Dynamics of an oscillator with a quadratic nonlinearity in the expression of the elastic force loaded with a step pulse

The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the elastic force under the action of an instantaneously applied constant force are described. The analytical solution of a second-order nonlinear differential equation is expressed in terms of periodic Jacobi elliptic functions. It is shown that the dynamic coefficient of a nonlinear system depends on the value of the instantaneously applied force and the direction of its action, since the elasticity characteristic of the system is asymmetric. If the force is directed towards positive displacements, then the characteristic of the system is "rigid" and the dynamic coefficient is in the interval , that is, it is smaller than that of a linear system. In the case when the force is directed towards negative displacements, the elasticity characteristic of the system is «soft» and the dynamic coefficient falls into the gap (2, 3), that is, it is larger than in the linear system. In the second case of deformation, there are static and dynamic critical values of the force, the excess of which leads to a loss of stability of the system. The dynamic critical force value is less than the static one. Since the displacement of the oscillator is expressed in terms of the Jacobi functions, the proposed formula for their approximate calculation using the table of the full elliptic integral of the first kind. The results of calculations are given, which illustrate the possibilities of the stated theory. For comparison, in parallel with the use of analytical solutions, numerical computer integration of the differential equation of motion was carried out. The convergence of the calculation results in two ways confirmed the adequacy of the derived formulas, which are also suitable for analyzing the motion of a quadratically nonlinear oscillator with a symmetric elastic characteristic. Thus, the considered nonlinear problem has an analytical solution in elliptic functions, and the process of motion depends on the direction in which the external force acts. In addition, when a force is applied towards a lower rigidity, a loss of system stability is possible. Keywords: nonlinear oscillator, quadratic nonlinearity, stepwise force impulse, Jacobi elliptic functions.

Pengaruh Perendaman Minuman Berkarbonasi terhadap Gaya Elastik pada Elastomerik Ligatur dengan Variasi Panjang Penarikan

Elastomeric ligature is used to fasten orthodontic wires with brackets and can be stretched 1-3 mm as a simulation of bracket in the oral cavity. Its elastic force could decrease caused by salivary pH and water absorption of the elastomeric ligature. Consuming carbonated drinks causes the oral cavity to become acidic which increases the loss of elastic force in the elastomeric ligature with length of stretch variations. This study was aimed to determine the effect of immersion in carbonated drinks on the elastic force of the elastomeric ligature with length of stretch variations. This was an experimental laboratory study with a post-test only control group design. There were a total of 24 samples of American Orthodontic brand elastomeric ligature with royal blue color divided into six groups, consisting of three control groups immersed in artificial saliva, and three treatment groups immersed in carbonated drinks. Each control group and treatment group were given three variations of stretch length, as follows: 1, 2, and 3 mm. The calculation of the elastic force on the elastomeric ligature was performed by using the Universal Testing Machine. Data were analyzed by using the One Way Anova test and LSD post hoc test (p <0.05). The One Way Anova test showed a significant difference in the 1, 2, and 3 mm length of stretch variations for treatment groups. In conclusion, carbonated drinks affect the elastic force of elastomeric ligature with length of stretch variations.Keywords: elastomeric ligature; carbonated drinks; length of stretch variations Abstrak: Elastomerik ligatur adalah alat yang digunakan untuk mengikatkan kawat ortodonti dengan braket, dapat diregangkan 1-3 mm sebagai simulasi braket dalam rongga mulut. Elastomerik ligatur mengalami penurunan gaya elastik salah satunya disebabkan oleh pH saliva, dan penyerapan air dari elastomerik ligatur. Mengonsumsi minuman berkarbonasi menyebabkan pH saliva menjadi asam sehingga meningkatkan kehilangan gaya elastik pada elastomerik ligatur dengan variasi panjang penarikan. Tujuan penelitian ini untuk mengetahui pengaruh perendaman minuman berkarbonasi terhadap gaya elastik pada elastomerik ligatur dengan variasi panjang penarikan. Desain penelitian ialah eksperimental laboratorium dengan post-test only control group design. Sebanyak 24 sampel elastomerik ligatur merek American Orthodontic dengan warna royal blue, dibagi menjadi enam kelompok, terdiri dari tiga kelompok kontrol perendaman pada saliva buatan, dan tiga kelompok perlakuan perendaman pada minuman berkarbonasi. Setiap kelompok kontrol dan perlakuan diberi tiga variasi panjang penarikan, yaitu penarikan 1, 2, dan 3 mm. Perhitungan gaya elastik pada elastomerik ligatur menggunakan alat Universal Testing Machine. Analisis data menggunakan uji One Way Anova dan uji post hoc LSD pada p<0,05. Hasil uji One Way Anova menunjukkan perbedaan bermakna pada penarikan 1, 2, 3 mm dalam perendaman minuman berkarbonasi. Simpulan penelitian ini ialah terdapat pengaruh perendaman minuman berkarbonasi terhadap gaya elastik pada elastomerik ligatur dengan variasi panjang penarikan.Kata kunci: elastomerik ligatur; minuman berkarbonasi; variasi panjang penarikan

3D print material study to reproduce the function of pig heart tissue

BACKGROUND: Three-dimensional (3D) printing technology for heart simulation can be represented as complex anatomical structures, and objective information can be provided. OBJECTIVE: We studied 3D print material to find a material with the same elastic coefficient as pig elastic coefficient. METHODS: Pig heart sample, Agilus sample, Tango sample, TPU sample, and silicone sample were studied. The elastic coefficient of each specimen was measured using an elastic coefficient measuring instrument. The analysis was performed using the average value of ten specimens of the same size. We suggested an equation to find the elastic coefficient of material by the thickness using the elastic coefficient of Agilus, Tango, and silicone. RESULTS: The sample with similar elasticity to the pig sample did not show the same coefficient of elasticity at the same sample size. In Tango, the 0.5 mm high elastic force was about 3 times higher than the pig sample 7 mm elastic force. CONCLUSIONS: The study was conducted using 3D print material and silicone which can reproduce the elasticity of pig heart. However, no material is currently available to reproduce pig heart sample of the same size. However, if the heart is developed considering only elasticity, it can be sufficiently reproduced using the research results.

Three-Dimensional Aeroelastic Model for Successive Analyses of High-Aspect-Ratio Wings

Next-generation civil aircraft and atmospheric satellites will have high-aspect-ratio wings. Such a design necessitates successive analysis of static, frequency, and time-domain dynamic responses based on a three-dimensional nonlinear beam model. In this study, a new successive-analysis framework based on an absolute nodal coordinate formulation with mean artificial strains (ANCF-MAS) is developed. While retaining the advantages of other 3D ANCF approaches, such as constancy of the mass matrix and absence of velocity-dependent terms, ANCF-MAS uses the elastic force of the mean artificial strains to remove cross-sectional deformations that cause locking problems. The equation becomes a differential equation with an easily linearized elastic force that enables not only static and dynamic analyses but also frequency analysis using standard eigenvalue solvers. The solutions converge to the analytical frequencies without suffering from locking problems. A proposed successive-analysis method with model-order reduction reveals that the frequencies vary with the nonlinear static deformation because of the 3D deformation coupling. This reduced-order model agrees well with nonlinear models even when the wing experiences a large nonlinear dynamic deformation.

Neural control of rhythmic limb motion is shaped by size and speed

Over many size and time scales, behaviors such as locomotion or feeding require mechanical movements. Size and time in turn determine a behavior’s dominant mechanical properties: mass, stiffness or viscous damping. The constraints for limbed behaviors can thus be quantified by two variables: limb size and limb speed, defining a ‘mechanics space’ that shows the relative magnitude of each mechanical property for animals ranging from fruit fly to elephant. The mechanics space has three distinct regions: 1) an inertia-dominated region; 2) a gravity or elastic-force-dominated region; and 3) a viscous-force-dominated region. In the mass-dominated region, associated with large limbs moving rapidly, muscle work is translated into primarily kinetic energy. Thus, stable motion requires compensatory control and active damping. In the elastic-force-dominated region, associated with small limbs moving slowly, muscle energy is translated into primarily gravitational or elastic potential energy. Thus, compensatory control and active damping are unnecessary. Lastly, in the viscous region, associated with small limbs moving quickly, joint viscosity acts to damp actuation, resulting in exclusively stable movements. Control and stability of a limb thus depends almost entirely on the size and speed of limb movement, and this has fundamental implications for neural control.

Development in Liquid Crystal Microcapsules: Fabrication, Optimization and Application

A liquid crystal (LC) is an intermediate phase between a liquid and solid whose molecular orientation can be well-ordered but its shape is like a flow. As the elastic force...

Influence of the shaper parameters on the characteristics of acceleration pulses reproduced by mechatronic shock machines

In this paper the influence of the shaper parameters on the characteristics of acceleration pulses (peak value and duration) reproduced on mechatronic shock machines is analyzed. A comparison of the acceleration pulses obtained experimentally and by computational methods is presented. Recommendations for clarifying the requirements for methodological calculations of pulse parameters are given. The dependence of the elastic force of the shock pulse shaper on its deformation is presented. The influence of this characteristic on the peak value and duration of the acceleration pulse is estimated. The influence of the height of the shaper on the parameters of the acceleration pulses is analyzed. The concept of a device that allows you to automatically change the height of the shaper to obtain a wider range of acceleration pulses is presented. The interaction of the shock table with the shaper by means of computer modeling is modelled. Conclusions about the dependences of the duration and peak value of the acceleration pulses on the parameters of the shaper (stiffness and height) are drawn. Recommendations for selecting the parameters of the shaper to obtain acceleration pulses with the desired parameters are given.