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This study aims to analyse slender thin-walled anisotropic box-beams. Fiber-reinforced laminated composites could play an important role in the design of current and future generations of innovative civil aircrafts and unconventional unmanned configurations. The tailoring characteristics of these composites not only improve the structural performance, and thus reduce the structural weight, but also allow possible material couplings to be made. Static and dynamic aeroelastic stability can be altered by these couplings. It is, therefore, necessary to use an accurate and computationally efficient beam model during the preliminary design phase.

A proper structural beam scheme, which is a modification of a previous first-level approximation scheme, has been adopted. The effect of local laminate stiffness has been investigated to check the possibility of extending the analytical approximation to different structural configurations. The equivalent stiffness has been evaluated for both the case of an isotropic configuration and for simple thin-walled laminated or stiffened sections by introducing classical thin-walled assumptions and the classical beam theory for an equivalent system. Coupling effects have also been included. The equivalent analytical and finite element beam behaviour has been determined and compared to validate the considered analytical stiffness relations that are useful in the preliminary design phase.

The work has analyzed different configurations and highlighted the effect of flexural/torsion couplings and a local stiffness effect on the global behaviour of the structure. Three types of configurations have been considered, namely, a composite wing box configuration, with and without coupling effects; a wing box configuration with sandwich and cellular constructions; and a wing box with stiffened panels in a coupled or an uncoupled configuration. An advanced aluminium experimental test sample has also been described in detail. Good agreement has been found between the theoretical and numerical analyses and the experimental tests, thus confirming the validity of the analytical relations.

The equivalent beam behaviour that has been determined and the stiffness calculation procedure that has been derived could be useful for future dynamic and aeroelastic analyses.

The article presents an original derivation of the sectional characteristics of a thin-walled composite beam and a numerical/experimental validation.

The purpose of this paper is to present a methodology for the determination of the stiffness when using simplified substitutive model of the joint. The usage of detailed finite element (FE) model of the joint in complex assemblies is not convenient; therefore, the substitutive model of the joint is used in FE models.

The detailed and simplified FE model of the joint is created in ABAQUS software and the analysis as well. The results of displacements are used for the determination of the stiffness of connecting element in simplified substitutive FE model. The approach is presented based on the general view on the different regions in the joint.

A simple FE modelling approach for the joint including the equivalent stiffness is presented. The particular solution is performed for Magna-Lok type of the rivet. The results show the same displacement for the detailed and simplified FE models. The analytical formula for stiffness determination in the load case with minimal secondary bending is introduced.

The approach for stiffness determination is straightforward and so no stiffness “tuning” is necessary in the simplified FE model.

The new approach for definition of simple FE model of the joint is introduced. It is not necessary to model a complex structure with detailed joints. The equivalent stiffness can be determined by presented procedure for every joint without limitation of the type.

This paper aims to understand the vibration characteristics of full ceramic ball bearings under grease lubrication, reduce the vibration of the bearings and improve their service life.

The Hertz contact stiffness formula for full ceramic ball bearings is constructed; the equivalent comprehensive stiffness calculation model and vibration model of full ceramic ball bearings are established. The dynamic characteristic test of full ceramic ball bearing under grease lubrication was carried out by using the bearing life testing machine, and its vibration was measured, and its vibration acceleration root-mean-square was obtained by software calculation and compared with the simulation results.

At the rotational speed of 12,000 r/min, the root-mean-square value of vibration acceleration is maximum 10.82 m/s², and the error is also maximum 7.49%. As the rotational speed increases, the oil film stiffness decreases. In the radial load of 600 N, the vibration acceleration root-mean-square is minimum 6.40 m/s², but its error is maximum 6.56%. As the radial load increases, the vibration of the bearing decreases and then increases, so under certain conditions increasing the radial load can reduce the bearing vibration. With different types of grease, the best preload is also different; low-speed heavy load should be used when the viscosity of the grease is large, and high-speed light load should be used when the choice of smaller viscosity grease is made.

It provides a theoretical basis for the application of full ceramic ball bearings under grease lubrication, which is of great significance for reducing the vibration of bearings as well as enhancing the service life of bearings.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0094/

The purpose of this paper is to investigate the effects of misalignment on the static and dynamics characteristics of bump-type foil bearings (BFBs). High-speed and high-temperature oil-free turbomachinery can be realized with the use of gas foil bearings (GFBs). GFBs have a flexible supporting structure; thus, they can tolerate a higher degree of misalignment compared with rolling element bearings.

A test rig for GFBs has been developed to measure the effects of misalignment on the structure characteristics of bump-type foil bearings. The link-spring model, which is the foil structure model presented previously by the authors, is used as a basis in the present study to predict the static and dynamic performances of the foil structure. In general, predictions of the dynamic characteristics exhibit good agreement with the measurements acquired from the dynamic load tests.

Results from the static tests show that GFBs develop high stiffness when the misalignment angle increases. Moreover, the dynamic characteristics of GFBs are identified by considering the test bearing supported by a non-rotating shaft as a one-degree-of-freedom system. The results indicate that the dynamic characteristics of GFBs strongly depend on excitation frequency and excitation amplitude because of the variation in the dynamic friction force within the foil structure. The structural stiffness and equivalent viscous damping increase with an increase in the misalignment angle.

The present study focuses on the misalignment of GFBs and investigates experimentally the effects of misalignment on the structure characteristics of GFBs.

Ultrasonic additive manufacturing (UAM) is a solid-state joining technology used for three-dimensional printing of metal foilstock. The electrical power input to the ultrasonic welder is a key driver of part quality in UAM, but under the same process parameters, it can vary widely for different build geometries and material combinations because of mechanical compliance in the system. This study aims to model the relationship between UAM weld power and system compliance considering the workpiece (geometry and materials) and the fixture on which the build is fabricated.

Linear elastic finite element modeling and experimental modal analysis are used to characterize the system’s mechanical compliance, and linear system dynamics theory is used to understand the relationship between weld power and compliance. In-situ measurements of the weld power are presented for various build stiffnesses to compare model predictions with experiments.

Weld power in UAM is found to be largely determined by the mechanical compliance of the build and insensitive to foil material strength.

This is the first research paper to develop a predictive model relating UAM weld power and the mechanical compliance of the build over a range of foil combinations. This model is used to develop a tool to determine the process settings required to achieve a consistent weld power in builds with different stiffnesses.

Based on the character of R‐C frame, the calculation formula of VED is derived from the sub‐structure plan of lateral resistant force, the definition of equivalent stiffness matrix and equivalent additional viscoelastic force vector of VED is given and the seismic dynamic equation of R‐C frame controlled by VED is set up, the viscoelastic additional force vector of VED should be considered as outside load of structure and be calculated through the pseudo‐loading method, the programs of calculating the dynamic characteristic, calculating the elastic seismic response and calculating the elastic‐plastic seismic response of R‐C frame controlled by VED are compiled. Through the calculation of a inclined crossed R‐C frame, the results show that VED is effective in controlling the seismic response of frame and the pseudo‐loading method is reliable in the calculation.

The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author develops the equations for transverse vibrations of the axially loaded helical springs. The method is based on the concept of an equivalent column. Second, the author reveals the effect of axial load on the fundamental frequency of transverse vibrations and derive the explicit formulas for this frequency. The fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring. The reduction of frequency with the load is demonstrated. Finally, when the frequency nullifies, the side buckling spring occurs.

Helical springs constitute an integral part of many mechanical systems. A coil spring is a special form of spatially curved column. The center of each cross-section is located on a helix. The helix is a curve that winds around with a constant slope of the surface of a cylinder. An exact stability analysis based on the theory of spatially curved bars is complicated and difficult for further applications. Hence, in most engineering applications a concept of an equivalent column is introduced. The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The transverse vibration is represented by a differential equation of fourth order in place and second order in time. The solution of the undamped model equation could be obtained by separation of variables. The fundamental natural frequency of the transverse vibrations depends on the current length of the spring. Natural frequency is the function of the deflection and slenderness ratio. Is the fundamental natural frequency of transverse oscillations nullifies, the lateral buckling of the spring with the natural form occurs. The mode shape corresponds to the buckling of the spring with moment-free, simply supported ends. The mode corresponds to the buckling of the spring with clamped ends. The author finds the critical spring compression.

Buckling refers to the loss of stability up to the sudden and violent failure of seed straight bars or beams under the action of pressure forces, whose line of action is the column axis. The known results for the buckling of axially overloaded coil springs were found using the static stability criterion. The author uses an alternative approach method for studying the stability of the spring. This method is based on dynamic equations. In this paper, the author derives the equations for transverse vibrations of the pressure-loaded coil springs. The fundamental natural frequency of the transverse vibrations of the column is proved to be the certain function of the axial force, as well as the variable length of the spring. Is the fundamental natural frequency of transverse oscillations turns to be to zero, is the lateral buckling of the spring occurs.

The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The more accurate model is based on the equations of motion of loaded helical Timoshenko beams. The dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain) is to be derived. Unfortunately, that for the spatial beam models only numerical results could be obtained.

The closed form analytical formulas for fundamental natural frequency of the transverse vibrations of the column as function of the axial force, as well as the variable length of the spring are derived. The practically important formulas for lateral buckling of the spring are obtained.

In this paper, the author derives the new equations for transverse vibrations of the pressure-loaded coil springs. The author demonstrates that the fundamental natural frequency of the transverse vibrations of the column is the function of the axial force. For study of the stability of the spring the author uses an alternative approach method. This method is based on dynamic equations. The new, original expressions for lateral buckling of the spring are also obtained.

A newly developed frequency-independent lumped parameter model (LPM) is the purpose of the present paper. This new model’s direct outcome ensures high efficiency and a straightforward calculation of foundations’ vertical vibrations. A rigid circular foundation shape resting on a nonhomogeneous half-space subjected to a vertical time-harmonic excitation is considered.

A simple model representing the soil–foundation system consists of a single degree of freedom (SDOF) system incorporating a lumped mass linked to a frequency-independent spring and dashpot. Besides that, an additional fictitious mass is incorporated into the SDOF system. Several numerical methods and mathematical techniques are used to identify each SDOF’s parameter: (1) the vertical component of the static and dynamic foundation impedance function is calculated. This dynamic interaction problem is solved by using a formulation combining the boundary element method and the thin layer method, which allows the simulation of any complex nonhomogeneous half-space configuration. After, one determines the static stiffness’s expression of the circular foundation resting on a nonhomogeneous half-space. (2) The system’s parameters (dashpot coefficient and fictitious mass) are calculated at the resonance frequency; and (3) using a curve fitting technique, the general formulas of the frequency-independent dashpot coefficients and additional fictitious mass are established.

Comparisons with other results from a rigorous formulation were made to verify the developed model’s accuracy; these are exceptional cases of the more general problems that can be addressed (problems like shallow or embedded foundations of arbitrary shape, other vibration modes, etc.).

In this new LPM, the impedance functions will no longer be needed. The engineer only needs a limited number of input parameters (geometrical and mechanical characteristics of the foundation and the soil). Moreover, a simple calculator is required (i.e. we do not need any sophisticated software).

This paper aims at developing a mechanical-based model for predicting the thermally induced axial forces and rotation of steel top and seat angles connections with and without web angles subjected to elevated temperatures due to fire. Finite element (FE) simulations and experimental results are used to develop the mechanical model.

The model incorporates the overall connection and column-beam rotation of key component elements, and includes nonlinear behavior of bolts and base materials at elevated temperatures and some major geometric parameters that impact the behavior of such connections when exposed to fire. This includes load ratio, beam length, angle thickness, and gap distance. The mechanical model consists of multi-linear and nonlinear springs that predict each component stiffness, strength, and rotation.

The capability of the FE model to predict the strength of top and seat angles under fire loading was validated against full scale tests. Moreover, failure modes, temperature at failure, maximum compressive axial force, maximum rotation, and effect of web angles were all determined in the parametric study. Finally, the proposed mechanical model was validated against experimental results available in the literature and FE simulations developed as a part of this study.

The proposed model provides important insights into fire-induced axial forces and rotations and their implications on the design of steel bolted top and seat angle connections. The originality of the proposed mechanical model is that it requires low computational effort and can be used in more advanced modelling applications for fire analysis and design.

This study examines two distinct bearing stiffness calculation methods, both of which are based on the displacement-load function. Previous research typically incorporated one type of bearing stiffness into their system mechanics or vibration analysis. However, these two methods of calculating stiffness lead to different vibration models. This implies that the choice for vibration investigation is not merely about selecting one of the two types of stiffness, but also about how to appropriately implement that chosen stiffness within a model. The primary objective of this work is to compare these two methods of bearing calculation and to discuss the suitable applications of each method in both static and dynamic analyses.

This study compares two distinct methods for calculating bearing stiffness. It explores the relationships between varying bearing stiffnesses, their internal structures, and contact features. Furthermore, it examines the impact of external loads on the static properties and dynamic characteristics of different bearing stiffnesses. Finally, based on the outcomes observed under various operating conditions, the study discusses the suitability of each method for static and dynamic analysis.

Mean stiffness is more suitable for calculating load transmissibility in a static state or capturing the delivery performance at instantaneous equilibrium positions in a dynamic state. Since the variation of the equilibrium positions is ignored, the alternating stiffness model is better suited for capturing the fluctuating properties of the vibration behaviors, especially under variable external load conditions.

We compare the two bearing calculation methods and discuss the appropriate applications of each method for static and dynamic analysis.