In this study, using the classical analytical solution for wave motion in the sagittal plane, the authors show that the spectral distortion induced from the artificial finite periodicity are the manifest results of spatial aliasing in the wavevector domain.
Recognizing that the introduction of nanoparticles in the foam material creates local stress concentrations around the inclusions we also examine the local strength of the impregnated foam using the classical Goodier solution for dilute particles and the Mori–Tanaka based stress analysis for a finite particle concentration.
Most AFM-based studies of the mechanical behavior of living cells (e.g., Wu et al. 1998; Rotsch and Radmacher 2000; Mathur et al. 2001) are interpreted using the classical Hertz solution for the indentation of an elastic half-space (e.g., Sneddon 1965).
Comparisons among the critical loads obtained using these three approaches and those using the classical Euler solutions for classical column cases are presented.
The energy governing equations for far-field propagating out-of-plane waves in the Mindlin plate were newly derived by using the classical displacement solutions for out-of-plane motions in the Mindlin plate.
Now we are ready to present the first theorem by using the classical representation of solution (2) derived by Khusainov et al. [2].
A modified 1-D model using the classical (exact) Kirchhoff solution for a plane wave in a narrow tube is also presented.
In the following section, we intend to prove the existence of a positive solution for (1.6) by using the classical bifurcation result of Rabinowitz [17].
The same solutions using the classical VIM can be found in [26].
Remark 3.15 If f is Lipchitz continuous in the second variable u, then in Theorem 3.13, one has uniqueness of the solution by using the classical Banach contraction fixed-point theorem.
The motion equations are properly formulated considering the hypotheses of thin shells and the solution is obtained using the classical separation of variables method.
