Vol. 7, No. 4 (2023): Regular Issue

In this paper, a prey, intermediate predator and top predator interaction model has been developed. Here all parameters of the model have been considered as triangular fuzzy number. Positivity and boundedness of solutions of the proposed model have been investigated. Possible equilibrium points of the model are determined and also local stability of the model around these equilibrium points have been studied. Global stability of the model around the interior equilibrium point is also studied. Conditions for the existence of Hopf bifurcation have been investigated with respect to $\alpha$ (degree of uncertainty). It is found that the uncertain values of the parameters have a great influence in the solution of the proposed model. From the analysis of the model, it is observed that intra-species competition rate of prey as well as intermediate predator can be stabilized the system. It is also observed that the harvesting rate of intermediate predator has the ability to stabilize the system. Some complex behaviour of the system have been seen due to the increase of death rate of top predator species. Finally some numerical simulation results have been presented to verify the analytical findings.

In this study, we consider an undamped mass-spring system that experiences piecewise constant forces and analyze the solutions of this system. We investigate the solutions of undamped mass-spring system by using the method of steps. In addition to investigating the solutions, stability and convergency analyses are performed for the solutions of nonhomogeneous undamped mass-spring system. The results are stated in terms of the parameters of the systems. Simulations are given to illustrate and support the findings for different values of the parameters.

Aiming at the problems that the complex rotor system is difficult to carry out and monitor due to variable load and bad working conditions, the design method of software platform based on digital twin technology is studied, and the architecture and main function realization of digital twin software platform are explored from six aspects: physical layer, virtual layer, data layer, functional layer, client layer and connection layer. A method to establish the digital twin model of rotor system integrating geometric model and mechanism model is proposed. The digital twin model of the existing rotor test-bed is constructed. Based on the digital twin software platform of the rotor test-bed, the rationality of the design and implementation method is verified by comparison with the experiment.

Laser interferometers are often adopted in high-precision motion control systems but seldom used for experimental vibration analysis. This is partly because their installation and mounting are invasive to dynamical systems as opposed to non-contact position sensors such as vibrometers. However, as the industry moves towards light manufacturing structures out of economical and environmental considerations, metrology systems that already utilize laser interferometry, such as profilometry in semiconductor manufacturing, may benefit from interferometer measurement for vibration analysis. This study investigates the use of laser interferometry for vibration analysis and system identification through a piezoelectrically actuated cantilever beam mounted with a retroreflector. The dynamics of the beam, which include the piezoelectric actuator and optical measurement components are modeled through the Euler-Bernoulli beam theory. This leads to a continuous system, which is then transformed into a discrete system represented in a state-space form, through the method of separation of variables. The frequency response at the retroreflector location is obtained through the Laplace transformation of the state-space form. A recursive adaptive filter following the ARMAX structure is formulated to identify the transfer function of the discrete system from its random noise excitation. The transfer function and its frequency response is analytically predicted, then compared to the simulation and experimental results from the adaptive filter. The high-precision measurement of interferometers is well-suited for applications of signal processing such as system identification.

This study aims to determine the effect of a flow disruptor on the performances of a cantilever piezoelectric energy harvester invested by an airflow. The purpose of the flow disruptor is to increase the turbulence intensity of the incoming flow and therefore the momentum transferred to the piezoelectric beam. The height of the flow disruptor and the distance between the flow disruptor and the energy harvester were investigated to determine the optimal configuration. Results indicate that for an energy harvester with a frontal area of $\mathrm{\sim}$18 cm${}^{2}$ (7 cm by 2.54 cm), the flow disruptor should have a height of 4 cm and should be placed 13 cm away from the harvester. Also, a shift in the frequency of vibration occurs when the flow disruptor is placed in front of the harvester.

In view of the vast potential applications of flexible thin rotating disks, the knowledge of their vibration characteristics has been considered by many investigators. Rotating disks are the main components in various machinery applications, such as space structures, flywheels, torsional disk dampers, grinding wheels, turbine rotors, circular saw blades, computer storage devices and brake systems. Dynamic response and stability of rotating disk depend on its rotational speed. The knowledge of the in-plane vibration of rotating disks is also essential for the design of spinning disks. In most cases, to rotating a disk at a certain speed, a knowledge of modal vibrations and critical speeds of the disks are essential. An analytical solution is investigated to determine in-plane modal vibration characteristics of high speed rotating annular disks. A systematic approach based on the established governing equation for the linear in-plane free vibrations of disks is developed, and the displacements and stresses compatibilities are considered. The disk material is elastic homogeneous, thin, and isotropic and is rotating at constant angular speed. The developed analytical solution is obtained by implementing the two-dimensional plane stress theory. In this research, several possible boundary conditions for the annular disks are investigated, and natural frequencies and mode shapes of rotating disks are computed. The mode shape functions for displacements and stresses in the radial and circumferential directions are determined. In addition, variations of nondimensional modal frequencies versus a wide range of dimensionless rotational speeds for several radius ratios are presented.