Archive of Applied Mechanics

It is well known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the inhomogeneity of elastic media. However, the reported new linear elasticity equations for inhomogeneous media may appear in different forms. This paper tries to clarify this issue by investigating the form-invariance of the Lagrangian under local temporal or spatial gauge transformations. In this way, these new equations in different forms can be easily understood as the results from different choices of gauge fixing schemes. It recommends to choose appropriate gauges with clear physical meanings to simplify calculations.

This paper deals with the parametric resonance of steel bridges pylons due to time-depended traffic loads. The analysis follows the basic lines of Bolotin’s technique for the solution of nonlinear problems of dynamic instability. In this work, the cases of forced vibrating pylons with and without damping subjected to periodic external dynamic forces acting axially are investigated. The effect of bridge vibration due to traffic loads has been also taken into account. Through the aforementioned technique, useful results regarding the dynamic stability of pylons are obtained, and illustrative examples for various cases of geometry and loading are presented in the form of plots and diagrams.

This paper shows that dynamic air gap torques in converter-fed induction motors may not only cause torsional vibrations in the drive train, but may also cause lateral vibrations of the motor itself—including bending vibrations of the rotor shaft—, if the motor is mounted on a soft foundation. Based on a simplified analytical model, the mathematical correlation between rotor-stator interaction, oil film characteristics of sleeve bearings, the influence of a soft foundation—coupling angular and lateral displacement of the stator—and excitation from dynamic air gap torques is shown. In addition to the absolute orbits of the rotor, stator, shaft journals and bearing housings, also the relative orbits between rotor and stator and between shaft journals and bearing housings are mathematically described. Further, the paper shows the influence of the oil film coefficients of the sleeve bearings on the elliptical shape of the orbits. Therefore, the paper presents a possibility to optimize the whole system—converter, motor and foundation—concerning lateral vibrations, caused by dynamic air gap torques.

In this paper the analog equation method (AEM), a BEM-based method, is employed for the nonlinear analysis of a Timoshenko beam with simply or multiply connected variable cross section undergoing large deflections under general boundary conditions. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the AEM. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The influence of the shear deformation effect is remarkable.

This paper proposes a study of the kinetics and dynamics of slalom waterskiing. The discipline of slalom waterskiing is first described. Then the forces applied on a “static” skier, i.e. just pulled behind a boat, are expressed as a function of water drag coefficients, speed and pitch angle. A slalom point model is finally proposed, made of three major contributions: water friction, water lift and an additional water drag contribution on the slalom skier, creating the traverse motions. Assumptions are made in order to quantify the three angles characterizing the ski position during the slalom traverses. The model is simulated on an EXCEL worksheet, for a large range of conditions (boat speed between 52 and 58 km/h, rope length between 18.25 and 13 m, and three skier masses of 60, 80 and 100 kg). The water friction coefficient was fitted to a value allowing to simulate successful slalom courses. The simulations provide a significant set of kinematics and dynamics parameters (skier velocity, acceleration, tangential force and rope tension). The model duly renders the variations of the skier velocity, and it reflects the increasing difficulty for the skier to complete the slalom at higher boat speed and shorter rope length.