagating in a random medium are derived by using the path integral formulation.
The key parameters of an optimally coupled GaAs saturable absorber Q-switched laser are determined and several design curves are generated from these expressions for the first time.
General expressions for the first and second chromatographic moments of components and waves are given by taking into account axial dispersion, film mass transfer resistance, and intraparticle diffusion resistance for chromatographic column packed with inert core adsorbents.
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