Owing to the importance of fourth-order two-point boundary value problems in describing a large class of elastic deflection, there is a wide literature that deals with the existence and multiplicity results for such a problem with different boundary conditions (see, for instance, [3 8] and the references therein).
Three Levy-type solutions for a plate with different boundary conditions are studied.
In this regard, the effect of the nonlocal parameter on the vibration frequencies of a DWNT with different boundary conditions of each tube has been examined in our analysis, and some novel numerical results are presented perhaps for the first time.
In the conventional lumped-mass (model) transfer matrix method (LTMM), one must use different frequency equation and the associated initial parameters to determine the natural frequencies and the corresponding mode shapes of a beam with different boundary (supporting) conditions as one may see from the Appendix at the end of this paper.
To test the predictive power of the parameterized Cosserat model we use the determined material parameters in a simulation with qualitatively different boundary conditions.
Experimental measurements aiming at validating the theoretical predictions showed that the technique permits detecting the impact area (inside/outside the frame) as well as an accurate estimation of the impact energy if the latter occurred inside the frame, both on a steel plate (with different boundary conditions) and an anisotropic composite structure.
Later refinements (see, e.g., [12, 13, 19]) show that the knowing eigenvalues associated with a number of different boundary conditions can also determine the potential uniquely.
The behaviour of highly convective problems is then investigated via a series of analyses where convective heat transfer along a soil bar is simulated, with recommendations on the choice of an adequate discretisation with different boundary conditions being provided to avoid oscillatory solutions.
Since no literature results readily available to the authors' knowledge, we now investigate the problem of free vibrations of a nonlocal DWNT with different boundary conditions of inner and outer tubes.
Ayub et al. [5 7] presented acoustic diffraction in a trifurcated waveguide with different boundary conditions (hard, soft, impedance etc).. Demir and Cinar [8] considered the propagation of sound in a two-part circular cylindrical duct carrying a mean gas flow, inserted in a larger infinite outer duct with wall impedance discontinuity.
