Fundamental Principles Of Mechanics Research Articles

Rocking stiffness of electrical cabinets with tubular base in nuclear power plants

Safe operation of nuclear power plants during an earthquake requires continued operation of safety related electrical equipment as intended. Such equipment are mounted in electrical cabinets and are seismically qualified by using an in-cabinet response spectra (ICRS). Generation of ICRS requires a good understanding of the cabinet’s dynamic characteristics. Past studies have shown that the rotational stiffness associated with the cabinet base and the mounting arrangement plays a primary role in the dynamic behavior of the cabinet. This rotational stiffness is needed to evaluate and characterize the global rocking mode of cabinet vibration. Existing studies have developed formulations to calculate the rocking stiffness for a few mounting arrangements that are typically found in United States and some other western countries. However, existing formulations could not be applied to cabinets in South Korean nuclear plants due to the differences in cabinet mounting type. This study is focused on consideration of tubular mounting arrangement that is typically found in South Korean plants. First, closed-form formulations are developed using fundamental principles of mechanics for two separate cases of this mounting arrangement. Then, detailed nonlinear finite element (FE) analyses are conducted for different mounting arrangements corresponding to different properties and dimensions of the tubular base. The FE models are used to calibrate the proposed closed-form formulations for various different configurations and structural or geometrical properties of tubular members. The proposed formulations provide a simple and accurate estimation of cabinet rocking stiffness which otherwise is difficult to evaluate without a shake table test or a detailed finite element analysis.

THE TECHNICAL INGENUITY OF AL-JAZARI AND ITS RELEVANCE TO CONTEMPORARY ENGINEERING AND DESIGN

and polymath, and his relevance to contemporary technology and design. Al-Jazari's contribution to the history of technology is significant, as he is known for his pioneering inventions in various fields, including mechanics, automata, and fluid mechanics. His works are characterized by their intricate and sophisticated design, which not only served practical purposes but also revealed an artistic and aesthetic sensibility. Through an analysis of Al-Jazari's works, this article highlights the innovation and creativity that characterized his approach to technology and design. It shows how his inventions were based on a deep understanding of the fundamental principles of mechanics and fluid dynamics, as well as the use of novel materials and techniques. The influence of Al-Jazari's inventions on later developments in technology and design is also explored. It is shown how his ideas have influenced the design of modern machines and mechanisms. The article concludes with the assertion that Al-Jazari's technical ingenuity is of great importance to contemporary engineering and design. By studying Al-Jazari's works and ideas, engineers and designers can gain a deeper understanding of the fundamental principles of mechanics, fluid dynamics and materials science, as well as an appreciation for the artistry and aesthetic qualities of well-constructed machines. In addition, his inventions can serve as a source of inspiration for contemporary design, as they demonstrate the possibilities of combining functional efficiency with beauty and elegance. Overall, this article highlights the continued relevance of Al-Jazari's technical ingenuity to contemporary engineering and design.
 

On the dynamics of dilute gases

The evolution of a gas can be described by different mathematical models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide mutually consistent predictions. In particular, for rarefied gases, it is expected that the equations of the kinetic theory of gases can be obtained from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford (1975) has shown that the Boltzmann equation does indeed appear as a law of large numbers in the low density limit, at least for very short times. The aim of this paper is to present recent advances in the understanding of this limiting process.

Dry Friction and Mechanical System Motion Implicit Equations

It is shown that forces acting on the mechanical system points could depend on accelerations of the system points. Differential equation system of the mechanical system motion appears to be implicit. It is not resolved with respect to senior derivatives. Fundamental mathematical problems appear associated with possibility and uniqueness of these equations' solution with respect to the senior derivatives. Such problems are common in mechanical systems with dry sliding friction and rolling friction. Such problems are missing in the point dynamics. However, such problems are rather typical in more complex mechanical systems appearing in the study of a rigid body motion, which entire mass is concentrated in a single point, as well as in systems with one degree of freedom. Four fairly simple examples of mechanical systems are considered, and their motion is described by implicit differential motion equations. Situations could appear in these systems, when motion equations are not solvable with respect to the senior derivatives (motion equations are missing), as well as situations, when there are several solutions with respect to senior derivatives (there are several different systems of the mechanical system motion equations). At the same time, one of the fundamental principles of mechanics is not fulfilled, i.e., the principle of determinism

Why are tensile cracks suppressed under dynamic loading?—Transition strain rate for failure mode

Mechanical properties of rocks under dynamic loading are significantly different from those under quasi-static loadings. This difference is driven by more fundamental mechanical principles of materials at failure and will influence subsequent macroscale cracking behaviour. Understandings on this fundamental mechanism, however, are still controversial significantly. This paper tries to provide a feasible explanation of the underlying connections between the rate-dependent strength and the cracking behaviours. Open-flaw marble specimens, which provide good stress concentration at possible fracture initiation and material homogeneity, have been investigated experimentally and mathematically. We observe that experimentally the tensile strength is more sensitive to strain rate than the compressive strength. Meanwhile, tensile cracks are suppressed under dynamic loading, and shear cracks appear first along the flaw boundary. We incorporate the “localized strain rate effect” concept into the analytical study and propose the “transition strain rate” as a watershed for the different fracturing behaviours under quasi-static and dynamic loadings. This model successfully explains why the tensile cracks are suppressed in rocks under dynamic loadings, while quasi-statically, the stress distribution nonuniformity would suggest otherwise cracking behaviours. The well-correlation between the experimental and modelling results indicates that the model can be introduced to quantitatively analyse more complex macroscopic problems involving high strain rates in material science, geology and civil engineering.

The design of plane earthwork structures on pile foundations

AbstractA newly developed design concept for plane earthwork structures on pile foundations is presented. This design concept is based on a complex mathematical background that has been derived using fundamental mechanical principles. The mechanical system comprises the arching effect in a plane earthwork structure on punctual supports. It incorporates the effect of an elastic membrane that is formed by orthogonal ribs of geogrids, the modulus of subgrade reaction between the piles and the elastic settling of the piles. Some practical design examples are shown. The important aspects of the analysis and the design are pointed out. The complete mathematical background and a comprehensive design tool for free use have been prepared and are provided through a download link: https://gft‐pes.blogspot.com.

Mechanical Mechanisms of Chromosome Segregation.

Chromosome segregation—the partitioning of genetic material into two daughter cells—is one of the most crucial processes in cell division. In all Eukaryotes, chromosome segregation is driven by the spindle, a microtubule-based, self-organizing subcellular structure. Extensive research performed over the past 150 years has identified numerous commonalities and contrasts between spindles in different systems. In this review, we use simple coarse-grained models to organize and integrate previous studies of chromosome segregation. We discuss sites of force generation in spindles and fundamental mechanical principles that any understanding of chromosome segregation must be based upon. We argue that conserved sites of force generation may interact differently in different spindles, leading to distinct mechanical mechanisms of chromosome segregation. We suggest experiments to determine which mechanical mechanism is operative in a particular spindle under study. Finally, we propose that combining biophysical experiments, coarse-grained theories, and evolutionary genetics will be a productive approach to enhance our understanding of chromosome segregation in the future.

Investigation of Stresses Induced Due to the Mismatch of the Coefficients of Thermal Expansion of the Matrix and the Strengthening Particle in Aluminum-Based Composites

An experimental and theoretical investigation of the strength properties of aluminum alloys strengthened by dispersed nanoparticles, as well as the determination of the significance of various mechanisms responsible for the strengthening of the material, was carried out. Results of experimental investigation demonstrate that the hardening of aluminum alloy A356 by Al2O3 and ScF3 nanoparticles leads to an increase in the yield strength, ultimate tensile strength, and plasticity. Despite the similar size of Al2O3 and ScF3 nanoparticles, the physicomechanical properties of nanoparticles significantly affect the possibility of increasing the mechanical properties of the A356 aluminum alloy. A physicomathematical model of the occurrence of thermal stresses was developed caused by the mismatch of the coefficients of thermal expansion (CTEs) of the matrix and strengthening particles on the basis of the fundamental principles of mechanics of a deformable solid and taking into account the elastic properties of not only the matrix, but also the particle. The forming of thermal stresses induced due to the mismatch of the coefficients of thermal expansion of the matrix and the strengthening particle in aluminum-based composites was investigated. In the case of thermal deformation of dispersion-hardened alloys, when the CTE of the matrix and particles noticeably differ, an additional stress field is created in the vicinity of the strengthening particle. Thermal stresses increase the effective particle size. This phenomenon can significantly affect the result of the assessment of the yield strength. The strengthening caused by thermal mismatch makes the largest contribution to the yield strength improvement. The yield strength increments due to Nardon×Prewo and Orowan mechanisms are much lower.

The sliding ladder problem revisited in phase space

This paper solves the problem of a sliding ladder for the cases with and without friction at the wall and at the floor. Solutions for arbitrary initial conditions are obtained by strict application of the fundamental principles of mechanics. The validity of these solutions is discussed in context with the loss of contact of the ladder with the wall. A phase space representation is used to visualize for which initial conditions the ladder stays in contact with the wall and at which angle it would lose contact.

Shear deformable rod theories and fundamental principles of mechanics

We discuss the role of the principle of virtual work, of the objectivity and of the energy balance in the formulation of planar static rod theories, in a large deformations framework and consider the effects of transverse shear. According to these principles, we also discuss the differences of Haringx approach to equilibrium and buckling over Engesser approach, as well as the advantages of choosing the curvature strain measure as the derivative of the rotation of the cross section with respect to the reference, rather than current, arc length.

Towards a 3D passive dynamic walker to study ankle and toe functions during walking motion

The ankle–foot complex in the human body is one of the major determinants in normal human walking. Most of the research study ankle and foot motion by observing people as they move, measuring desired kinematic and kinetic data indoor or outdoor, and numerical simulations in computer. However, very few studies are able to explore the fundamental mechanical principles underlying human musculoskeletal system. In this paper, we developed a three-dimension (3D) passive dynamic walker with flat feet, toes and ankle springs to investigate the impact of the ankle and toe stiffness in the walking motion. The results suggest that the ankle springs have a main impact on the walking motion, where the anterior spring, over any other position, plays a main role in providing sagittal stability. The springs from the sagittal plane control the pitch angle of the robot which impacts on its velocity and step length. The stability got worse along with the step length and velocity increasing especially when the step length overcame 8 cm. The fact that the best configuration of the ankle joint has stiffer stiffness in the sagittal plane than the coronal plane complies in nature with humans where Tibialis Anterior, Soleus and Gastrocnemius muscles are much stronger than other muscles around the ankle. Furthermore, it can be stated that the medial toe plays a more important role than the lateral one, as blocking the medial toe with the stiffest joint (rigid joint) has a negative effect on walking motion. In conclusion, we show that the ankle stiffness of the robot in anterior–posterior position should be higher than that in medial–lateral position and the stiffness in any position should exceed a minimum level to maintain walking stability. Also, adding toes (medial one should be softer than the lateral) in the foot of the robot may benefit biped locomotion especially when taking longer step length.

Determination of the stiffness properties of a complex RF MEMS by superposition and finite elements method

In this study, the deflection and stiffness of a micro cantilever beam with a rectangular notch are derived analytically by considering a non-uniformly distributed load as a cause of deflection, since the shape of a distributed load at the exact collapse time is not uniform in the real scenario. In order to calculate the deflection, due to the design of the beam structure, the superposition method is employed as well as the fundamental principles of mechanics. Moreover, it is also utilized in the subsequent stiffness calculations. Particularly, the stiffness concept is discussed under three different subsets: natural, actuation, and release stiffness, as they are essentials for the switching operations. In addition to the analytical study, FEM simulations are also carried out using CoventorWare in order to compare with the derived models. As the results reveal that accuracies of both the analytical models and simulations are acceptable, this study provides a utilitarian framework for designing different complex MEMS.

Speed of transverse waves in a string revisited

In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the considered wave pulse and the related velocity and acceleration distributions. In this paper, we derive the named formula by applying Newton’s second law or the work-energy theorem to a finite element of the string, making no assumptions about the shape of the wave. We argue that the suggested method can help the student gain a deeper insight into the nature of waves and the related process of energy transport, as well as provide a new experience with the fundamental principles of mechanics as applied to extended and deformable bodies.

Models to Predict Mechanical Responses in Rigid Pavements

AbstractThe most recent tendencies in pavement engineering design are directed to the return of the use of fundamental mechanical principles of engineering to predict design life through the concep...

Stress Wave Analysis and Optical Force Measurement of Servo-Hydraulic Machine for High Strain Rate Testing

Based on fundamental mechanical principles, a force measurement method for a servo-hydraulic tensile machine at strain rates from quasi-static up to 103/s is proposed in this paper. Analytical and numerical stress wave analyses were performed at first to understand the principles of the force signal oscillation. The result of this FEM simulation indicates that the elastic vibration within the tensile specimen has a higher frequency and much lower amplitude than at the piezoelectric force sensor of the test machine. Based on this finding, a noncontact optical force measurement method was developed, which provides a fast and reliable force measurement directly on the specimen with little disturbance from the system ringing effect at strain rates up to 103/s.

SIMULATION OF PNEUMATIC MOTOR USED IN PNEUMOBILE

One of the alternative powertrain systems of cars, commercial vehicles and mobile machines are hybrid drives with pneumatic motors for compressed air. This paper presents a mathematical model and the results of simulation calculations of piston pneumatic motor. Mathematical model was based on the fundamental principles of mechanics, thermodynamics and rights of airflow. For simulation model parameterization, prototype of such engine was built and installed on dedicated test stand. Performed experimental research allowed achieving values of coefficients and components characteristics used for model estimation. One of the important tasks of this study was to create the control system of the compressed-air supplied engine. For this purpose an appropriate pneumatic and electronic component were selected and also an algorithm was created which would facilitate changing of the engine settings in order to obtain the best performance. Using elaborated simulation model, series of calculation were performed for different parameters of pneumatic motor, like cylinders diameter and stroke, length of the crank, compressed air pressure and valves size. A lot of attention was devoted to determine the influence of control system settings, such as valves opening and closing in reaction to crankshaft position, on motor properties. When discussing the results of calculations considerable attention was paid to the power, torque and efficiency values. To illustrate performance of designed engine, simplified model of light vehicle was used to calculate possible to achieve acceleration, velocity and travel distance.

A Friendly Beast of Burden: A Human-Assistive Robot for Handling Large Payloads

This article presents a novel robotic assistive device for the handling of large payloads. The design of the robot is based on the application of the following fundamental mechanical principles: inertia is minimized, a parallel closed-loop cable/belt routing system is used to kinematically decouple the transmission from fixed actuators and to the end-effector, and variable static balancing is used to minimize the actuation forces required for vertical motion. As a result, the device requires only low power, thereby improving safety, and can be operated manually, even in the event of a power failure (with minimum backup power for brake release). A novel force/torque sensor is also introduced along with a control algorithm based on variable admittance that provides a very intuitive interface for physical human-robot cooperation. Finally, a full-scale prototype integrating all of the above concepts is presented.

The inverse problem of Lagrangian mechanics for Meshchersky’s equation

Variable-mass systems are not included in the conventional domain of the analytical and variational methods of classical mechanics. This is due to the fact that the fundamental principles of mechanics were primarily conceived for constant-mass systems. In the present article, an analytical and variational formulation for variable-mass systems will be proposed. This will be done from the solution of the here called ‘inverse problem of Lagrangian mechanics for Meshchersky’s equation’. The first problem of this nature was posed in 1887, by Helmholtz (J. reine angew. Math. 100:137–166, 1887). Investigations on the matter are far from being exhausted. Within mechanics, it means the construction of a Lagrangian from a given equation of motion. To the authors’ best knowledge, aiming at general results, the inverse problem of Lagrangian mechanics has not been properly connected to Meshchersky’s equation yet. This is the main goal of this article. We will address the issue by assuming that mass depends on generalized coordinate, generalized velocity and on time. After the construction of a Lagrangian from Meshchersky’s equation, a general and unifying mathematical formulation will emerge in accordance. Therefore, variable-mass systems will be accommodated at the level of analytical mechanics. A variational formulation, which will be written via a principle of stationary action, and a Hamiltonian formulation will be both stated. The latter could be read as the ‘Hamiltonization’ of variable-mass systems from the solution of the inverse problem of Lagrangian mechanics. An energy-like conservation law will naturally appear from the simplification of the general theory to the case of a system with mass solely dependent on a generalized coordinate.

Damage evaluation of Timoshenko beams using invariant stress resultants

This paper presents an explicit damage evaluation methodology that utilizes the fundamental principles of mechanics to relate the changes in the physical properties of an undamaged and damaged structure to measurable response quantities. The proposed methodology is based on the principle of invariant stress resultants and the Timoshenko beam theory. First, damage in a structure is expressed in terms of local decreases in the bending stiffnesses of structural members. These stiffness decreases are in turn related to appropriate response quantities utilizing the Timoshenko beam theory. Next, a set of numerical experiments using results from two dimensional finite element models of cantilever and fixed–fixed beams are introduced to evaluate the performance of the proposed damage evaluation scheme. Results indicate that the proposed methodology can identify the location, the extent, and the severity of the local stiffness degradations in beams of arbitrary aspect ratios.

The generalized Hamilton’s principle for a non-material volume

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii, efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the generalized Hamilton’s principle for a non-material volume. First studies on the subject go back at least four decades with the article of McIver (J Eng Math 7(3):249–261, 1973). However, it is curious to note that the extended form of Hamilton’s principle that is derived by McIver does not recover the Lagrange’s equation for a non-material volume which is demonstrated by Irschik and Holl (Acta Mech 153(3–4):231–248, 2002). This does suggest additional theoretical investigations. In the upcoming discussion, Reynolds’ transport theorem is consistently considered regarding the original form of the principle of virtual work, and so the generalized Hamilton’s principle for a non-material volume is properly derived. It is finally shown that the generalization of Hamilton’s principle that is here proposed is in harmony with the Lagrange’s equation which is demonstrated by Irschik and Holl.