With the insufficient satisfaction rates and high cost of operative treatment for osteoarthritis (OA), alternatives have been sought. Furthermore, the inability of current medications to arrest ...disease progression has led to rapidly growing clinical research relating to mesenchymal stem cells (MSCs). The availability and function of MSCs vary according to tissue source. The three primary sources include the placenta, bone marrow, and adipose tissue, all of which offer excellent safety profiles. The primary mechanisms of action are trophic and immunomodulatory effects, which prevent the further degradation of joints. However, the function and degree to which benefits are observed vary significantly based on the exosomes secreted by MSCs. Paracrine and autocrine mechanisms prevent cell apoptosis and tissue fibrosis, initiate angiogenesis, and stimulate mitosis via growth factors. MSCs have even been shown to exhibit antimicrobial effects. Clinical results incorporating clinical scores and objective radiological imaging have been promising, but a lack of standardization in isolating MSCs prevents their incorporation in current guidelines.
A square metal plate (Chladni plate) is excited harmonically by a vibration shaker, while the whole system is set in an anechoic chamber to stop reflections, isolate the system from sound entering ...from the surroundings, and deal with direct sounds only. As far as the authors are aware, such an arrangement has not been achieved so far. Vibration modes are visualized by using poppy grains scattered over the upper surface of the plate and are also recorded by a camera located above it, inserted among the acoustic wedges on the roof of the chamber, which made it possible to record the patterns and avoid unpleasant sounds associated with some of them. Four distinctive vibration modes of the plate are then originally identified using vibrational and acoustic mode identification. These responses from the plate are measured both by an accelerometer attached to the central point of the plate and by a microphone set on the same vertical line as the accelerometer but above it, measuring the direct sound. The signals from the accelerometer and the microphone are then compared in two experimental arrangements, and their forms and the frequency contents are found to be equivalent. It is shown that the existing symmetry, i.e., the exact correspondence between vibrational and acoustic responses, can be used as the identifier of the patterns formed on the plate and the associated modal frequency.
This paper is concerned with an oscillator attached to a crank-slider mechanism, where the driving torque is not assumed as constant, but as dependent on its angular velocity. Moreover, it is ...affected by the motion of the oscillator, i.e. it represents the so-called non-ideal excitation. The displacement of the oscillator is limited by a barrier, and the impact can occur. Consequently, the system response can be both impact and non-impact, which makes the influence on the driving torque unknown, and important to predict for practical applications in hand-held percussion machines, pile driving machines, cutting and grinding machines, etc. This work provides the analytical analyses of the regular behaviour of such vibro-impact system with non-ideal excitation system for the first time. New insight into its dynamics is gained, in terms of the appearance of impact and non-impact solutions, values of the impact velocity and their dependence on other system parameters. Amplitude–frequency diagrams are also obtained, showing the regions of non-impact, impact behaviour, non-existence of period-one steady-state response, stable and unstable solutions and oblique jumps in the amplitude and frequency. The stability issue is also investigated, and novel results are obtained with respect to the impact velocity and the associated steady-state response. The analytical solutions are verified numerically, confirming their validity and accuracy.
This study presents two different groups of models of bio-inspired hierarchically organized oscillatory mechanical models exhibiting a localization phenomenon, when only certain parts of the system ...oscillate. The first group of models corresponds to an idealized sympodial tree-type branched structure consisting of branches represented by physical pendula attached mutually via hinges and linear rotational springs. The localization phenomenon is examined analytically and numerically in the structures with a different level of hierarchy, i.e. with a different level of branches, and the corresponding localized modes and their respective natural frequencies are found. The cases of small and large-amplitude vibration are considered. The second group of models has the form of a chain of hierarchically organized block masses attached mutually via tension–extension springs. The case of an arbitrary number of masses attached via linear springs is considered to show which localized modes exist at certain frequencies and the theorem related to the number of localized models is formulated and proven. It is pointed out that localized modes appear also in a system with nonlinear (pure cubic) springs. The results obtained can further be used in theoretical dynamical studies of these systems with different types of excitations, as well as for appropriate biomimetic applications, especially related to their utilization as vibration absorbers.
This study is concerned with a double pendulum and its regular behaviour associated with low energy levels and the influence of the associated initial conditions on the frequency of normal modes. The ...case of nonlinear oscillations described by the exact equations of motion is examined. A global qualitative insight is provided via energy diagrams and Poincaré maps. Then, the case of linear oscillations, their normal modes and associated frequencies is analysed. Further, quantitative insights via two approaches (Lindstedt–Poincaré method and harmonic balancing) are also achieved to determine analytically the influence of initial amplitudes on the existence and frequency of nonlinear normal modes. These results are compared with the one corresponding to the linear normal modes as well as with the corresponding numerical solutions of the exact equations of motion.
This research focuses on the analysis of the model and performance of lightweight metastructures encompassing a distributed array of internal homogenous oscillators, integrated into the host ...structure to create a single-piece element. This metastructure performs longitudinal vibrations, whose axis is colinear with the direction of the transverse vibration of the internal oscillators. First, the mechanical models of the separate elements of the metastructure and the metastructure as a whole are created and considered. The first modal frequencies of longitudinal vibrations of the metastructure with blocked and free internal oscillators are tuned to the first modal frequency of transverse vibration of one internal oscillator, yielding the optimal number of internal oscillators for this to be achieved, which is a new result for the proposed design. This theoretical result is then checked experimentally with the metastructures produced by 3D printing technology, comprising a different number of internal oscillators, all of which have the same natural frequency. Besides validating the theoretical results, experimental investigations with blocked and freely vibrating internal oscillators of the constant natural frequency are used to explore other performance characteristics, such as the width of the regions where the reduced amplitude is achieved. Finally, based on the theoretical and additional numerical results, the internal oscillators are modified in two ways, which is an original approach: their natural frequency is increased linearly and nonlinearly along the metastructure in accordance with the previous new theoretical results. The benefits of such new redesigns for the multi-modal performance characteristics of the metastructure are discussed.
•Conservative antisymmetric constant force oscillators are considered.•Two approaches are developed for obtaining their motion in terms of Jacobi elliptic functions.•First approach starts from the ...period of vibrations.•Second approach starts from the expression for the acceleration.•Both computational approaches give original and new results for this kind of oscillators.
This study presents how the motion, velocity and acceleration of conservative antisymmetric constant force oscillators can be expressed in terms of Jacobi elliptic functions. Two approaches have been developed. In the first approach, one starts from the known period of vibrations and the solution for motion expressed in terms of Jacobi elliptic functions. The second approach is also shown, starting from the expression for the acceleration in terms of the Jacobi elliptic functions, and then deriving the expression for the velocity and motion. As far as the author is aware, both computational approaches give original and new results for this kind of oscillators.
This study presents quantitative and qualitative insights into the analysis of data obtained by tracking the motion of reflective markers arranged along the trunk of a pole-like potted tree, which ...was recorded by a state-of-the-art infrared motion-tracking system. The experimental results showed in-plane damped trajectories of the markers with lateral displacements, i.e. out-of-plane vibrations of the tree under consideration. To explain such response and to determine the corresponding oscillatory characteristics, a completely new and original utilisation of the recorded in-plane damped trajectories is presented. The quantitative insight gained is based on the mechanical model that consists of two orthogonal springs and dampers placed in the plane where the motion takes place, and it is then directed towards the determination of the characteristics of the related orthogonal oscillations: two natural frequencies, the position of the principal axes to which they correspond, and two damping ratios. The qualitative insight gained involves analysing the shape and narrowness of the trajectory to assess how close-valued two natural frequencies are, and how small the overall damping is. The quantitative and qualitative methodologies presented herein are seen as beneficial for arboriculture, forestry and botany, but given the fact that orthogonal oscillations appears in many natural and engineering systems, they are also expected to be useful for specialists in other fields of science and engineering as well.
This work presents a methodology on how to use exact closed-form solutions for the response of free undamped linear and nonlinear oscillators to design the external excitation of undamped or damped ...nonlinear oscillators to get such steady-state response. A variety of examples, including Duffing-type oscillators and purely nonlinear oscillators, are given to illustrate this methodology.
•External excitations are designed to achieve a desired steady-state response.•This response has the exact closed-form solution.•Linear oscillators are excited in a specific way to respond as free Duffing oscillators.•Duffing oscillators are excited in a specific way to have a single-harmonic response.•The cases with linear viscous damping are also considered.
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