Hyper-elliptic Nambu flow associated with integrable maps

We study hyper-elliptic Nambu flows associated with some $n$ dimensional maps and show that discrete integrable systems can be reproduced as flows of this class.Comment: 13 page

Obtaining mechanical shock fragility statistics for simple stochastic cushioning design.

Proper cushioning to prevent product damage and over-packaging must consider the mechanical-shock fragility of the product. Furthermore, improved cushioning design can be achieved by performing stochastic cushioning design using mechanical-shock fragility statistics and transport hazard statistics. However, many samples are required to obtain mechanical-shock fragility statistics from standard testing comprising critical velocity change tests and critical-acceleration tests (the “conventional method”). In many cases, the required number of samples cannot be prepared. Thus, this research is designed to develop testing methods requiring half the number of samples of the conventional method. Thus far, test method with one sample has been developed by improving the standard testing method required two samples. Hence, we propose a new statistical method (the “proposed method”) that obtains statistics by multi-sample testing using a test method with one sample. The proposed method is one in which the shock of a single velocity change (the “test velocity change”) is given by increasing the acceleration in a step-wise fashion, and the results indicate the failure rate at the test velocity change and provide the critical-acceleration statistics. In these experiments, the critical-acceleration statistics for a test velocity change larger than the critical velocity change were equivalent to those obtained from the conventional method. The accuracy of the failure rate at test velocity changes was clarified. Moreover, examples are provided showing the results when the proposed method is applied to simple stochastic cushioning design

A Method for Generating Random Vibration Using Acceleration Kurtosis and Velocity Kurtosis

Random vibration tests for packaging are conducted to confirm safety during shipping by truck. However, there is a difference between the traditional random vibration tests and the real vibrations on the truck bed. One reason for this difference is the shock caused by road roughness. Hence, many studies have been conducted to improve random vibration testing. In these studies, the root mean square, power spectral density, kurtosis, and probability density of acceleration are considered. In this study, we show that the kurtosis and probability density of velocity are also important factors for such tests and propose a new method for generating vibrations with arbitrary kurtosis of acceleration and velocity. By bringing the kurtosis and probability density of velocity closer to those of real vibration, it is possible to conduct more accurate vibration tests

Experimental verification on the effectiveness of random vibration testing with controlling acceleration and velocity kurtosis

Random vibration tests for packages are conducted to confirm the safety of these packages during shipping. In our previous study, a method of generating the random vibration controlling the power spectral density and kurtosis of acceleration and the kurtosis of velocity was proposed. The aim of the present study is to verify the effectiveness of the proposed method. Three vibrations were generated in this study and compared with the real vibration, which replicates the truck bed. In the first case, control of the acceleration and velocity kurtosis was neglected. In the second case, the vibration controlling the acceleration kurtosis was considered. The third case corresponded to the vibration controlling both the acceleration and velocity kurtosis generated by the proposed method. In the present study, an aluminum plate simulating the product was fixed to a table for evaluating the vibrations. The natural frequency of the plate was varied by varying the mass of the weight placed on the plate. The relative displacement of the plate was calculated from the difference between the readings of two laser displacement meters. The vibrations were evaluated via the root mean square, kurtosis, and skewness of the relative displacements of the plate. Kurtosis and skewness of the relative displacement of the proposed method were similar to those of the real vibration. However, the kurtosis and skewness of the other generated vibrations were far from those of the real vibration. Results provided experimental verification that the kurtosis of velocity is an important factor for random vibration tests

Experimental and Theoretical Evaluation of the Effect of Panel Geometry on the Failure of Corrugated Board Panel

McKee’s formula is widely used to predict the compression strength (CS) of corrugated boxes and panels. It can accurately estimate the compression strength of boxes that are within a practical size range, but recently, larger and smaller corrugated boxes than before have been extensively developed. Therefore, there is a need for a CS prediction formula that works beyond the application range of McKee’s formula. Recent researches consider the failure mode as a combination of collapsing and buckling failure and remove the constraints and the assumptions associated with McKee’s formula. This makes it possible to more accurately estimate the CS of boxes that are not covered by McKee’s formula. Many CS formulae are derived logically from material mechanics, but doing so can make it difficult to account for various actual behaviors in detail up to when the box fails. Instead, by analyzing the behavior up to failure in detail, we explored relationships that could account for the CS consistently based on its behavior

Proposal of Hybrid Damping Package Design

To protect products from shock and vibration during transport, Cushioning Packaging Design is implemented. The cushioning performance and anti-vibration performance of a package is tested by a drop test and a vibration test. The effectiveness of the cushioning during a drop test is predictable because the cushioning material`s thickness and bearing area are determined by the cushion curves which are plotted based on the results of the tests. However, an effective package-design method which can predict the package vibration of all the static stresses that are suitable for cushioning package design has not been established yet.thus, it remains uncertain until actually vibration tests are conducted and redesigns are developed to correct the failures during the tests. Redesigning efforts are expensive and time consuming. Therefore, in this study, we propose the “Hybrid Damping Package Design” wherein both the Cushioning Packaging Design and the Anti-vibration Package Design will be implemented. In particular, Multibody Dynamic simulation is applied as an aided design tool for Anti-vibration Package Design so that numerical analysis a package’s vibration response becomes possible. Furthermore, we discuss a case study to demonstrate how to analyze and compare multiple package designs in order to determine the best candidates based on cushioning performance, anti-vibration performance, and material cost

Damping package design using structural corrugated board

Packaging is designed to protect products from shock and vibration during transport. In recent years, paper cushioning materials, such as corrugated board and pulp molded packaging, are being increasingly used because they are environmentally friendly and easy to recycle. However, because no efficient packaging-design method yet exists for paper cushioning material, packaging engineers must rely on previous experience and the so-called trial-and-error method to design packaging. One reason for this situation is that, for most cases, the paper cushioning material used for protective packaging has a complicated structure and deforms after being subjected to repetitive shock and vibration. To address this shortcoming, we propose a damping design method for corrugated-board packaging that includes shock-absorbing and vibration damping elements. To verify that the resultant packaging functions as intended, we test three types of packaging in the following way: First, we use an existing design method to create cushioned packages and examine them via free-fall drop tests. Next, to test the robustness of packaging against vibration (i.e., for packaging destined for various modes of transport), we study the three packaging types by subjecting them to (i) vibration-only tests and (ii) drop-plus-vibration tests. For vibration-only tests, the packaging with highest static stress gives the best result, its “vibration fatigue” accounts for approximately 52% of the worst result given by packaging with the lowest static stress. In the drop-plus-vibration tests, the best packaging is that with the lowest static stress; its “vibration fatigue” is approximately 31% of the worst packaging, which has an intermediate value of static stress. This approach allows us to determine the packaging with the best shock-absorbing and vibration damping characteristics