Internal Damping Research Articles

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.

An exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping

This paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of Kelvin–Voigt viscoelastic dampers. Typical external and internal dampers are considered, as grounded translational, tuned mass, rotational and axial dampers, for bending and axial vibrations, respectively. Using the theory of generalised functions within a 1D formulation of equations of motion, exact closed-form expressions are derived for beam dynamic Green’s functions and frequency response functions under arbitrary polynomial load, for any number of dampers. For a plane frame, exact global frequency response matrix and load vector are built, with size depending only on the number of beam-to-column nodes, for any number of dampers and point/polynomial loads along the frame members. From the nodal displacement solution, the exact frequency response in all frame members is also obtained in closed analytical form. Numerical applications show many of the advantages of the proposed method.

An Investigation of Internal Viscous Damping Effects on the Vibration of a Microbeam Made of Functionally Graded Materials

In this paper, effect of the internal viscous damping on the frequency shift and damping ratios of a microbeam made of functionally graded materials is investigated for different boundary conditions. To achieve this goal the FGM microbeam is modeled by an Euler-Bernoulli beam and utilizing Hamilton principle the governing partial differential equation of motion and corresponding boundary conditions are obtained. Applying mode summation method, the governing ordinary differential Eq. is derived from the PDE. Solving the ODE analytically, frequency shift ratio of the FGM microbeam is evaluated for different boundary conditions. Results are presented in terms of material damping coefficient. The effects of design parameters such as boundary conditions, geometrical parameters, distribution function and viscous damping coefficient on the frequency shift and damping ratios are assessed.

The interior working mechanism and temperature characteristics of a fluid based micro-vibration isolator

Micro-vibration isolation is a hot topic in spacecraft vibration control, and fluid based vibration isolators alternatively provide a good and reliable solution to this challenging issue. In this paper, a novel fluid based micro-vibration isolator (FBMVI) is investigated. According to its inherent working principle and deformation pattern, the generation mechanisms of the damping and stiffness characteristics are derived, which are nonlinear functions of the environmental temperature. Then a lumped parameter model which is expressed by the physical design parameters (PDPs) is constructed, and the corresponding performance objective indices (POIs) are also obtained by applying the equivalence of mechanical impedance. Based on the finite element analysis of the internal damping component, a single variable method is further adopted to carry out the parametric study, and the influences of each PDP on the POIs are analyzed in details. Finally, experiments are conducted to identify the variation of fluid bulk modulus with the outside environmental temperature, and to validate the performance of the isolator under different temperature environments. The tested results show great consistence compared with the predicted tendencies of the parametric study. The results of this study can provide a very useful insight into and/or an important guidance for the design and application of this type of FBMVIs in engineering practice.

Fluctuation-dissipation theorem and 1/f noise of bulk acoustic wave cavities

The short time stability in quartz crystal ultra-stable oscillators is limited by some intrinsic frequency fluctuations with a 1/f power spectral density. The physical origin of this 1/f noise is still unknown. In this paper, the fluctuation dissipation theorem is used to numerically evaluate the importance of the contribution of internal damping of thickness fluctuations on the level of noise for bulk acoustic wave cavities. A 1/f contribution to the power spectral density of frequency noise for the shear mode usually used is obtained. Its study provides a possible explanation for the fact that, for the best resonators, the 1/f noise amplitude is usually disconnected from the quality factor measured at resonance.

Influence of Homogenization Annealing on Internal Damping Depending on the Vibration Amplitude Measured on Specimens AZ31 and AZ91

Damping capacity of alloys is closely tied to the presence of defects including solute atoms, second phases and voids. The interaction between moving dislocations and point defects is one of the major internal damping mechanisms of magnesium alloys so the precipitates influence the damping capacity and contribute to damping properties. The article is focused on the analysis of the internal damping changes depending on the amplitude of the magnesium alloys AZ31 and AZ91 in as cast state and after homogenization annealing. In experimental measurements only resonance method was used. This method is based on continuous excitation of oscillations of the specimen and the entire apparatus vibrates at a frequency which is near to the resonance. Starting resonance frequency for all measurements was about f = 20500 Hz.

Investigation of hysteresis friction in elements under complex stress state

Recent studies have indicated that the best type of damping in vibration isolation system is hysteresis (internal) damping, which effectively reduces vibration amplitudes at resonance, and it does not increase as compared with viscous damping vibration amplitudes after the resonance. Modern damping investigation methods are based on the experimental determination of the loss factor for a certain form of vibration isolators with fixed dimensions and loading parameters. At the same time, with the emergence of complex nonlinear vibration isolators, such as discussed by the authors, there is a task of expanding this theory on the case of complex designed vibration isolators. In this paper, we consider the problem of calculating the loss factor in the beam—columns of variable cross-section under complex loading conditions. A method for calculating the amount of losses in the nonlinear vibration isolators is based on Panovko's energy theory, which consists of experimental loss factor determination in the materi...

Mass Detection in Viscous Fluid Utilizing Vibrating Micro- and Nanomechanical Mass Sensors under Applied Axial Tensile Force.

Vibrating micro- and nanomechanical mass sensors are capable of quantitatively determining attached mass from only the first three (two) measured cantilever (suspended) resonant frequencies. However, in aqueous solutions that are relevant to most biological systems, the mass determination is challenging because the quality factor (Q-factor) due to fluid damping decreases and, as a result, usually just the fundamental resonant frequencies can be correctly identified. Moreover, for higher modes the resonance coupling, noise, and internal damping have been proven to strongly affect the measured resonances and, correspondingly, the accuracy of estimated masses. In this work, a technique capable of determining the mass for the cantilever and also the position of nanobeads attached on the vibrating micro-/nanomechanical beam under intentionally applied axial tensile force from the measured fundamental flexural resonant frequencies is proposed. The axial force can be created and controlled through an external electrostatic or magnetostatic field. Practicality of the proposed technique is confirmed on the suspended multi-walled carbon nanotube and the rectangular silicon cantilever-based mass sensors. We show that typically achievable force resolution has a negligibly small impact on the accuracy of mass measurement.

Energy management through topology optimization of composites microstructure using projected gradient method

In this paper the projected gradient method is applied as an effective gradient-based topology optimization algorithm in order to direct energy propagation through the desired region of composites microstructure. Rayleigh Damping model is also used in order to take the effect of internal damping mechanisms into account and thus, to fill in the gap between the designed layouts and those in reality. The success of the proposed algorithm is illustrated through several numerical experiments by revealing a set of various designed optimal layouts besides their corresponding energy distributions.

On nonlinear wave equations of Carrier type

This paper is concerned with the initial-boundary value problem of the n-dimensional Carrier equation with an internal damping. This damping is a fractional power of the velocity of the points of the material. The Faedo–Galerkin method, Tartar approach and compactness arguments provide the global existence of solutions of the above problem with restriction on the size of the initial data. The decay of solutions is obtained by the perturbation method.

Damped vibration of the system of changing the crane boom radius

This study formulates and solves the problem of transverse damped vibration in the system of changing the boom radius in a truck crane with advanced cylinder design for controlling the boom radius. The dissipation of vibration energy in the model adopted in the study occurs as a result of internal damping of the viscoelastic material (rheological Kelvin-Voigt model) of the beams that model the system and movement resistance in the supports of the cylinder and crane boom to the bodywork frame of the crane. Damped frequencies of vibrations and degree of vibration amplitude decay were calculated. The study also presents eigenvalues of system vibration with respect to changes in damping coefficients and system geometry for a selected load.

The nematode C. elegans as a complex viscoelastic fluid.

The viscoelastic material properties of the model organism C. elegans were probed with a micropipette deflection technique and modelled with the standard linear solid model. Dynamic relaxation measurements were performed on the millimetric nematode to investigate its viscous characteristics in detail. We show that the internal properties of C. elegans can not be fully described by a simple Newtonian fluid. Instead, a power-law fluid model was implemented and shown to be in excellent agreement with experimental results. The nematode exhibits shear thinning properties and its complex fluid characteristics were quantified. The bending-rate dependence of the internal damping coefficient of C. elegans could affect its gait modulation in different external environments.

Realistic and stable animation of cloth

AbstractResearchers have proposed various techniques for cloth simulation in the last decades. The crucial problem in interactive animation for cloth is how to speed up simulation with a stable system. In this paper, we describe a realistic and stable scheme for cloth simulation based on mass‐spring system. This scheme modifies semi‐implicit integration used in cloth simulation system with an efficient damping method. Semi‐implicit integration methods have been widely used in dynamic simulation because of acceptable speed and stability. However, internal damping forces are generated with respect to rotational rigid motions, which are only depending on relative velocities. Undesirable change in global movement of dynamic cloth could result in damping artifact. We replace the internal damping forces with an optimal damping method which is based on iterative spring damping but the limit can be computed directly. The method provides simple damping parameter estimation and guarantees conservation of global movement. As a result, complex clothes can be realistically and stably simulated in real time. Copyright © 2015 John Wiley & Sons, Ltd.

Investigation of two different friction models from the perspective of friction-induced vibrations

In this paper, we investigate different friction models by examining the dynamic responses of a single-degree-of-freedom system exhibiting friction-induced vibration. Specifically, we examine models developed by Dankowicz [1] and our recent model [2,41], which is developed by modifying the well-known LuGre model. We perform linear stability analysis to obtain the stability boundary corresponding to the Hopf bifurcation point. Numerically obtained bifurcation diagrams show the bifurcation to be subcritical in nature. A detailed parametric study is carried out to understand the influence of different friction parameters on the system responses and the friction force–relative velocity relations. An internal damping term is included for the first time in this paper and its influence on the dynamics of the system is investigated.

Falling vertical chain of oscillators, including collisions, damping, and pretensioning

A chain of point masses connected by linear springs and sometimes dashpots is considered. The chain hangs in a vertical equilibrium configuration, held by its top mass. Then the top mass is released, and the chain falls. Internal damping, modeled by the dashpots, causes the bottom mass to move faster. As the system falls, upper masses sometimes accelerate faster than gravitational acceleration, and collisions may occur between adjacent masses. The types of collisions treated here include elastic, inelastic, and perfectly inelastic (in which colliding masses often stick together thereafter). The unstretched lengths of the springs, and a compressive force caused by pretensioning, may significantly affect the characteristics of the motion. Analytical and numerical results are presented for cases involving a few masses, and some generalizations are made for systems with an arbitrary number of masses. Also, the vertical chain may be used to model the motion of a falling Slinky after release at its top end. The bottom of the continuous Slinky does not move until the coils above it have collapsed onto it, and the collapse time is estimated here using the discrete chain model. For a metal Slinky with 86 masses, the estimated time is close to that previously obtained by a continuous elastic analysis.

Exponential stabilization of a viscoelastic wave equation with dynamic boundary conditions

In this paper, we study the stabilization of a semi-linear viscoelastic wave equation subject to semi-linear and dynamical boundary conditions. The kernels used are of strongly positive definite type. We prove that internal and boundary memory damping are strong enough, via transmission process (\({u|_{\Gamma} = v}\)), to stabilize the whole system.

Quaternion Variational Integrators for Spacecraft Dynamics

A general method for deriving variational integrators for systems with quaternion state variables is introduced. These integrators exhibit realistic energy and momentum behavior while having computational costs comparable to or less than low-order Runge–Kutta methods, making them suitable for both simulation and real-time estimation and control applications. Integrators are derived for several systems, including rigid bodies with momentum actuators and internal viscous damping. Numerical examples illustrate the performance of the integrators and an application to attitude determination using an extended Kalman filter is presented.

Combining vibrational linear-by-part dynamics and kinetic-based decoupling of the dynamics for multiple elastoplastic smooth impacts

This article proposes a linear-by-part approach for elastoplastic 3D multiple-point smooth impacts in multibody systems with perfect constraints. The model is an extension of a previous version, restricted to the perfectly elastic case, able to account for the high sensitivity to initial conditions and for redundancy without assuming any particular collision sequence (Barjau et al., Multibody Syst. Dyn. 31:497–517, 2014). Energy losses associated with compression and expansion in percussive analysis is a matter as complex as the physical phenomena involved, at the nanoscale level, for different materials. Simplified models can be developed for specific purposes, which can retain the most relevant trends of internal damping and at the same time be suitable for a particular analytical approach of impact mechanics. In the context of this article, energy dissipation due to material deformation is introduced through a linear-by-part elastoplastic model consisting on two elementary sets of springs and dry-friction dampers. The first set accounts for inelastic behavior (energy loss without permanent indentation), whereas the second one introduces plasticity (that is, permanent indentation). In inelastic and plastic collisions, instantaneous unilateral constraints may appear, thus reducing the number of degrees of freedom (DOF) of the system. The calculation of the corresponding normal contact force at the constrained points is then necessary in order to detect whether the constraint holds or disappears (either because a new compression or an expansion phase starts, or because contact is lost). Different simulated application examples are presented and thoroughly discussed.

Exponential stabilization of magnetoelastic waves in a Mindlin–Timoshenko plate by localized internal damping

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047–1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin–Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function \({{{\mathbf{p}}}({\mathbf{x}},{\mathbf{U}}_t)}\), that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin–Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

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.