Using the criterion of resistibility to assess of a structural limit state

Introduction. Subject of research: behaviour characteristics of an arbitrary structure under the loads that approach the limit load value. Goals: development of an objective and sufficiently universal methodology for the identification of the bearing capacity of a structure, which could allow to stop using any subjective assessments of their limit bearing capacity. Materials and methods. Behaviour characteristics are assessed by analyzing a curve of equilibrium states. The curve is constructed using the characteristic displacement, understood as the generalized displacement q, which energetically matches applied generalized force λ in the sense that the product of λdq is the growth of work performed by generalized force λ in respect of the growth of displacement dq. Results. The article shows that the system’s response, no matter what fixed conditions it is in, is not always sufficient for the assessment of the reliability of the system in case of the variable interaction with the environment. The co-authors use the V.V. Katyushin concept about supplementing the notion of the limit state with the characteristics of the system’s beha­viour determined by the velocity of a change in the system’s response caused by the change in the external action. According to the co-authors’ suggestion, the meter should represent the reduction in the slope of the curve of equilibrium states, which characterizes the loss of resistibility and, consequently, it can be used to assess the closeness of the structure to the state of failure, which arises if the resistibility of the system is equal to zero. The suggestion is to use the value of the slope of the curve of equilibrium states as the limit state, when the resistibility has reduced, and the velocity of deformation intensification has gone up 100 times if compared with the behaviour of an unloaded system. This suggestion is illustrated by the case of the analysis of a reinforced concrete diaphragm of a building. Conclusions. The proposed calculation methodology can be applied in the design of loadbearing structural elements, whose finite-element computational model has components that are different from the rod ones.

EFFECTS OF IMPACTS OF COVERING ROLLERS ON GENERAL FORCES OF SMALL-SIZED TILLAGE MACHINE

Increasing the efficiency of agricultural production, in particular the production of crop products in personal subsidiary plots, depends on the development and implementation of high-tech machines and their working units. The need for small-sized tillage equipment is increasing from year to year. But in order to increase the functionality of the equipment and the quality of soil preparation for sowing, it is necessary to study the possibility of using various additional working units. The purpose of the work is theoretical studies of the movement and kinematic connection of a trailed slatted-spiral roller with a walk-behind tractor, which make it possible to substantiate rational design and technological parameters of a small-sized tillage tool. The study used the provisions of classical mechanics and analytical geometry, methods of equilibrium and motion of mechanical systems based on differential and integral principles of mechanics. The design of active and passive rollers for a walk-behind tractor is considered, which allows to qualitatively prepare the soil for sowing at the depth of seeding, the influence of potential and non-potential effects on their generalized forces is revealed, the angular velocity and their acceleration are determined, as well as the dynamic characteristics of the moment of inertia of the rollers relative to the axes of rotation X4 and Z4 and their frames relative to the axes of rotation X3 and Z3. The difference in the generalized force for a passive roller relative to the angle φ 5.49 N∙m was obtained. The angular speed of the active roller is 23.0 rad/s higher than that of the passive roller, and as a result of research it was revealed that the moments of inertia of the active roller and its frame relative to the axles are significantly higher than that of the passive roller. Generalized forces for an active roller relative to the angle q = 2.58 N∙m and relative to the angle φ = 1.98 N∙m, for a passive roller - relative to the angle q = 2.32 N∙m and relative to the angle φ = 7.47 N∙m. The generalized forces for the potential effects of an active roller are Qθa=1.58 N∙m, Qφa=2.26 N∙m, for a passive roller Qθn=1.32 N∙m, Qφn= 4.60 N∙m. Mθa = 1 N∙m, Mφa = 114.63 N∙m; passive roller - respectively Mθn = 1 N∙m, Mφn = 178.9 N∙m

Study of a Stripper Header for Grain Harvesting as a Vibrating System

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

Acoustic and Dynamic Response of Unbaffled Plates of Arbitrary Shape

In this study, a method for determining the effects of fluids on the dynamic characteristics of an aerospace structure and the response of the structure when it is excited by the acoustical loads produced during a rocket launch, has been developed. Elevated acoustical loads are critical in the design of large lightweight structures, such as solar arrays and communication reflectors, because of the high acceleration levels. The acoustic field generated during rocket launch can be considered as a diffuse field composed of many uncorrelated incident plane waves traveling in different directions, which impinge on the structure. A boundary element method was used to calculate the pressure jump produced by an incoming plane wave on an unbaffled plate and the fluid–structure coupled loads generated through plate vibration. This method is based on Kirchhoff’s integral formulation of the Helmholtz equation for pressure fields. The generalized force matrix attributed to the fluid loads was then formulated, taking the modes of the plate in vacuum as base functions of the structural displacement. These modes are obtained using a finite-element model. An iteration procedure was developed to calculate the natural frequencies of the fully coupled fluid–plate system. Comparison of the results obtained using the proposed method with those of other theories and experimental data demonstrated its efficiency and accuracy. The proposed method is suitable for analyzing plates of arbitrary shape subjected to any boundary conditions in a diffuse field for low to medium values of the frequency excitation range.

Potential Energy as Design Criterion in Planar Multistable Mechanisms

Toggle mechanisms are used throughout engineering to accomplish various tasks, for example residential electrical switching. The design of toggle mechanisms can be broken into three categories: determination of a topology, geometric parameterization, and optimization. While topological determination and optimization have well established processes for use in design, geometric parameterization which includes defining link lengths and spring stiffness has largely been left to engineering judgement. This paper presents a design methodology using potential energy graphs which informs the engineering decisions made in choosing mechanism parameters, giving designers higher confidence in the design. A kinematic analysis coupled with Lagrange’s equation determines the relationship between the mechanism parameters and the potential energy curve. Plotting the potential energy with respect to the generalized coordinate yields a graph with a slope that is the generalized force or moment. The relationships between parameters and their effects on the mechanism are difficult to observe in the equations of motion, but potential energy plots readily provide information pertinent to the design of toggle mechanisms and decouple their effects. The plots also allow design by position rather than time which makes the design process faster. The design process is applied to three examples: a simple toggle mechanism, a compliant mechanism, and a reconfigurable mechanism to show the nuances of the approach.

Optimization Based Dynamic Human Motion Prediction with Modular Exoskeleton Robots as Interactive Forces: The Case of Weight Lifting Motion

The optimization-based dynamics model is formulated for the weight lifting motion with human and exoskeleton model as interactive force term in this chapter. In the optimization algorithm, the human motion is defined as variables so that the motion which we want to generate (box lifting motion in this case) can be predicted. The objective function or cost function is defined as performance measure which can be switched by developer. In this paper we use the summation of each joint torque square which is considered as the dynamic effort for the motion. Constraints are defined as joint limits, torque limits, hand position, dynamic balance, exoskeleton assistive points, etc. Interaction force form exoskeleton robot can be derived as generalized coordinates and generalized force which are related to inertial reference frame and human body frame. The results can show how effective the exoskeleton robots are according to their assistive force.