MSGeneral 4

The delivery of medical products by drone is potentially game-changing and promises shorter delivery times, particularly when trying to service hard to reach rural areas, and reduced carbon emissions. However, this raises a number of technical challenges, one of which being what is the vibration signature of drone platforms given that some medical products can become unstable and lose their efficacy when exposed to vibration. Medicines are transported in standard packaging containers which have been designed principally for thermal insulation performance and containment of spillages, not vibration isolation. The aim of this study was to design and experimentally evaluate a medical goods package capable of mitigating the vibration experienced specifically during transportation by drone. Two similar designs have been developed that feature coil spring and wire rope isolators respectively. Transmission of vibration by these prototype packages was bench tested on a shaker in the laboratory. Transportation trials were also conducted for a multicopter drone and a conventional road vehicle. In flight tests, the predominant excitation occurred at the blade passing frequency in the 63 Hz octave band, significantly above the fundamental suspension modes. The prototype packages reduced overall vibration levels by a factor of six compared with standard commercially available packaging. Isolation performance was slightly worse when transported by car since road inputs occur at characteristically lower frequencies. The prototypes are significantly heavier than the standard product when empty but this is partly off-set by a reduction in the number of cool packs facilitated by the use of high performance vacuum insulation panels for thermal insulation. Future work will seek to establish acceptable vibration thresholds for medical products through vibration and pharmaceutical laboratory testing to inform the design of medical packaging and its securement within the cargo hold.

This paper provides explicit closed-form analytical expressions for eigenfrequencies, and mode shapes of a uniform Euler-Bernoulli beam subjected to free undamped transverse vibration. The beam is having uniformly distributed mass with an elastic translational spring support at an intermediate location and carrying a concentrated mass at the location of the translational spring. One end of the beam has a an in-plane elastic rotational restraint while the other end is freely supported. The exact mathematical expressions for bending eigenfrequencies and explicit mathematical equations of eigenfunctions have been derived from the fundamental principle of vibration of a continuous system under the condition of undamped free vibrations. Special mathematical functions such as infinitely peaked Dirac-delta function and Heaviside-step function coupled with methods such as Laplace transformations are employed to deal with the fourth-order partial differential equation of motion. An example calculation with numerical values of natural frequencies for few significant eigen-modes has been presented in a tabular form considering various ranges of translational and rotational spring stiffnesses. The numerical results are then subsequently compared with the output of the Modal analysis of Finite element models using ANSYS and SESAM GeniE software. The general shapes of few meaningful eigenmodes are also compared with the Modal analysis output of Finite element program of ANSYS and SESAM GeniE software. The output of this comparative study reveals an excellent agreement among the closed-form solutions with that of output of ANSYS and SESAM GeniE. The analytical expression of this paper can be further deployed to study the free vibration characteristics, and derive the natural frequencies, and mode shape functions of several cases of Euler-Bernoulli beams having classical and non-classical boundary conditions. It is worth noting that all these cases, both classical and non-classical have significant real-world applications in Industry, especially in Mechanical and Structural Engineering to study the vibration characteristics of dynamical systems and to investigate the sensitivity when subjected to external forced excitation. While there are literatures and references that address similar problems related to eigenfrequencies however, the Author is not aware of any such article or technical paper which specifically provides an explicit mathematical expression of the eigenfunction for such a problem. The solution method that has been adopted can further be extended and generically applied to establish classical mathematical expressions for similar problems of varying complexities. As for illustration, be it a tall guyed mast or a free-standing steel chimney (including the effect of soil flexibility) etc., transcendental equations derived in this paper, when properly implemented to matching scenarios, will allow engineers to obtain a reasonable perception of dynamic characteristics of the system prior to conducting a rigorous free and forced vibration analysis using finite element software packages.

Current standards like ISO 14837-32:2015 or DIN EN 1998-1/NA:2021 allow for using correlations between the results of in-situ soil penetration tests and shear wave velocity (or shear modulus) to determine soil properties to be used in dynamic analyses. While the ISO standard even provides some recommendation on the specific correlation to be used, the DIN standard does not provide any guidance. Due to the statistical nature of such correlations their general applicability has to be verified. We collected data sets from test sites from Germany as well as New Zealand at which cone penetration tests (CPT) as well as seismic methods were conducted. These sites comprised sandy soils as well as clayey soils, mixed soils as well as glacial soils. We compare the results of several correlations between CPT results and shear wave velocity applied to the in-situ results found in the literature. The accuracy of such correlations is assessed with respect to the accuracy of seismic in-situ tests. It turns out the for clean sands such correlations between CPT and Vs have a similar order of variability as seismic in-situ tests conducted at the same site. The higher the fines portion of the soil, the higher the variability of the statistical correlations, and consequently the less the general applicability. For glacial soils and other special soil types usage of statistical correlations to determine dynamic soil properties is not recommended.