On rain-wind induced vibrations of a seesaw oscillator

In this paper the rain-wind induced vibrations of a seesaw oscillator will be stud- ied. The model equations will be derived under the assumption that the position of the rivulet of water on the oscillator varies in time. The eigenfrequency of the oscillator and the frequency of the movement of the water rivulet on the oscillator are assumed to be close to each other. Several Hopf and saddle node bifurcations will occur when the amplitude of the movement of the water rivulet on the oscillator is varied.Electrical Engineering, Mathematics and Computer Scienc

On the influence of gravity on the static state of an inclined tensioned string

In this paper the static state of an inclined stretched string due to gravity is considered. The string is stretched between two fixed supports which are situated at two different levels. It is assumed that the tension in the string is suffiently large such that the sag of the string due to gravity is small. The static displacements due to gravity of the string in the direction along the string and in the direction perpendicular to the string are determined by solving a nonlinearly coupled system of two second order, ordinary dierential equations.Electrical Engineering, Mathematics and Computer Scienc

On the applicability of the method of separation of variables for partial difference equations

Electrical Engineering, Mathematics and Computer Scienc

On the influence of lateral vibrations of supports for an axially moving string

In this paper the transverse oscillations in travelling strings due to arbitrary lateral vibrations of the supports will be studied. Using the method of Laplace transforms (exact) solutions will be constructed for the initial-boundary value problems which describe these transverse oscillations.Electrical Engineering, Mathematics and Computer Scienc

On the in-plane response of an inclined stretched string due to a forcing at one of the boundaries

The longitudinal and the transversal in-plane displacements of an inclined stretched string are studied. At one end of the string a parametrical and transversal excitation is applied and at the other end the string is kept fixed. By applying Kirchhoff's approach the coupled system of partial differential equations (PDEs) to describe the in-plane displacements of the string is reduced to a single PDE. The effect of gravity and of the external excitation on the in-plane displacements of the string are studied in detail. Complicated internal resonances can occur when the excitation-frequency is near an eigenfrequency of the linearized system. The existence and the stability of time-periodic solutions are investigated.Electrical Engineering, Mathematics and Computer Scienc

On oscillations in a system with a piecewise smooth coefficient

Electrical Engineering, Mathematics and Computer Scienc

On a characteristic layer problem for a weakly damped string

In this paper initial-boundary value problems for a string (a wave) equation are considered. One end of the string is assumed to be fixed and the other end of the string is attached to a dashpot system, where the damping generated by the dashpot system is assumed to be small, and is assumed to be proportional to the vertical and the angular velocity of the string in the endpoint. This problem can be regarded as a rather simple model describing oscillations of flexible structures such as for instance overhead power transmission lines. A semigroup approach will be used to prove the wellposedness of the singularly perturbed problem. It will be shown how a multiple scales perturbation method can be used effectively to construct asymptotic approximations of the solution on long timescales. Based on these asymptotic results the effectiveness of the dashpot system is discussed.Electrical Engineering, Mathematics and Computer Scienc

On the periods of the periodic solutions of the nonlinear oscillator equation x+x + x1=(2n+1) = 0

Electrical Engineering, Mathematics and Computer Scienc

An asymptotic analysis of a class of nonlinear hyperbolic equations

Electrical Engineering, Mathematics and Computer Scienc

On invariance factors and invariance vectors for difference equations

Electrical Engineering, Mathematics and Computer Scienc