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In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton’s principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus, the equations become independent from geometry and material properties. The method of multiple scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modeling the axial movement. String as a continuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency Ω. Stability analysis is carried out for these three cases, and stability boundaries are determined for the principle parametric resonance case. Thus, differences between ideal and nonideal boundary conditions are investigated.

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Since considerable amount of energy is spent in water heating processes in the world, solar energy systems are of great importance while heating water. Amongst these systems, flat-plate solar collector systems have an extensive area of use in residences. Therefore, nanofluid system has been investigated in order to enhance the efficiency in water heating through flat plate solar collectors and to benefit from solar energy more effectively. A simplified model has been taken into consideration to design the model of this system and complete the analyzes more rapidly. To identify the accurateness of the model, comparisons have been made against an experimental and a numerical study; and, a decent convergence to the experimental data has been obtained. Nanofluids used in the system have been applied in hybrid structure. The analysis has been conducted for the case of that two different nanometer-sized metal nanoparticles (SiO 2 and Cu) are mixed in water-based base fluid with different volume concentrations. Influences of nanofluids in different volume fractions on thermal performance have been investigated and compared against water and each other. In the system having 30 angle, diversified flow rates and heat fluxes have also been evaluated. It is concluded that water-based nanofluids enhances thermal performance; and, amongst these, the nanofluid including Cu nanoparticles augments thermal performance much better. To avoid precipitation problems within the system, thermal performance has been increased by virtue of using nanofluids with lower volumetric concentrations in hybrid form by adding certain amount of Cu nanoparticle instead of using high volumetric concentrations of SiO 2 nanoparticles. In comparison to water, these nanofluids we utilized have increased thermal performance in the rates of 2.03% (2%SiO 2 + 1%Cu-H 2 O), 3.218% (1%SiO 2 + 2%Cu-H 2 O), 0.943% (3%SiO 2 -H 2 O), 4.076% (3%Cu-H 2 O), 4.083% (3%SiO 2 + 2%Cu-H 2 O), 4.935% (2%SiO 2 + 3%Cu-H 2 O), 1.569% (5%SiO 2 -H 2 O), and 6.508% (5%Cu-H 2 O).

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