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A tractable transfer matrix method based on the classical beam theory is developed and is subsequently used to investigate the effects of the axial tensile load and moving speed on the natural frequencies of axially moving beams under three different end conditions. The differential equation for the proposed method is solved in a closed analytical form. The transfer matrix method is derived from the relationship between displacements and forces specified at both ends of the axially moving beam. The accuracy of the method is validated through a comparison between the predicted results and those of previous studies. The critical speed for the fundamental frequency of an axially moving beam is analyzed by investigating the moving speed value in the vicinity of divergence instability. The numerical results for the end conditions considered provide useful information for capturing the divergence instability.

In this study, a transfer matrix method is developed to analyze the effect of the centrifugal force on the natural frequencies of a rotating double-tapered beam, whose cross-sections have linearly reduced height and width. The root of the differential equation is determined based on the Bernoulli-Euler theory and the effects of the hub radius, taper ratio, and rotation speed, by applying the Frobenius method. In particular, the effect of the centrifugal forces is analyzed based on the relationship between the bending and additional strain energies generated by centrifugal stiffening. The shape function of the displacements depends on the variations in the taper ratio and rotation speed. In addition, the strain energies are varied. Various examples are presented to demonstrate the influences of the strain energies. Furthermore, the effects of the centrifugal force on the natural frequencies of the rotating double-tapered beam are investigated by analyzing the variation in the predicted strain energy.

In this study, the effects of cracks on the natural frequencies of a rotating Bernoulli–Euler beam are investigated using a new numerical method in which these effects can be computed simply using the transfer matrix method. The present method using the crack model of a rotating beam developed by considering the distributed mass can determine the desired number of accurate natural frequencies for rotating cracked beams regardless of the size and location of the crack, and this method can produce accurate results by using the minimum number of subdivisions. The Frobenius method is used to determine the roots of the relevant differential equation. An open crack is considered, and each crack is modeled as a rotational spring. With these assumptions, the additional bending displacement generated by the crack is formulated as a separate transfer matrix. The computed results are compared with those discussed of a previous work to demonstrate the accuracy of the proposed method. The effects of the crack on the natural frequencies of rotating beams at different rotational speeds and hub radii are investigated through a parametric study with respect to the size and location of the crack.

Unlike the continuous-time case, algebraic necessary and sufficient conditions for a single output discrete-time system to be state equivalent to a nonlinear observer canonical form have been found and are easier to verify for those who are not accustomed to differential geometry. The geometric conditions look very different from the algebraic conditions. In this paper, we show direct equivalence of the geometric conditions and the algebraic conditions in order to enhance the understanding of the geometric conditions.

A geometric design algorithm for a slotted disc spring is proposed in this study. By using the proposed algorithm, all geometric dimensions of a slotted disc spring can be parameterized to satisfy a target nonlinear load-displacement function. This target nonlinear load-displacement function is plotted using the available prediction formulation. The defined geometric dimensions for the target function are then purposely set to be unknown design variables. Inversely, only the target function is referred to in order to propose a set of geometric dimensions of a slotted disc spring that satisfies the plotted target function. A comparison between the target function and the predicted function that are plotted using the calculated dimensions from the proposed algorithm are shown. Both design variables that are used to plot the target and are calculated from the proposed algorithm are also compared to validate the effectiveness of the proposed geometric design algorithm. These comparisons show the effectiveness of the proposed algorithm that enables inverse calculation to propose geometric designs by only having a given target nonlinear function.

A wide range of proteins and RNA molecules in plants have been recently identified as non-cell autonomous, phloem-mobile molecules and suggested to play important roles in physiological and developmental processes. Systemic movement of both protein-coding mRNAs and non-coding small RNAs is shown to correlate with the epigenetic changes brought about across grafting junctions, supporting their potential roles as long-distance signaling molecules. Plants appear to have evolved this unique RNA-based signaling mechanism to control systemic regulation of various responses to environmental stimuli and challenges such as photoperiods, nutrient availabilities, and pathogen attacks. This mechanism may have been exploited by viroids, non-coding RNA pathogens, to spread infection cell to cell and through phloem. A model describing potential molecular mechanisms by which the systemic RNA trafficking occurs will be presented.

The evolution of intercellular communication had an important role in the increasing complexity of both multicellular and supracellular organisms. Plasmodesmata, the intercellular organelles of the plant kingdom, establish an effective pathway for local and long-distance signalling. In higher plants, this pathway involves the trafficking of proteins and various forms of RNA that function non-cell-autonomously to affect developmental programmes.