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J. Vib. Acoust. 2017;140(1):011001-011001-9. doi:10.1115/1.4037214.

This paper presents an experimental study to find out an effective parameter which is useful to enhance the progression rate of drifting vibro-impact systems excited by a harmonic force. It is assumed that the system performance would be better if the excitation force stays in a harmonious relationship with the natural motion of the impact mass. This hypothesis has been numerically analyzed and then experimentally verified. The phase lag between the excitation force and the motion of the impact mass is used to identify the best situation, where the system progression rate is maximal. It has been found that the highest progression rate of the system can be obtained when the phase lag is around one-eighth of the excitation period.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011002-011002-18. doi:10.1115/1.4037176.

A new global spatial discretization method (NGSDM) is developed to accurately calculate natural frequencies and dynamic responses of two-dimensional (2D) continuous systems such as membranes and Kirchhoff plates. The transverse displacement of a 2D continuous system is separated into a 2D internal term and a 2D boundary-induced term; the latter is interpolated from one-dimensional (1D) boundary functions that are further divided into 1D internal terms and 1D boundary-induced terms. The 2D and 1D internal terms are chosen to satisfy prescribed boundary conditions, and the 2D and 1D boundary-induced terms use additional degrees-of-freedom (DOFs) at boundaries to ensure satisfaction of all the boundary conditions. A general formulation of the method that can achieve uniform convergence is established for a 2D continuous system with an arbitrary domain shape and arbitrary boundary conditions, and it is elaborated in detail for a general rectangular Kirchhoff plate. An example of a rectangular Kirchhoff plate that has three simply supported boundaries and one free boundary with an attached Euler–Bernoulli beam is investigated using the developed method and results are compared with those from other global and local spatial discretization methods. Advantages of the new method over local spatial discretization methods are much fewer DOFs and much less computational effort, and those over the assumed modes method (AMM) are better numerical property, a faster calculation speed, and much higher accuracy in calculation of bending moments and transverse shearing forces that are related to high-order spatial derivatives of the displacement of the plate with an edge beam.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011003-011003-8. doi:10.1115/1.4037142.

This paper examines an approach for determining the entropy of coupled oscillators that does not rely on the assumption of weak coupling. The results of this approach are compared to the results for a weakly coupled system. It is shown that the results from each methodology agree in the case of weak coupling, and that a correction term is required for moderate to strong coupling. The correction term is shown to be related to the mixed energy term from the coupling spring as well as the geometry and stiffness of the system. Numerical simulations are performed for a symmetric system of identical coupled oscillators and an asymmetric system of nonidentical oscillators to demonstrate these findings.

Topics: Entropy
Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2017;140(1):011004-011004-9. doi:10.1115/1.4037300.

This research presents a study of the free vibration of thin, shallow elliptical shells. The equations of motion for the elliptical shell, which are developed from Love's equations, are coupled and nonlinear. In this research, a new approach is introduced to uncouple the transverse motion of the shallow elliptical shell from the surface coordinates. Through the substitution of the strain-compatibility equation into the differential equations of motion in terms of strain, an explicit relationship between the curvilinear surface strains and transverse strain is determined. This latter relationship is then utilized to uncouple the spatial differential equation for transverse motion from that of the surface coordinates. The approach introduced provides a more explicit relationship between the surface and transverse coordinates than could be obtained through use of the Airy stress function. Angular and radial Mathieu equations are used to obtain solutions to the spatial differential equation of motion. Since the recursive relationships that are derived from the Mathieu equations lead to an infinite number of roots, not all of which are physically meaningful, the solution to the eigenvalue problem is used to determine the mode shapes and eigenfrequencies of the shallow elliptical shell. The results of examples demonstrate that the eigenfrequencies of the thin shallow elliptical shell are directly proportional to the curvature of the shell and inversely proportional to the shell's eccentricity.

Commentary by Dr. Valentin Fuster

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