Advances In The Modeling And Dynamic Simulation of Reeving Systems Using The Arbitrary Lagrangian-Eulerian Modal Method

This paper presents new advances in the arbitrary Lagrangian-Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance the sheave without including any non-linear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces.

Dynamic Stiffness Formulation for Out-of-Plane Natural Vibration of Elastically Supported Functionally Graded Plates

In this paper, the natural vibration characteristics of elastically supported functionally graded material plate are investigated using the dynamic stiffness method (DSM). Power-law functionally graded (P-FG) plate, the material properties of which vary smoothly along the thickness direction following the power-law function, that has been used for the analysis. Classical plate theory and Hamilton’s principle are used for deriving the governing differential equation of motion and associated edge conditions for P-FG plate supported by elastic foundation. During the formulation of dynamic stiffness (DS) matrix, the concepts of rotary inertia and neutral surface are implemented. Wittrick–Williams (W-W) algorithm is used as a solving technique for the DS matrix to compute eigenvalues. The results thus obtained by DSM for the isotropic, P-FG plate, and the P-FG plate with elastic foundation compare well with published results that are based on different analytical and numerical methods. The comparisons indicate that this approach is very accurate. Furthermore, results are provided for elastically supported P-FG plate under four different considerations in order to see the differences in frequencies with the inclusion or exclusion of neutral surface and/or rotary inertia. It is noticed that the inclusion of rotary inertia and neutral surface influences the eigenvalues of P-FG plate, and that cannot be discounted. The study also examines the influence of plate geometry, material gradient index, edge conditions, and elastic foundation modulus on the natural frequency of P-FG plate.

Development of an Energy- Efficient Rotary Inertia Device for Briquetting Household Solid Waste (HSW)

Today, increasing volumes of household solid waste (HSW) pose a serious problem throughout the world. The solution to this problem is involvement of secondary raw materials and waste in production. The disposal of HSW includes laborious stages of its collection and transportation. Aggregates of the garbage truck work inefficiently, only pressing HSW into a shapeless mass, not subject to sorting and processing. The suggested re-equipment of a special vehicle with aggregates with the combined functions of «loading–forwarding–grinding–pressing– briquetting» will significantly reduce the energy consumption of the transportation process by providing simultaneous processing and briquetting of garbage at the time of its transportation. A scientific and technical problem arises in development of a technique for technical re-equipment of high-performance special equipment with given nominal energy and power characteristics of the machines. It was proposed to solve this problem by combining recuperative systems with reuse of the energy of gravity of the own mass of garbage. Thus, the objective of the work is to develop a rotor-inertial device with reduced energy intensity. Methods of analytical and statistical research of the model range of special equipment with an analysis of its technical characteristics have been applied. To solve the problem of developing a kinematic diagram of a briquetting device, a calculation was performed based on the method of modeling the structure of composite aggregates. Modeling was performed in SolidWorks program in Simulation application package. The developed kinematic diagrams of units and aggregates for briquetting and pressing garbage operate at rated power characteristics of hydraulic equipment achieved due to distribution of drive power among the most energy- loaded operations. The article presents the rationale for effectiveness of the developed rotary- inertia device for briquetting HSW. The originality of the design lies in the structural arrangement of the briquetting unit and the grinding mechanism. The use of the principles of inertial moments and gravity of own mass of garbage allowed us to significantly (by 25 %) reduce the energy consumption of the pressing process and formation of the finished briquette. The use of mechanical energy of the conveyor belt tensioners and of the mass of the roll increased with briquetting under its own weight, allowed to reduce the work spent to form compacted HSW from 48000 kJ to 11970 kJ, to reduce the volume of the pressed roll, to increase the utilization rate of load carrying capacity, to reduce the energy intensity of the process.

Natural Frequency Characteristics of the Beam with Different Cross Sections Considering the Shear Deformation Induced Rotary Inertia

Based on the classical Timoshenko beam theory, the rotary inertia caused by shear deformation is further considered and then the equation of motion of the Timoshenko beam theory is modified. The dynamic characteristics of this new model, named the modified Timoshenko beam, have been discussed, and the distortion of natural frequencies of Timoshenko beam is improved, especially at high-frequency bands. The effects of different cross-sectional types on natural frequencies of the modified Timoshenko beam are studied, and corresponding simulations have been conducted. The results demonstrate that the modified Timoshenko beam can successfully be applied to all beams of three given cross sections, i.e., rectangular, rectangular hollow, and circular cross sections, subjected to different boundary conditions. The consequence verifies the validity and necessity of the modification.