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Plates with periodic cavities show excellent vibration attenuation characteristics. This behavior can be attributed to the presence of frequency bandgaps on account of interference between the incident wave and the reflected wave from the cavities. The present work investigates the vibration attenuation/bandgap characteristics of plates with varying shapes of periodic cavities, such as square, circular, vertical rectangle, and horizontal rectangle, through experiments and simulation. Vibration responses of different periodic plates have been studied by carrying out frequency sweep on a vibration shaker. The investigation has been restricted to flexural vibrations of the plates, which are the predominant mode of vibration in many practical vibration scenarios. The frequency bandgaps, observed through the experiment, have been compared with the numerical simulation by harmonic analysis and by carrying out dispersion analysis on a unit cell of the periodic structure using Floquet–Bloch theory. Dispersion curves of the periodic plates yielded bandgaps, which were observed to be in agreement with the bandgaps from the experiment. The effect of variation in the aspect ratio of the cavities, that is length-to-width ratio, on the bandgaps has also been examined. It has been demonstrated that by suitable selection of the shape/size of the periodic cavity, desired vibration attenuation bandgaps can be realized for a 2-dimensional structure.

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

There is an ever-increasing demand in the automotive sector to continuously improve the performance and reduce cost through weight reduction in the structure of the vehicle. In the present scenario, it is also necessary to meet the standards set by crash safety regulating authorities in various parts of the world. In automobiles, the crash box is placed in the anterior region to absorb the impact energy in the event of an accident. Glass fiber reinforced plastic crash boxes have a high strength-to-weight ratio and also are good in energy absorption, particularly useful in this scenario. In this paper, the effectiveness of different triggers in combination with various geometries is investigated for Glass fiber reinforced plastic crash boxes using drop-weight impact testing. A trigger is a geometric irregularity introduced in the crash box design to alter the energy as well as force levels by modifying the deformation mode under loading. Comparison of change in force level, absorption of impact energy, specific energy absorption values was performed for composite crash boxes made of various types of cross-sectional geometries along with multiple patterns of triggers. Force versus displacement (F–D) curves are drawn for all the cases of the glass fiber reinforced plastic crash boxes to understand the behavior of each combination formed with various types of geometries and triggers, under impact loading. Strength-to-weight ratio was considered as the deciding factor for the comparisons to know the best and worst cases of the crash boxes made of different cross-sections along with various trigger types. This study provides detailed insights into the drop-weight impact testing procedure including the preparation of specimens, setting up the drop-weight impact test, preparation of specimen clamps, safety precautions involved, data acquisition from the test and its processing.

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