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The emf of the cell is measured to investigate the HCl + NaCl + H2O + CH3OH mixed electrolyte systems. The experimental data are obtained over the electrolyte molality ranging from 0.005 mol kg–1 up to about 3.5 mol kg–1, at 298.15 ± 0.01 K, by using a cell containing a pH and a silver chloride electrode in different alcohol mass fractions x(CH3OH) in H2O (where x = 0.10, 0.20, 0.30, 0.40, and 0.50). The mean activity coefficients of HCl in the mixtures are computed. Modeling is implemented by the classical Pitzer (CP) equation and original Pitzer (OP) equation that are included by the additional terms which are arising from interactions of neutral species and finally the modified Pitzer equation by Merida et al. (MP). The different aspects of proper parameter choosing in fitting processes especially for pure and mixed electrolytes in mixed solvent systems are signified in the results.

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In this paper, primary resonances of a simply supported rotating shaft with stretching non-linearity are studied. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of Hamilton's principle and then transformed to the complex form. To analyse the primary resonances, the method of multiple scales is directly applied to the partial differential equation of motion. The frequency—response curves are plotted for the first two modes. It is shown that these resonance curves are of the hardening type. The effects of eccentricity and the damping coefficient are investigated on the steady-state response of the rotating shaft.

In this paper, the effect of nonlinearity on vibration of a rotating shaft passing through critical speed excited by nonideal energy source is investigated. Here, the interaction between a nonlinear gyroscopic continuous system (i.e. rotating shaft) and the energy source is considered. In the shaft model, the rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The nonlinearity is due to large deflection of the shaft. Firstly, nonlinear equations of motion governing the flexural–flexural–extensional vibrations of the rotating shaft with nonconstant spin are derived by the Hamilton principle. Then, the equations are simplified using stretching assumption. To analyze the nonstationary vibration of the nonideal system, multiple-scale method is directly applied to the equations expressed in complex coordinates. Three analytical expressions that describe variation of amplitude, phase, and angular acceleration during passage through critical speed are derived. It is shown that Sommerfeld effect in specific range of driving torque occurs. Finally, effect of damping and nonlinearity on occurrence of Sommerfeld effect is investigated. It is shown that the linear model predicts the range of Sommerfeld effect occurrence inaccurately and, therefore, nonlinear analysis is necessary in the present problem.

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