Internal Material Damping Research Articles

NONLOCAL IN TIME MODEL OF MATERIAL DAMPING IN COMPOSITE STRUCTURAL ELEMENTS DYNAMIC ANALYSIS

In this paper the problem of numerical simulation of composite bending elements dynamic considering internal (material) damping. For this purpose the nonlocal in time damping model, called damping with memory, is proposed as an alternative to the classic local Kelvin-Voigt model. Damping with memory makes damping forces not only dependent on the instant value of the strain rate, but also on the previous history of the vibration process. Since finite element analysis is the most common method of structural analysis, the nonlocal damping model is integrated into FEA algorithm. The FEA dynamic equilibrium equation is solved using the explicit scheme. The damping matrix was developed using the stationary full energy requirement. One-dimensional nonlocal in time model was implemented in MATLAB software package. The results of three-dimensional numerical simulation of the composite beam vibration obtained in SIMULIA Abaqus were used for model calibration. The obtained results were compared to the results based on classic Kelvin-Voight damping model.

Nonlinear Damping and Forced Response of Laminated Composite Cylindrical Shells with Inherent Material Damping

In this paper, the nonlinear damping and forced response behaviors of laminated composite cylindrical shells considering the internal damping of composite materials are investigated. Based on Donnell nonlinear shell theory, the dynamic governing equations of composite cylindrical shells with geometrical nonlinearity are established by using the Hamilton principle, in which the inherent material damping is taken into account by complex modulus method. The dependence of nonlinear damping on vibration amplitude and amplitude–frequency response are analytically obtained by the Galerkin method in conjunction with harmonic balance method. By comparing the results of natural frequency and modal damping with those in the literature, the correctness of the above theoretical analysis is verified. Furthermore, the effects of the circumferential wave number, lamination schemes, vibration amplitude and geometric configuration on the nonlinear damping and forced responses of the composite cylindrical shell with unidirectional, angle-ply and cross-ply laminations are analyzed. The results show that the damping dissipation capacity of the composite cylindrical shell is amplitude-dependent, and the effect of the amplitude on the nonlinear damping characteristics gradually decreases with the increase of the length-to-radius ratio. The ply angle not only affects the value of the resonance peak, but also significantly changes the degree of the soft and hard spring characteristics of the composite cylindrical shell. With the increase of internal material damping, the amplitude-frequency curve of the composite cylindrical shell changes from the coexistence of hard and soft characteristics to the only soft characteristics.

Relationship between internal viscous damping and stiffness of concrete material and structure

AbstractThis study focuses on the relationship between the internal viscous damping and the stiffness of concrete material and structure having small deformation amplitude. New damping parameters were proposed to describe the energy dissipation capacity and the vibration–amplitude attenuation rate. An improved damping suspension test method for predicting the essential material parameters, elasticity modulus and loss modulus, was developed and validated. The results show that the viscous damping energy dissipation capacity of concrete material and structure having small deformation amplitude is proportional to the product of the loss factor and the stiffness, and the vibration‐amplitude attenuation rate is proportional to the product of the damping ratio and the natural frequency. The variation in dimensionless damping mainly results from the change in the stiffness of concrete material and structure. The porosity shows the smallest elasticity modulus and the largest energy dissipation capacity of nano‐phase in cement paste under constant loading conditions. The improved damping suspension test method is proposed based on theoretical analysis and is validated using an experiment and finite element analysis.

Piezoelectric Disc Transformer Modeling Utilizing Extended Hamilton's Principle

Piezoelectric transformers (PTs) are resonant electromechanical voltage conversion devices used in a variety of applications including voltage boosting and galvanic isolation. They offer advantages over electromagnetic voltage transformers, including high energy density as well as the potential for monolithic fabrication, making them well suited to small-scale microelectromechanical applications. Among various PT topologies, circular discs lend themselves to microfabrication, and are considered here. In order to gain fundamental understanding of disc PT dynamics, this work applies the extended Hamilton's principle of variational calculus to the piezoelectric electric enthalpy, using cylindrical coordinates, in order to derive electromechanical constitutive equations for bulk disc transformers. The use of the Hamilton approach in this work supports the integration of mechanical tethers that physically support the disc, allowing the model to be applied to device designs that are compatible with monolithic microfabrication from sheets of bulk piezoelectric material. Using the integrated model, voltage gain (output voltage/input voltage) is predicted as a function of multiple variables including electrode area ratio, device size, tether stiffness, internal material damping, and output load impedance, and is compared against finite element numerical and experimental prototype results for verification. Prototype 4-mm diameter tethered disc PTs on the order of 0.002 cm3, two orders smaller than the bulk PT literature, were fabricated to validate the proposed model, and had peak voltage gains over 2.

Damped vibrations of the Γ type frame with open cracks

This paper discusses the formulation and solution for the problem of damped transverse vibrations of the Γ type frame with open cracks. Dissipation of vibration energy in the frame results from the movement constraint in the column and bolt support (constructional damping) and internal damping of viscoelastic material of the frame (rheological model by Kelvin-Voigt). Presence of a crack impacts local flexibility that has an effect on frame vibration response. The boundary problem for the above system was formulated based on the Hamilton’s principle and solved numerically for the complex eigenvalues ω*. The effect of the crack depth and its location on damped vibration was presented. The effect of both types of damping on the degree of amplitude decay was also presented.

Stability analysis of internally damped rotating composite shafts using a finite element formulation

This paper deals with the stability analysis of internally damped rotating composite shafts. An Euler–Bernoulli shaft finite element formulation based on Equivalent Single Layer Theory (ESLT), including the hysteretic internal damping of composite material and transverse shear effects, is introduced and then used to evaluate the influence of various parameters: stacking sequences, fiber orientations and bearing properties on natural frequencies, critical speeds, and instability thresholds. The obtained results are compared with those available in the literature using different theories. The agreement in the obtained results show that the developed Euler–Bernoulli finite element based on ESLT including hysteretic internal damping and shear transverse effects can be effectively used for the stability analysis of internally damped rotating composite shafts. Furthermore, the results revealed that rotor stability is sensitive to the laminate parameters and to the properties of the bearings.

Damped Vibrations of Hydraulic Cylinder with a Spring-damper System in Supports

The description of the damped vibrations of hydraulic cylinder has been presented in this paper. The dissipation of vibration energy was caused by different kinds of damping on vibrations of hydraulic cylinder. Damping in adopted model is a result, of taken into account internal damping of viscoelastic material of beams that modelled the system, external viscous damping and constructional damping of supports. In this paper, the problem of transverse and longitudinal damped vibration of hydraulic cylinder was formulated and solved. The influence on the damped vibration frequency and the degree of vibration amplitude decay of damping coefficient and spring rigidity coefficient were presented.

Dynamic study of viscoelastic rotor: Reduction of higher order model using different techniques

Finite element formulation of general viscoelastic rotor reaches a higher order configuration due to the inherent material properties, resulting in a complicated system. The interest of this paper is the application of suitable reduction technique, which helps to rewrite the system equations with important coordinates. In order to understand the best methodology to reduce the higher order model, two different reduction techniques have been used: (i) Iterative Improved Reduction System, (ii) Balanced Realization System. In first case, an iterative algorithm is used to improve the transformation matrix by achieving convergence. Whereas, in second case, Hankel Singular Value Decomposition assures to predict the most controllable and observable states, which helps to reduce the system matrices accurately. The benefit of implementing these techniques is to tackle the problems caused due to skew-symmetric matrices that emanate for an addition of internal material damping and gyroscopic effects. The effectiveness of reduced model is well examined using various dynamic parameters. The agreement between reduced and original system predict the usefulness of this study.

Influence of electromagnetic field damping on forced vibrations of induction rotors caused by dynamic rotor eccentricity

The paper shows an analytical rotordynamic model for induction rotors, supported in sleeve bearings, especially focusing on the influence of electromagnetic field damping on the forced rotor vibrations. The analytical model contains electromagnetic forces in respect of electromagnetic field damping, stiffness and internal material damping of the rotor, typical dynamic eccentricities of an induction rotor – mass eccentricity, bent rotor deflection and magnetic eccentricity –, stiffness and damping of the support, and stiffness and damping of the oil film of the sleeve bearings. With this rotordynamic model a useful possibility is shown, how to consider electromagnetic field damping, when analyzing forced vibrations caused by dynamic eccentricities. The aim of the paper is to show a method – based on a simple rotor dynamic model – how to consider electromagnetic field damping, which can also be adopted in Finite‐Element‐Analysis.

Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method

Parametric instability problem of a rotating shaft subjected to a periodically varying axial force has been studied by using a numerical simulation method—discrete singular convolution. External viscous damping and internal material damping (Voigt–Kelvin model) have been considered. Parametric instability regions have been presented to illustrate the influence of spinning speed and damping. Numerical results reveal that for rotating shafts with no damping, parametric instability regions under different spinning speeds are ‘V’ shapes, and do not vary obviously with spinning speed increasing. While, for rotating shafts with damping, parametric instability regions are enlarged significantly as spinning speed increases. It may be considered that spinning speed has a great effect on parametric instability of rotating shafts with damping, but little influence on that of rotating shafts with no damping. Moreover, the increase of damping results in reduction of parametric instability regions, which is helpful to improve dynamic stability of systems. And it is also found that effects of internal material damping and external viscous damping on parametric instability regions are similar. Compared to the results by using theoretical methods of Floquet and Bolotin, it is observed that the numerical results support Floquet’s method, disagree with Bolotin’s method for parametrically excited rotating shafts. In consideration of Bolotin’s method leading to enlargement of instability regions, it is strongly recommended that Bolotin’s should not be applied to parametric instability analysis of rotating systems.

Asymptotic Periodicity for Flexible Structural Systems and Applications

We study the existence of pseudo S$S$-asymptotically ?$\omega$-periodic mild solutions for an abstract version of the damped wave equation u?+?u?=βΔu+?Δu?+f$u''+\alpha u'''=\beta\Delta u +\gamma\Delta u'+f$ which model the vibrations of flexible structures possessing internal material damping and external force f$f$. We show concrete applications of our methods to flexible structures, heat conduction, fractional equations and viscoelasticity.

Damping effect on supersonic panel flutter of composite plate with viscoelastic mid-layer

The panel flutter of composite plate with viscoelastic mid-layer in supersonic airflow is investigated in this study. The hysteric damping model is used to describe the viscoelastic property of the mid-layer material and the first piston theory to model the aerodynamic forces. Hamilton’s principle is employed to derive the partial differential equations governing the vibrations of the laminated composite plate. By Galerkin method the governing partial differential equations are truncated into a set of ordinary differential equations. The critical dynamic pressure for panel flutter has been studied by considering the eigenvalue problem of the set of ODEs. It was concluded that the introduction of aerodynamic damping postpones the threshold of flutter, while the viscoelastic damping of the soft mid-layer presents a phenomenon of dual effect. When the viscoelastic damping value is low, the internal material damping shows detrimental effect to the flutter depression. If the viscoelastic damping is increased further, the flutter resistance of the composite plate will be enhanced. The convergence of the Galerkin method is also discussed in this study. The influences of some parameters to the convergence have been investigated in details.

Lp‐boundedness and topological structure of solutions for flexible structural systems

This work deals with Lp‐boundedness of mild solutions for an abstract version of the damped wave equation u′′+αu′′′=βΔu + γΔu′+f that models the vibrations of flexible structures possessing internal material damping and external force f. We prove that the set consisting of mild solutions for this problem is compact and connected in the space of continuous functions. This property is known in the literature as the Kneser's property. Copyright © 2015 John Wiley & Sons, Ltd.

A BEM–FEM using layered half-space Green׳s function in time domain for SSI analyses

This paper presents a numerical method based on a three dimensional boundary element-finite element coupled formulation in the time domain. The proposed model allows studying soil–structure interaction problems. The soil is modelled with the boundary element method, where the radiation condition is implicitly satisfied in the fundamental solution. Layered half-space Green׳s function including internal material damping is considered as the fundamental solution because of the influence of soil stratification on soil–structure interaction problems is large. This fundamental solution is computed from the exact expressions for the response in the underlying half-space and from a modal solution for the layers. The finite element method is used to represent the structure. In this paper the proposed method is validated by comparison with analytical and numerical results, and an experimental study is done. Afterwards, the dynamic behaviour of a building subjected to an incident wave field is studied.

Modelling and analysis of damped vibration in hydraulic cylinder

The study presents a formulation on the basis of Hamilton’s principle and solution for the problem of damped vibration in hydraulic cylinders. The physical model took into consideration the energy dissipation in a vibrating cylinder as a result of external viscous damping and internal damping of viscoelastic material in beams used to construct a model of a cylinder (rheological model by Kelvin–Voigt). Constructional damping in the points of the cylinder connection with the components of the basic structure was also considered. The example computation was made for a cylinder used in a mining prop. The results of the computations concern the determination of the relationships between the first eigenvalue of transverse vibration in the cylinder and its extension length with two values of load and determination of the amplitude decay factor for the first and the second eigenvalue versus the extension length. Furthermore, the study also focused on determination of the relationships between the amplitude decay factor of the first and second mode of vibration for a particular length of the cylinder.

Rotordynamic analysis of asymmetric turbofan rotor due to fan blade-loss event with contact-impact rub loads

Loss of a blade from a running turbofan rotor introduces not only huge imbalance into the dynamical system rather it makes the entire rotor asymmetric as well. In a nonsymmetric rotor, the various terms of mass, gyroscopic and stiffness matrices also become time-dependent. In this paper, all the dynamical equations include the effect of the rotary inertia and gyroscopic moments as a result of both shaft bending as well as staggered blades flexing in-and-out of the plane of the disk. The governing equations also account for internal material damping in the shaft and the external damping in the support bearing system. In addition to the unbalance load at the disk location, the shaft may also be subjected to a torque and axial forces. Here, the fan blades are modeled as pre-twisted thin shallow shells. They have coupled flexural–torsional motion in the lateral out-of-plane direction as well as extensional degrees-of-freedom in the longitudinal spanwise direction of the blade airfoil. The effect of blade tip rub forces being transmitted to the shaft are analyzed in terms of the dynamic stability of the rotor, especially during windmilling.

ENERGY DECAY RATES FOR THE KELVIN-VOIGT TYPE WAVE EQUATION WITH ACOUSTIC BOUNDARY

In this paper, we study uniform exponential stabilization of the vibrations of the Kelvin-Voigt type wave equation with acoustic boundary in a bounded domain in <TEX>$R^n$</TEX>. To stabilize the systems, we incorporate separately, the internal material damping in the model as like Gannesh C. Gorain [1]. Energy decay rates are obtained by the exponential stability of solutions by using multiplier technique.

Computational Tradeoff in Modal Characteristics of Complex Rotor Systems Using FEM

Modal analysis of complex rotor-bearing systems using the finite element method (FEM) may become controversial when considering the tradeoff between geometric complexity and elastodynamic integrity of the FEM model. In this paper, the modal characteristics of an actual multi-impeller rotor-bearing system with complicated geometry are estimated and verified using two modeling schemes. The first scheme invokes a developed finite element elastodynamic model that accounts for gyroscopic effects, torsional-bending inertia coupling, internal material damping, shear and anisotropic bearings. In this model, the intricate details of the impeller were ignored, and only the inertial properties of the impeller disk are considered. The second scheme employs a general-purpose finite element code, wherein the complicated impeller geometry is included in lieu of ignoring some of the rotational effects and inertia coupling effects. The obtained results shed the light on the tradeoffs involved in modal analysis of complicated rotor systems using the FEM. Comparisons with experimental values showed that the first scheme, which adopts simplified impeller geometry while accounting for all the rotational effects is more accurate in estimating the modal characteristics of such complex rotor-bearing systems.

Existence of asymptotically almost automorphic solutions for a third order differential equation

This paper deals with results on existence of asymptotically almost automorphic solutions for a third order in time abstract differential equation which model, on one side, high intensity ultrasound in acoustic wave propagation, while on the other side, vibrations of flexible structures possessing internal material damping. We established the asymptotically almost automorphy of the output solution subject to the asymptotically almost automorphy of the input distur- bance.

Modal analysis of rotor-shaft system under the influence of rotor-shaft material damping and fluid film forces

The present work attempts to study the influences of internal rotor material damping and the fluid film forces (generated as a result of hydrodynamic action in journal bearings) on the modal behaviour of a flexible rotor-shaft system. This is relevant as both journal bearing and the internal material damping introduce tangential forces increasing with the rotor spin speed. Such forces considerably influence the dynamic behaviour of a rotor and tend to destabilize the rotor-shaft system as spin speed increases. Under this system of forces the modal behaviour of the rotor-shaft is studied to get better ideas about the dynamic behaviour of the system, estimated in terms of modal damping factors, stability limit speed, the frequency response functions, as well as the direction of whirl of the shaft in different modes. It is seen that correct estimation of internal friction, in general, and the journal bearing coefficients at the rotor spin-speed are essential to accurately predict the rotor dynamic behaviour. This serves as a first step to get an idea about dynamic rotor stress and, as a result, a dynamic design of rotors.