Abstract: The electrohydrodynamic stability of two cylindrical interfaces influenced by a periodic tangential field is studied. The model allows for general forms of deformations of the interfaces. Two simultaneous ordinary differential equations of the Mathieu type are obtained. The coupled equations are solved by the method of multiple scales and stability conditions are discussed. It is found that the constant tangential field has a stabilizing effect while the tangential periodic field has a stabilizing influence except at resonance points. Graphs are drawn to illustrate the resonance regions in a parameter space. It is also found that the thickness of the jet plays a role in the stability criterion. The frequency of the modulated field can be used to control the position of the resonance regions. The special cases of large modulation and small modulation are also examined. It is found that for large modulation the electric field exhibits an enhanced destabilizing influence.

Abstract: The effect of fluid compressibility on the dynamic stability of a two-dimensional flow through a flexible channel is analysed. The compressibility parameter Q is defined as the ratio of a reference elastic wave speed of the wall to the local speed of sound. As the fluid speed increases, the walls become dynamically unstable at the critical fluid speed S0 and start to flutter at critical frequency ω0. The effect of three other dimensionless parameters on the critical condition is also analysed. These are the ratio γ of fluid damping to wall damping, the ratio B of wall bending resistance to elastance, and the ratio μ of wall to fluid mass. Nonlinear analysis using the Poincare–Lindstedt method shows stiffening at supercritical speeds. Further stability analysis using the method of multiple scales shows that the amplitude growth is finite and the nonlinear fluttering state is stable. Both symmetric and antisymmetric modes of oscillation are analysed. A frictionless system is found to be a singular case in the nonlinear theory. The hydraulic approximation employed in the analysis is shown to be a particular limiting form of the corresponding Orr–Sommerfeld system.

Abstract: A procedure has been developed t o identify the parameters of a nonlinear structural dynamic system with a single degree of freedom. A cubic nonlinearity has been assumed for purposes of illustration. In comparison t o the direct identification procedures, that depend on (a) either the availability of data on all four variables, namely, velocity, acceleration, displacement and the input t o the system or (b) the formulation of a numerical algorithm that can be used a t each iterative step, the developed procedure requires the data on only one of the field variables. The input t o the system is also treated a s an unknown. The results from the perturbation identification procedure have been compared with the results from two direct identification procedures.

Abstract: In this paper, problems of buckling of an annular thin plate under the action of in-plane pressure and transverse load are studied by using the method of multiple scales. We obtain N-order uniformly valid asymptotic expansion of the solution. In the latter part of this paper we discuss a particular example, and calculate the critical value of in-plane pressure. We see that the asymptotic expansion obtained by the multiple scales is completely consistent with that of the exact solution.

Abstract: Asymptotic solutions of the nonlinear ordinary differential equation d2θ/dZ2 +a dθ/dZ +f(θ)=0 for large a are obtained by the singular perturbation method of multiple scales analysis. They are in the form of θ(Z)=A(Z/a)+B(Z/a)exp(−aZ). Initial and boundary value problems are discussed. The special case of f(θ)=γ+cos 2θ(γ<1), encountered in shearing nematic liquid crystal soliton problems and other physical systems, is solved in detail. Previously obtained analytic solutions are recovered and justified. Our results are applicable to the unsteady shearing nematic problem.