Internal Damping Research Articles

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

AbstractThis paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated.

Polynomial Stability of the Laminated Beam with One Discontinuous Local Internal Fractional Damping

Polynomial Stability of the Laminated Beam with One Discontinuous Local Internal Fractional Damping

DLC-Coated Thermoplastics: Tribological Analyses under Lubricated Rolling-Sliding Conditions

The goal of this work is to evaluate the potential of diamond-like carbon (DLC) coatings on thermoplastic polymers for friction and wear reduction in highly stressed rolling–sliding contacts. Therefore, hydrogen-containing DLC coatings were deposited on the polymer surface by a low-temperature high power pulsed magnetron sputtering (HPPMS) physical vapor deposition (PVD) process. The rolling-sliding contact between coated polyamide 66 (PA66) or coated polyether ether ketone (PEEK) against case-hardened steel 16MnCr5 is investigated in a twin-disk tribometer at normal loads up to FN = 1,000 N, sum velocities between 1 m/s ≤ vΣ ≤ 16 m/s and slip ratios up to s = 50%. Results show a friction reduction with the application of DLC on the considered polymers compared to uncoated polymers under specific lubrication conditions. High solid losses caused by the polymer’s internal damping properties dominate the temperature behavior of the polymer, even when coated with DLC. Regarding the wear behavior, DLC coatings show potential especially under severe mixed lubrication conditions with high-solid load portion and sliding. The knowledge gained about coated polymers can be used to improve the overall tribological performance in terms of friction and wear of thermoplastic machine elements like gears.

Stabilization of the laminated beams by internal and boundary dampings

Stabilization of the laminated beams by internal and boundary dampings

Dynamics of a non-linear Jeffcott rotor in supercritical regime

This work is concerned with the prediction and simulation of limit cycles of a nonlinear Jeffcott rotor. Geometrical nonlinearity (related to large flexural displacements) in both stiffness and internal damping is considered. Classical instabilities due to linear internal damping occurring in the supercritical range are modified by nonlinear effects and lead to oscillating limit cycles at a radius whose value is found analytically as a function of the rotating speed. If the rotor is additionally excited by unbalance, the response spectrum also contains the excitation frequency, and the bifurcation leads to quasi-periodic limit cycles. The dynamics of this system is studied numerically via the harmonic balance method, path continuation and bifurcation tracking. In particular, an original procedure for switching to a branch of quasi-periodic solutions is proposed. To preserve the integrity of the machine post bifurcation, one then considers the possibility of constraining the transverse displacement of the shaft. Such possible rotor–stator interaction generates three-frequency quasi-periodic oscillations. Frequency response curves show that the quasi-periodic solutions created by the bouncing rotor are mainly driven by the friction coefficient.

Experimental and simulation investigation of vertical response of stepped torsion bar spring for light motor vehicle suspension system

The straight torsion bar spring is widely used in automobile and military tankers suspension systems due to less occupation of space and high weight bearing capacity. In this present work, the vertical response of Stepped Torsion Bar Spring (STBS) in Light Motor Vehicle (LMV) suspension is investigated. The STBS consists of two segments in series. The segment-1 is larger diameter when compared to that of segment-2. Three cases of diameter ratio and length ratios combination of STBS are experimented and simulated. A 2-DOF (Degree of Freedom) quarter car model test rig is designed for the experimental work. A harmonic excitation is given as road input though a Cam. The damped and undamped vertical response and frequencies of STBS are experimented. The vertical response and its spectrum analysis are plotted and better responses of the low stiffness STBS is identified for comfort ride and the results are compared with MATLAB Simulink results. The results of the suspension parameters such as tire stiffness, damping coefficient of shock absorber, stiffness of STBS, internal damping of STBS and torsional to linear stiffness are investigated.

Application of vibration diagnostics methods in the creating of elements of personal electric transport

The study of vibration loading of the main elements of personal electric vehicles and the search for ways to reduce vibration characteristics was conducted. The issues of measuring vibration arising on a bicycle, which is driven by human muscle power and an electric drive, are considered. Measurements of vibration acceleration and frequency spectra in a certain area of motion were carried out using the “Octave-101VM” spectrum analyzer in three stages. At the first stage, the electric bike was driven by a pedal drive, at the second – by an electric drive, at the third – the pedals and the electric drive worked in parallel. As a result of the tests carried out, it was found that the greatest vibration occurred in the “Motor” mode during the use of an electric bicycle, the least vibration occurred when driving with the electric motor turned off. It was found that the electric drive increases the vibration level (at the same time, the electric bike does not exceed the maximum permissible values of vibration levels on all axes). In order to reduce the vibration arising from the electric motor on a personal electric vehicle, a 3D computer model has been developed and an airless wheel mover has been manufactured using this model on a 3D printer (a wheel for an electric scooter with internal damping has been manufactured). Bench tests have shown that the developed wheel, in comparison with a pneumatic tire, has a smaller (up to 45 %) contact spot. The results obtained can be used in the development of competitive products, in particular personal electric vehicles.

Conditional Disturbance Negation Based Control for an Omnidirectional Mobile Robot: An Energy Perspective

Disturbances widely exist in all control systems. Disturbance observers are commonly employed to estimate the disturbances which are often fully compensated in the control signal. However, one rarely recognized fact is that disturbances may be beneficial to the control performances and thus can be effectively exploited. In this letter, from an energy balance point, a conditional disturbance negation (CDN) control scheme is designed for an omnidirectional mobile robot, yielding a physically interpretable design. By energy analysis, the forces imposed on the robot are classified into workless force, internal damping force, and lumped disturbance force, wherein the later two are effectively exploited. A judgment function is designed to determine whether the disturbance is beneficial to the control performance, allowing the controller to selectively compensate the estimated disturbances. Convergence of the proposed control system is analyzed. Finally, both simulations and experimental results show that the proposed control scheme can achieve better performance against conventional full disturbance compensation control scheme, if the disturbances contain beneficial parts.

Existence and Stability of Solutions for a Nonlinear Beam Equation with Internal Damping

This manuscript deals with the global existence and asymptotic behavior of solutions for a Kirchhoff beam equation with internal damping. The existence of solutions is obtained by using the Faedo-Galerkin method. Exponential stability is proved by applying Nakao’s theorem.

СONTROL OF A NONLOCAL IN TIME FINITE ELEMENT MODEL OF THE DYNAMIC BEHAVIOR OF A COMPOSITE BEAM BASED ON THE RESULTS OF A NUMERICAL EXPERIMENT

The article presents numerical methods for controlling the parameters of temporal nonlocality of computer models of rod structures made of composite materials. The finite element method is the most widely used numerical method for solving practical problems of the analysis of mechanical systems. A nonlocal in time internal damping model is integrated into the algorithm of this method. The one-dimensional model of the Euler-Bernoulli beam is presented in the article. The equilibrium equation of a moving mechanical system is solved numerically using an implicit scheme. In the article the damping matrix obtained from the condition of stationarity of the total deformation energy was used. The article presents the study of non-local in time damping model properties. The model is integrated into the finite element method. The non-local model is algorithmized and programmed in the MATLAB software package.

Free and steady-state forced vibrations of a base-excited nonuniform cantilever Timoshenko beam with internal damping

Free and steady-state forced vibrations of a base-excited nonuniform cantilever Timoshenko beam with internal damping

Parametrically excited axially accelerating viscoelastic beam subjected to time-varying axial speed, longitudinally varying axial tension and internal resonance

The present work investigates the nonlinear characteristics of an axially moving viscoelastic beam of the Kelvin–Voigt model on a pulley mounting system. The equation of motion is developed by including the terms like external and internal damping, geometric cubic nonlinearity, Coriolis, time-dependent axial speed, and longitudinally varying axial tension. The direct perturbation method of multiple time scales (MMS) is adopted to get an approximate solution for the nonlinear integro-partial differential equation of motion which leads to a set of complex variable modulation equations. These modulated equations are solved numerically to study the trivial state stability plot considering the effect of the support stiffness parameter for the first time. In addition to this, the impact of material, and viscous damping parameters on stability boundary is also studied. Continuation algorithm is implemented to analyse the influence of the support stiffness parameter, internal and parametric detuning parameters, fluctuating velocity component, and longitudinal stiffness parameter on the stability and bifurcation of the steady state solutions. Variation in internal frequency detuning parameter and variable axial speed component reveals different kinds of equilibrium solution curves in the nonlinear travelling system. The stability and bifurcation features observed in the present nonlinear system with change in the above control parameters are interesting and also not available in the existing literature.

Influence of the Experimental Setup on the Damping Properties of SLM Lattice Structures

BackgroundMetal lattice structures obtained through Selective Laser Melting may increase the strength-to-weight ratio of advanced 3D printed parts, as well as their damping properties. Recent experimental results showed that AlSi10Mg and AISI 316L lattices are characterized by higher Rayleigh damping coefficients with respect to the fully dense material. However, some unclear or contradictory results were found, depending on the experimental setup adopted for modal analysis.ObjectiveIn this work the influence of the experimental setup when performing modal analysis on different SLM AISI 316L lattice structures was deeply investigated. The study provides a critical comparison of various experimental modal analysis approaches, allowing to evaluate the influence of external damping sources and material internal damping phenomena.MethodsThe dynamic behaviour of SLM AISI 316L specimens incorporating lattice structures was estimated by means of pulse testing and sinusoidal excitation through an electromagnetic shaker. The validity of the viscous damping model was assessed by means of sinusoidal excitation with different levels of vibration velocity. Moreover, the influence of experimental setup on modal analysis results was critically evaluated, by considering different actuators, contact and non-contact sensors and boundary/clamping conditions.ResultsThe classical viscous damping model describes with good approximation the damping properties of SLM lattice structures. When exciting single specimens in free-free conditions, those embedding lattice structure and unmelted metal powder filler were characterized by superior internal damping properties with respect to the specimens incorporating the lattice structure without any filler, which was however more effective than the full density equivalent material. Most of the other experimental setups introduced additional external damping sources, that could alter this important outcome.ConclusionsSLM lattice structures embedded into 3D printed components provide superior damping properties against mechanical and acoustic vibrations and the metal powder filler does significantly enhance such damping capacity. A correct estimation of material internal damping was achieved by applying non-contact sensors and free-free boundary conditions, whereas other experimental setups were partly inadequate.

Theoretical and experimental research of two-chamber pneumatic suspension with air damping

A mathematical model of a two-chamber air suspension with internal air damping is described, and the results of theoretical and experimental studies of the vibration-protective properties of a two-chamber air suspension with internal air damping are presented. Keywords: pneumatic suspension, air damper, internal air throttling, air spring, pressure, chamber, volume, sprung mass, resonance. nvv_60@mail.ru

Hygro-thermo-viscoelastic wave propagation analysis of FGM nanoshells via nonlocal strain gradient fractional time–space theory

Viscoelastic behaviors of nanosize waveguides cannot be determined via simple versions of nonlocal theories if the wavelength is close to the characteristic length of the nanostructure. In such cases, a coupling between small scale and internal damping must be considered. This study is arranged to capture this important issue to provide reliable data about wave propagation responses of viscoelastic functionally graded material (FGM) nanoshells subjected to hygro-thermal loading for the first time. To do so, a tempo-spatially coupled nonlocal strain gradient viscoelasticity framework is introduced for nanoshells located in a hygro-thermally stimulated environment. First-order shear deformation theory (FSDT) is utilized and mixed with Hamilton’s principle to formulate the problem for thin and moderately thick nanoshells. In the context of an analytical solution, the phase velocity of the dispersed waves is calculated. The provided data reveals that conventional size-dependent theories estimate faster damping trends for the phase velocity rather than fractional time–space theory. Also, it is demonstrated that the precision of the previously published data about viscoelastic behaviors of waves scattered in nanostructures is low in small ranges of a nonlocal parameter. This finding is attributed to the coupling between nonlocal and internal damping parameters which was not included in previous studies.

An ALE formulation for the geometric nonlinear dynamic analysis of planar curved beams subjected to moving loads

This paper presents an arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for the geometric nonlinear dynamic analysis of planar curved viscoelastic beams subjected to moving loads. In the ALE description, the beam nodes can be moved in arbitrarily specified ways to describe the moving loads’ material positions accurately. The pure deformation and the deformation rate of the element are measured in a curvilinear coordinate system fixed on a curved reference configuration that follows the rotation and translation of a corotational frame. Based on Hamilton’s principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. Then, a standard element can be embedded within the element-independent framework. An accurate two-node curved element and the Kelvin-Voigt model are introduced in this framework to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational efficiency, and versatility of the presented formulation. The effect of internal damping, external damping, the inertia force of a moving mass, and the moment of inertia of the mass on the dynamic response of the beam are investigated. Moreover, the driving force for a prescribed motion of a mass along the beam is investigated.

Numerical study on stability of composite cutter bar milling system in rotating coordinate frame

This paper studies the chatter stability of composite cutter bar milling system in rotating coordinate frame. The main contribution of this paper is establishing a continuous distributed chatter analysis model for a composite cutter bar milling system in rotating coordinate frame. The stability of the milling system with a rotary symmetric dynamic cutter bar is predicted using the semi-discrete time domain method. The effects such as internal damping, external damping, and symmetrical and asymmetric laminates on the stability of the milling system were analysed, and the results were compared between rotating and fixed coordinate frames. The results are consistent for symmetrical cutter bars in both the rotating and fixed coordinate frames. A new chatter instability zone appears at high rotating speeds due to the material internal damping of the rotating composite cutter bar.

Analysis of Cutting Stability of a Composite Variable-Section Boring Bar with a Large Length-to-Diameter Ratio Considering Internal Damping.

Chattering in composite deep-hole boring can directly affect surface processing quality and efficiency and has always been a research hotspot in machining mechanics. In this study, based on Euler–Bernoulli beam theory, the fine control equations for the cutting stability of composite variable-section boring bars were established using the Hamilton principle, in which the sectional change and internal damping of the material were considered. Next, using the Galerkin method and semi-discrete method, the effects of the taper ratio, damping ratio, length-to-diameter ratio, and ply angle on the free vibration characteristics and cutting stability were analyzed in detail. The results show that at a low damping ratio, both the first-order inherent frequency and boring stability can be enhanced with the increase in the taper ratio; at a large damping ratio, increasing the taper ratio can reduce the first-order inherent frequency and boring stability. Finally, the effects of the sectional change on the inherent frequency, displacement response, and convergence were analyzed. A numerical simulation was performed for the model reliability validation. The present research results can provide a theoretical basis and technical guidance for analyzing the cutting stability and fine control of composite variable-section boring bars with large length-to-diameter ratios.

Stability analysis of a spinning soft-core sandwich beam with CNTs reinforced metal matrix nanocomposite skins subjected to residual stress

The stability of a soft-cored spinning viscoelastic sandwich beam and carbon nanotubes (CNTs) reinforced metal matrix nanocomposites (MMNCs) skin subjected to residual stress have been investigated. The metal matrix nanocomposites (MMNCs) skins are symmetrical and isotropic. In addition, these skins reinforced with uniform and functionally graded (FG) distributions of carbon nanotubes (CNTs) are considered. The soft-core of the sandwich beam is deemed to be elastomeric and has internal damping of viscoelastic type. The skin layers of the sandwich beam are subject to residual stresses caused by the production process. Also, the effective material properties of skins are obtained using the rule of mixture (ROM) and Halpin-Tsai (H-T) micromechanics models. First, the governing equations of motion of a spinning viscoelastic sandwich beam are obtained using the Hamilton principle. Then, the sandwich beam's natural frequencies are calculated using the differential quadrature method (DQM). The effects of CNTs distribution, nanotube volume fraction, spinning speed, critical loading, the thickness of the core, axial force, and residual stress on the sandwich beam's natural frequency and stability regions are investigated. According to the results of this study, based on the sandwich beam's different spinning speeds, it is possible to estimate the optimal amount of core thickness to prevent instability, which can be very important in the design of spinning sandwich structures.

Singular perturbation and initial layer for the abstract Moore-Gibson-Thompson equation

We investigate the singular limit of a third-order abstract equation in time, in relation to the complete second-order Cauchy problem on Banach spaces, where the principal operator is the generator of a strongly continuous cosine family. Assuming that an initial datum is ill prepared, the initial layer problem is studied. We show convergence, which is uniform on compact sets that stay away from zero, as long as initial data are sufficiently smooth. Our method employs suitable results from the theory of general resolvent families of operators. The abstract formulation of the third-order in time equation is inspired by the Moore-Gibson-Thompson equation, which is the linearization of a model that currently finds applications in the propagation of ultrasound waves, displacement of certain viscoelastic materials, flexible structural systems that possess internal damping and the theory of thermoelasticity.