An Analysis of Thermal Induced Vibrations of Cantilever Beam with Tip Mass Under the Effect of the Axial Force

Modern timber structures represented by glulam structures have recently been widely developed. The joint connection performance is essential for the overall structural strength, especially in high-rise or large-span timber structures. In this paper, three-point bending tests were carried out on Buckling-Type (BT) and Reinforced-Type (RT) joints to investigate the damage modes and the effect of different axial forces on the connection performance. A finite element model (FEM) of the BT joint (belonging to the single-direction (SD) joint) was established based on ABAQUS and verified with the experimental results. The SD joint FEM was extended to the three-direction (TD) joint FEM, and the connection performance of the TD joint was analyzed under the action of combined axial forces in different directions. Experiments and finite element analyses showed that the BT joints were damaged by buckling of the upper part of the steel tube, and the RT joints were damaged by transverse cracking of glulam. The axial tension force can increase the ultimate bearing capacity, while the axial compression force has the opposite effect. Increasing the absolute value of the axial force can improve the initial rotational stiffness of the bolted group connection. The three directional flanges constrained to each other could provide additional strength and stiffness in the TD joint. When the relative values of axial compression and tension forces are constant, the combination of different directions of axial forces has little effect on the TD joint’s ultimate bearing capacity.

The aim. Subsequent development of procedure for calculation of the kinematic parameters of the process of tube deformation in the cold tube pilger roll rolling mills with purpose of decreasing the value of axial forces. Methods. The new method (procedure) for the choice of the rational relationship of values of the forced rolling radius and the roll barrel radius in the mill KPW (method of the work minimum) had been assumed as the basis of development of the procedure for calculating the kinematic parameters of the tube deformation process in the cold tube pilger roll rolling mills. The outcome. The main dependencies known for now, which are used for calculating the value of the natural rolling radius and the roll barrel radius had been considered in the present paper, as well as the main practice used for decreasing the value of axial forces in the CTR mills. A procedure had been proposed for calculating the kinematic parameters of the tube deformation process in the mills of the cold tube pilger roll rolling (the method of the work minimum). Basing on the outcomes of industrial exploitation of the given method one drew the conclusion as to effectiveness of the proposed procedure. The scientific novelty. Basing on existing dependencies, the development of procedure had been proposed for calculating the rational relationship of the forced rolling groove radius and the roll barrel radius in the cold tube rolling mills. The procedure is based on the intimate analysis of axial forces, which are determined proceeding from all the basic parameters of the process. The practical importance. The given method allows optimizing not only the maximum values of axial forces at the direct and reverse stroke of the stand, but also the intensity of forces distribution along the cone of deformation. The method (procedure) had been used while calculating a number of roll pass designs for rolling tubes of titanium alloys in the mill KPW–25.

Vibration of a Rayleigh cantilever beam with axial force and tip mass

The helicopter main rotor blade is the basic product that determines the reliability and service life of the helicopter as a whole. The problem of predicting and ensuring the specified blade life is an urgent problem considered at the stage of its design. To determine the fatigue life of the blade it is necessary to know the characteristics of the stress-strain state. A method has been developed for determining the characteristics of the stress-strain state of the spar of the regular part of the rotor blade of a helicopter using the ANSYS system. Application of numerical methods of stress-strain state characteristics calculation allows to reduce considerably time and cost of blade design. The calculation results of regular part of the Mi-8 main rotor blade at the hover mode when it is loaded by aerodynamic and inertial load from the rotation, as well as the force of its own weight are presented in the work. Using the ANSYS system, a finite-element model of the regular part of the blade, consisting of a set of beam elements of variable cross-section, was developed, the calculation was carried out taking into account the geometric nonlinearity of the structure behavior and the analysis of the obtained results. To describe the response of materials to external influences, an elastically deformable isotropic body model is used with assignment of the appropriate elastic constants of the material. Analysis of calculation results includes determination of reactions at attachment points, values of maximum displacements of structural elements and stresses in weak sections. Diagrams of internal force factors (axial and shear forces and bending moment) along the blade span are plotted. With the help of these diagrams weak sections are determined and values of axial force and bending moment in these sections are calculated. Axial force reaches its maximum value Nx = 333689 N in the section along the axis of rib № 1. In this section, the bending moment reaches a maximum value of Mymax = 3078.3 N×m. At cross section r = 0.73 between axes of ribs No. 13 and No. 14, where shear force equals to zero, value of bending moment My = -1147,5 N×m. Thus, regular part of the blade is in combined stressed state - bending with tension. Static strength of the blade has been estimated using safety factor. To estimate a static strength equivalent von Mises stresses were considered as the maximum stresses. Safety factor of static strength of regular part of the blade in the weak section was 1,7. To estimate fatigue strength, distribution of the first principal stresses in the load-carrying elements was analyzed in terms of typical stress concentrators. The maximum level of the principal stresses in the considered sections was s1 = 138 MPa, which indicates that the blade material operates in the range of high cycle fatigue.

Under vertical load, the composite foundation may be damaged due to insufficient lateral restraint capacity. If the lateral restraint pile is added to the edge of the composite foundation, the lateral stability can be effectively enhanced. This new reinforcement scheme is called a combined composite foundation. For the combined composite foundation, the lateral restraint piles will bear a certain force when the composite foundation is loaded, and the force may cause the piles horizontal displacement, instability, or even failure. After preload on the composite foundation, the mechanical behavior of lateral restraint piles will be more sophisticated. To study the mechanical behavior of lateral restraint piles under such condition, a laboratory model test was conducted. The results are suggested as follows: Axial force distribution curves tend to be “S” shape with two peak values at the upper and lower parts, respectively. The negative axial force is distributed at the upper part, and the positive axial force is distributed at the lower part. The bending moment and lateral soil pressure distribution of piles appear with the regularity of “increase-decrease” along the depth. Such a phenomenon is associated with the expansion of a potential slip surface. In accordance with the relative location of the potential slide surface and the piles, the lateral restraint piles can fall into three sections. Different sections get different stresses. The reinforcement scopes have an impact on the stress of different lateral restraint piles. With the increase of the reinforcement scope, the axial force, soil pressure, and bending moment show the regularity of increase. The values of axial force, the lateral soil pressure, and the bending moment increase with load growth and become stable when the load is larger than 60 kN. This is associated with the piles in the composite foundation, which verifies the reinforcement effect to prevent the soil slide and the foundation deformation.

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

Undercarriages of railway wagons, are frames in horizontal planes, subjected to axial forces of very high magnitude and of impulsive nature during shunting operations. With the help of the assumptions used in beam bending theory, the stiffness matrix is developed, with six degrees-of-freedom for each joint. When an axial load of comparable amount is applied at buffers, the stiffness function is no longer a linear function of axial load. The axial force in a member may be either tension or compression, but the latter is usually of greater interest because of the possibility of buckling. The modified stiffness matrix for a general beam element is generated in terms of stiffness method is applied. In the second cycle, the axial forces in members, as obtained from the first cycle, are used to determine the modified stiffness matrix. The second cycle is then completed, using modified stiffness and fixed-end actions, and new values of axial forces are obtained. The processes repeated until two successive analysis yield approximately the same result.

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important to know the natural frequencies of the coupled beam—mass system for a proper design of the structural elements. There is plenty of literature regarding the free vibration analysis of Bernoulli—Euler single-span beams carrying a number of spring—mass system and Bernoulli—Euler multi-span beams carrying multiple spring—mass systems, but less is available regarding Reddy—Bickford multi-span beam carrying multiple spring—mass systems with/without axial force effect. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of Reddy—Bickford beams. The model allows the influence of the shear effect and spring—mass systems on the dynamic behavior of the beams to be analyzed by using Reddy—Bickford beam theory. The effects of the attached spring—mass systems on the free vibration characteristics of one to four span beams are studied. The calculated natural frequencies of Reddy—Bickford and Timoshenko multi-span beams using a secant method for nontrivial solution of the different values of axial force are given. The mode shapes of Reddy—Bickford multi-span beams are also presented.

Multiple-step beams carrying intermediate lumped masses with/without rotary inertias are widely used in engineering applications, but in the literature for free vibration analysis of such structural systems; Bernoulli-Euler Beam Theory (BEBT) without axial force effect is used. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass systems, Bernoulli-Euler multiple-step and multi-span beams carrying multiple spring-mass systems and multiple point masses are plenty, but that of Timoshenko multiple-step beams carrying intermediate lumped masses and/or rotary inertias with axial force effect is fewer. The purpose of this paper is to utilize Numerical Assembly Technique (NAT) and Differential Transform Method (DTM) to determine the exact natural frequencies and mode shapes of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and/or rotary inertias. The model allows analyzing the influence of the shear and axial force effects, intermediate lumped masses and rotary inertias on the free vibration analysis of the multiple-step beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate lumped mass with rotary inertia, the step change in cross-section, left-end support and right-end support of the multiple-step Timoshenko beam are derived from the analytical solution. After the derivation of the coefficient matrices, NAT is used to establish the overall coefficient matrix for the whole vibrating system. Finally, equating the overall coefficient matrix to zero one determines the natural frequencies of the vibrating system and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equations of the motion. The calculated natural frequencies of Timoshenko multiple-step beam carrying intermediate lumped masses and/or rotary inertias for the different values of axial force are given in tables. The first five mode shapes are presented in graphs. The effects of axial force, intermediate lumped masses and rotary inertias on the free vibration analysis of Timoshenko multiple-step beam are investigated.

The determination of stress intensity factors (SIF) and crack opening area or displacements (COA or COD) is important constituent when performing the “leak before break” analysis of piping systems in NPPs. The tabulated parametrical results of their calculation are widely presented in modern scientific and normative literature. Nevertheless, there is one aspect of crack behavior, at least in thin walled pipes, which still had not obtained its due attention. We mean here the geometrically nonlinear effect, which can be the big enough to be accounted for in practical applications. It is considered in geometrically linear analysis that only the inner pressure opens the crack, and COA and SIF are directly proportional to it. SIF is presented usually as solution for infinite plate multiplied by so-called bulging factor, BF, which depends on dimensionless crack length, i.e. ratio of crack length divided on square root of product of radius, R, and wall thickness, t. Two loading factors in thin walled pipes can contribute to geometrically nonlinear behavior. The first one is axial stresses induced by value of axial force or bending moment. The second one – is the inner pressure itself. The most attention in present paper is given to influence of the axial force. With this goal the numerical models were created for pipes with different ratios of R/t (20, 30, 40, 50) and different dimensionless crack length (2, 4, 6, 8). To exclude the nonlinearity due to circumferential stress the inner pressure is kept as a very small value and dimensionless SIF and COD values are calculated with respect to axial force. To prove the correctness of choosing the finite element types, meshing, number of elements along the thickness, loading steps the auxiliary problem of nonlinear modeling of transverse beam loaded additionally by very big axial force is considered. The very good correspondence was attained. For the pipe with axial crack the careful verification of numerical model was performed by comparison with linear results existing in literature. The results obtained are presented as a percentage of difference between the linear and nonlinear results. They show that influence of geometrical nonlinearity is fairly essential to be accounted in practice and can reach for practically real cases almost 3–10%. The change of SIF in percentages due to geometrical nonlinearity for different axial stress levels and for different crack lengths can be fairly well presented as unique dependence from product of stresses, radius to thickness ratio, and square root of dimensionless crack length. The change COD in central point of crack is slightly bigger than for SIF and the same unique dependence can be formulated for COD with only exception for small cracks λ < 3.

In many centrifugal pump designs, the axial force is balanced by special balancing devices. Long cylindrical and short face throttles are the main constructive elements of such devices. The hydrodynamic characteristics of the cylindrical and face throttles depend on their geometry and operating parameters of the pump. The pressure distribution in the cylindrical throttle determines the pressure in the chamber of the automatic balancing device, the value of which affects the pressure distribution in the face throttle and the value of the resulting axial force. Since an automatic balancing device can be one of the most failure-prone components of centrifugal pumps, improving computational methods and designing such hydraulic units is still a significant problem. The Computational Fluid Dynamics method (Ansys CFX) is used to calculate the hydrodynamic characteristics of the traditional construction of the automatic balancing device. The pressure and velocity distributions are obtained. The value of axial force is calculated in a traditional balancing device. Some recommendations are given.

Wood–plastic composites (WPCs) increase the range of applications of materials by creating new material solutions. As part of this research, PLA (polylactic acid)- and HDPE (high-density polyethylene)-based composites were manufactured. Softwood sawdust or conifer bark with different sizes (large and small) were used as filler. In selected cases, the addition of 3% additives, such as calcium oxide in the case of PLA or polyethylene-graft-maleic anhydride in the case of HDPE, were tested. The manufactured composites were examined for their density profile and their susceptibility to drilling, defined by the value of the axial force occurring during drilling. The obtained results revealed that the type of matrix had the greatest influence on the axial forces during drilling. Regardless of the composite formulation, composites based on PLA had 25% to 56% higher axial forces during drilling than those based on HDPE. Furthermore, increasing the proportion of lignocellulosic fillers resulted in a decrease in the value of axial forces during drilling, with PLA composites experiencing a greater decrease than HDPE composites. The type and size of the filler had a minor impact on the axial force values during drilling. The statistical analysis indicated that the additives had a greater influence on HDPE than on PLA.

This work focuses on determining the causes of axial shrinkage of heat-shrinkable pipes made of cross-linked polyethylene at the expansion stage of their production process and the ways to eliminate this problem. For this purpose, thermomechanical behavior of products made of polymer materials with shape memory was numerically simulated. First, an appropriate physical model was selected in the ANSYS package to describe the thermomechanical behavior of polymer materials with shape memory, an experimental program was developed and implemented to identify the material constants of cross-linked polyethylene, and several verification tests were performed. Then, a simplified numerical simulation of the thermomechanical behavior of the heat-shrinkable tube was performed using the ANSYS software package, which does not take into account the movement of the work piece through the expander cavity. To eliminate longitudinal shrinkage, it is proposed to preserve the longitudinal size of the work piece by applying an axial force of a certain value. The axial force values corresponding to a longitudinal shrinkage not exceeding 1% and a 15% longitudinal shrinkage were found. It was established that the longitudinal shrinkage is caused by the extremely high axial force. The last section of the article presents a numerical simulation of the real technological stage of expansion of a heat-shrinkable tube. The values of the axial force acting in the work piece are calculated when the feed and extraction speeds of the work piece from the expander are equal to ensure the constancy of its length in the first case and when the initial elongation reaches 15% in the second case. The calculated data confirm the initial assumption about the causes of longitudinal shrinkage.

This paper presents the results of research on improving the efficiency of the mechanical agglomeration through describing the influence of the shape of the piston pressure face on the limit force value. The focus of this study is the geometrical parameters which are describing the shape of the piston pressure face. Where these parameters influence on the value of the limit stress in the process of mechanical agglomeration of crystallized carbon dioxide. The first part of the paper proposes a model describing the influence of the geometric parameters of the piston pressure face on the value of axial force during the subsequent compression phase of the process. The research part of the paper presents the empirical research results to verify the proposed model. The results of the work will be used to determine the influence of the described geometrical parameters of the dry ice residue on the axial force value. The derived mathematical model will be used for defining the design requirements as the starting point for the design and building of dry ice compression and granulation machines.

EFFECTS OF CENTRIFUGAL STIFFENING ON THE VIBRATION FREQUENCIES OF A CONSTRAINED FLEXIBLE ARM