The nonlinear dynamics of a transverse galloping blunt body oscillator is analyzed with respect to its geometric shape and size. The oscillator's equation of motion is studied using an approximation for the lateral aerodynamic force that is a polynomial function of the angle of attack. The harmonic balance method is used to solve the nonlinear differential equation of motion. This solution is u...

This paper is an extension of a previous work where a diagonally implicit harmonic balance method was developed and applied to simulate oscillatory motions of pitching airfoil and wing. A more detailed study on the accuracy, convergence, and the efficiency of the method is carried out in the current paperby varying the number of harmonics in the solution approximation. As the main advantage of ...

Robust stability and performance are the two most basic features of feedback control systems. The harmonic balance analysis technique enables to analyze the stability of limit cycles arising from a neural network control based system operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural based control of a non...

When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation energies. We develop a general geometrical framework within which these conditions can be systematically derived. We treat both adhesion to a rigid substrate as well...

Radio-frequency (RF) circuits exhibit several distinguishing characteristics that make them difficult to simulate using traditional SPICE transient analysis. The various extensions to the harmonic balance and shooting method simulation algorithms are able to exploit these characteristics to provide rapid and accurate simulation for these circuits. This paper is an introduction to RF simulation ...

We obtain the radius of convergence of the small–amplitude approximation to the period of the nonlinear oscillator ẍ + (1 + ẋ2)x = 0 with the initial conditions x(0) = A and ẋ(0) = 0 and show that the inverted perturbation series appears to converge smoothly from below. The interest in the nonlinear oscillator ẍ(t) + [1 + ẋ(t)]x(t) = 0 x(0) = A, ẋ(0) = 0 (1) apparently arouse from the fact that...

A generalized harmonic balance method is used to calculate the periodic solutions of a nonlinear oscillator with discontinuities for which the elastic force term is proportional to sgn(x). This method is a modification of the generalized harmonic balance method in which analytical approximate solutions have rational form. This approach gives us not only a truly periodic solution but also the fr...

There are a variety of abnormal running conditions in rotating machinery which lead to rotor/stator interaction dynamics which, in turn, can cause a rich mixture of effects associated with rub-related phenomena. These effects manifest themselves in the occurrence of multiple solutions for steady-state vibration response scenarios, including amplitude jumps during rotor acceleration, and vibrati...