Internal Damping Research Articles

Defect detection by laser shear interferometry based on the thermal response of materials with vibratory loading

Laser shear interferometry or shearography is one of the optical and non-contact methods for measuring surface displacements. Shearography can be used in non-destructive testing by applying a kind of excitation such as partial vacuum, mechanical and thermal loadings. Parameters of the excitation techniques significantly affect the test results. In many cases, these loading methods deform the whole surface reducing the detection capability of the technique. This paper considers the vibratory loading method as an alternative to the previously mentioned standard methods. In this method, local heat is generated at the defected area due to the internal and external damping of the piece. A simulation has been conducted using COMSOL software to estimate the generated local heat due to the vibratory loading. The local temperature at the defect area is measured, and the simulation results are validated with an experimental infrared thermography test. The experimental shearography setup is adjusted, and the defects are detected. By comparing the results with those of typical thermal loadings, it has been shown that the fringe patterns obtained by the presented method have higher quality.

Parametric studies on SEA parameters for coupled plates made of composite laminate

Statistical Energy Analysis (SEA) has been used to compute velocity responses and Coupling Loss Factors (CLF) for two composite laminates joined in a 'L' junction configuration. Two case studies were carried on SEA. The effect of fibre orientation on SEA parameters was studied. The effects of internal damping were also determined. The computation of SEA parameters has been done using classical wave approach and Finite Element Method using Nastran/Patran. CLF determined using classical wave approach is independent of fibre orientation and internal damping factor. This study using FEM reveals that the SEA parameters vary in comparison with classical wave approach as fibre orientation and internal damping are also considered in the analysis. Also, by classical wave approach, the CLF varied linearly with the increase in frequency while there was some scatter in CLF determined by finite element method.

Passive walking biped robot model with flexible viscoelastic legs

To simulate the complex human walking motion accurately, a suitable biped model has to be proposed that can significantly translate the compliance of biological structures. In this way, the simplest passive walking model is often used as a standard benchmark for making the bipedal locomotion so natural and energy efficient. This paper is devoted to a presentation of the application of internal damping mechanism to the mathematical description of the simplest passive walking model with flexible legs. This feature can be taken into account by using the viscoelastic legs, which are constituted by the Kelvin–Voigt rheological model. Then, the update of the impulsive hybrid nonlinear dynamics of the simplest passive walker is obtained based on the Euler–Bernoulli’s beam theory and using a combination of Lagrange mechanics and the assumed mode method, along with the precise boundary conditions. The main goal of this study is to develop a numerical procedure based on the new definition of the step function for enforcing the biped start walking from stable condition and walking continuously. In our previous work, it was shown that the period-one gait cycle can be produced by adding the proportional damping model with high damping ratio to the elastic legs. The present paper overcomes the practical limitations of this damping model and similarly demonstrates the stable period-one gait cycles for the viscoelastic legs. The study of the influence of various system parameters is carried out through bifurcation diagrams, highlighting the region of stable period-one gait cycles. Numerical simulations clearly prove that the overall effect of viscoelastic leg on the passive walking is efficient enough from the viewpoint of stability and energy dissipation.

Assessment of the Quality Losses of Cantaloupe Fruit during Transportation

Fruit quality is a crucial factor in affecting shelf-life and purchase choice for customers. Protecting the quality of cantaloupe fruits in the chain from harvest to marketing is a very important process. The objective of this study was to investigate the dynamic characteristics of cantaloupe fruit during excitation, to investigate the effect of vibration strength on the mechanical characteristics of cantaloupe fruit, and to show the effects of this strength on the mechanical damage of cantaloupe. Experiments were performed to measure the dynamic behavior of cantaloupe fruit during transportation and to evaluate the dynamic behavior of the packaging and the damage to the cantaloupes due to transient vibration during transportation. The results show that using the paper pulp tray packing method reduces cantaloupe damage and improves their quality during harvest and post-harvest processes. The range of resonance frequencies is important for the transporting of cantaloupes; a higher starting resonance is an indication of a stiffer cantaloupe bottom, and the paper pulp tray shifts the resonance frequency when compared to volume packing methods. Another interesting observation in this study is that a fruit with a high internal damping capacity is not as injured by exciting vibrations as a fruit with a low damping capacity, even if its natural frequency falls within the range of excitation.

Hydrodynamic characteristics and application of tuned liquid dampers with internal damping devices

SummaryThe hydrodynamic characteristics of rectangular tanks with internal damping devices, including baffles and paddles, are investigated using shaking table tests excited by colored noise. The complex second‐order blind identification method is employed to decouple fluid sloshing responses and to obtain mode shapes. The modal frequency and damping ratio are also identified by the modified Bayesian spectral density approach. The influence of baffle angle, paddle width, liquid depth, and excitation amplitude on the natural frequency and damping ratio of tuned liquid dampers (TLDs) is analyzed. Results show that the natural frequency is reduced due to the added mass produced by the damping devices, and the reduction increases gradually with the increase in the size of the damping devices, indicating that the influence of the added mass should be considered in the design. This result is essentially different from the conclusion of the existing finding that the modal frequency of TLD increases continuously with the increase in the baffle angle. Therefore, the tuning of TLD cannot be realized by rotating the baffles. Moreover, the damping ratio of TLD with paddles shows a nonlinear relationship with the fluid response. The nonlinear empirical model fitted by the test results can predict the damping ratio with high accuracy and can be used in the preliminary design of TLD for the wind‐induced vibration control of super‐tall buildings.

Polynomial decay of a internal nonlinear damping structurally acoustic models with variable coefficients

In this paper we derive an energy decay estimate of the wave equation with variable coefficients and acoustic boundary condition in a bounded domain under some certain conditions. Our system includes a nonlinear internal damping term, under some checkable conditions on the coefficients, the polynomial decay rate is obtained by the compactness-uniqueness theorem and the Riemannian geometry method.

Active Disturbance Rejection Control of Euler-Lagrange Systems Exploiting Internal Damping.

Active disturbance rejection control (ADRC) is an efficient control technique to accommodate both internal uncertainties and external disturbances. In the typical ADRC framework, however, the design philosophy is to "force" the system dynamics into a double-integral form by an extended state observer (ESO) and then the controller is designed. Especially, the systems' physical structure has been neglected in such a design paradigm. In this article, a new ADRC framework is proposed by incorporating at a fundamental level the physical structure of the Euler-Lagrange (EL) systems. In particular, the differential feedback gain can be selected considerably small or even 0, due to the effective exploitation of the system's internal damping. The design principle stems from an analysis of the energy balance of EL systems, yielding a physically interpretable design. Moreover, the exploitation of the system's internal damping is thoroughly discussed, which is of practical significance for applications of the proposed design. Besides, a sliding-mode ESO is designed to improve the estimation performance over traditional linear ESO. Finally, the proposed control framework is illustrated through tracking control of an omnidirectional mobile robot. Extensive experimental tests are conducted to verify the proposed design as well as the discussions.

Dynamics of a Non-Ideal Gyroscopic Rotor System with Translational-Rotational Coupling Effect of External and Internal Damping

Dynamics of a Non-Ideal Gyroscopic Rotor System with Translational-Rotational Coupling Effect of External and Internal Damping

Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix

We present two novel results for small damped oscillations described by the vector differential equation Mx¨+Cx˙+Kx=0, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. The first result is a novel formula for the solution X of the Lyapunov equation ATX+XA=−I, where A=A(v) is obtained from M,C(v)∈Rn×n, and K∈Rn×n, which are the so-called mass, damping, and stiffness matrices, respectively, and rank(M)=n−1. Here, C(v) is positive semidefinite with rank(C(v))=1. Using the obtained formula, we propose a very efficient way to compute the optimal damping matrix. The second result was obtained for a different structure, where we assume that dim(N(M))≥1 and internal damping exists (usually a small percentage of the critical damping). For this structure, we introduce a novel linearization, i.e., a novel construction of the matrix A in the Lyapunov equation ATX+XA=−I, and a novel optimization process. The proposed optimization process computes the optimal damping C(v) that minimizes a function v↦trace(ZX) (where Z is a chosen symmetric positive semidefinite matrix) using the approximation function g(v)=cv+av+bv, for the trace function f(v)≐trace(ZX(v)). Both results are illustrated with several corresponding numerical examples.

Coupled bending torsional vibrations of viscoelastic rotors with fractional damper

The behavior of a Jeffcott rotor with lateral-torsional coupling is investigated in the presence of internal and external damping and eccentricity. The governing equations are derived based on the Lagrange method. Also, the Laplace method and linearization is used to solve the governing equations for free vibrations analysis. For a rotor with unbalance, the instability occurs when the real part of eigenvalues has positive values, and at the same time, it is the intersection point between the lines of natural frequencies. The instability speed increases with increasing the external damping, yet dependent on the internal damping and unbalance. Also, it is demonstrated that the rotor critical speed is affected by the order of fractional derivatives.

Non-isothermal squeeze film damping in the test of gravitational inverse-square law

For the experiments of testing the Newtonian inverse-square law (ISL) at short range, we have analyzed the residual gas damping effect under the assumption of the temperature of the gas is isothermal (Ke J et al 2020 Class. Quantum. Grav. 37 205008). However, when the test mass squeezes the gas, the temperature of the gas will change accordingly and may cause additional noise. It is essential to study this phenomenon in pursuit of higher precision test of ISL. Here, we discuss the non-isothermal squeeze film damping by using the differential equations of energy conservation and change in molecular density. The results show that this kind of Brownian motion torque noise is larger than that estimated previously and is influenced by the degrees of freedom of molecules. Namely, a larger accessible distance between test bodies is needed in comparison to the internal damping of the pendulum.

Vibration control of a bi-disk rotor using electro-rheological elastomers

Smart materials are widely used for vibration control of rotating machines. This paper considers the control of vibration of a bi-disk rotor bearing system using electro-rheological elastomer (ERE) rings inserted in the bearings. The bi-disk rotor is selected so that vibration response can be studied in a rotating speed range which includes the first two critical speeds. The rotor bearing system is modelled using the finite element method taking into account the gyroscopic effect of the rotor and the internal damping of the shaft. The influence of the active elastomer when it is subjected to different levels of the electric field on the critical speeds is first investigated. Then, the vibration response is determined for both steady-state and transient running up and running down conditions. Simulation results show the potentials of the ERE when used in passive mode for vibration reduction in the steady-state and transient running up and down conditions of the rotor system. In the active mode, the application of an electric field to the EREs shifts slightly the resonant speeds to higher frequencies due to the increase of the stiffness of the bearings while increasing the vibration amplitudes in the steady-state and transient running up and down conditions in the vicinity of the resonant speeds. Nevertheless, it has been shown that the rotor steady-state vibration response can be reduced at other rotating speed range when an electric field is applied.

Influence of Internal Rubber Damper on Cable External Viscous Damper Effectiveness

In practice, the internal rubber dampers are widely installed inside the cable guide pipe between the external viscous damper and the cable anchorage. In order to study the effect of the internal damper on the performance of the external viscous damper, the theoretical analysis model of a taut cable with an internal rubber damper and an external viscous damper is established in this paper, where the internal damper is assumed to be a high damping rubber damper with a flexible support and the external damper is considered to be a linear viscous damper. Then, the numerical iterative formula and approximate solution expression for the cable modal damping ratio are derived. Based on the approximate solution, the parameters of the internal rubber damper are analyzed comprehensively, and its influence on the cable modal damping in cable multimode is studied as well. Results show that, except for the support flexibility of the internal rubber damper, other parameters will have a negative effect on external viscous damper effectiveness. From the perspective of cable multimode vibration control, the installation of an internal rubber damper significantly weakens the modal damping, and this effect is more pronounced in lower frequency modes.

Stability Analysis of Rotor with a Spline Coupling

Abstract The spline coupling is widely used in aero-engines. Once the spline coupling fails, it will cause great damage to the engine. In this paper, the stability of a rotor with a spline coupling was studied. The internal damping instability model of the rotor with spline coupling is deduced, and the instability mechanism is explored. The stability boundary is analyzed by using the R-H criterion. The mechanism of rotor instability is analyzed by simulation. An experimental system of rotors with different structural parameters of spline coupling was built. The influence of the positioning surface clearance on the stability was analyzed. The modeling results show that the internal friction of the spline coupling will introduce additional damping and anti-symmetrical cross stiffness to the rotor, the additional damping will reduce the vibration response, and the anti-symmetrical cross stiffness will cause the rotor to become unstable. The simulation and experimental results show that the rotor system will not be unstable when the two positioning surfaces of the spline coupling are in an interference fit. When one of the positioning surfaces is a clearance fit and the other is an interference fit, the internal friction will cause the rotor to become unstable. The instability threshold speed is higher than the first-order critical speed. At the same time, due to the additional damping introduced by the sleeve tooth structure, there will be a transition stage of instability. At this time, the rotor will vibrate with sub-harmonic components, but the vibration amplitude of the rotor will decrease. When the two positioning surfaces are clearance fit, the rotor is unstable and the amplitude increases suddenly. The obtained instability characteristics of the rotor with spline coupling have important value for the instability fault diagnosis, and provide help for the stability control.

An Arbitrary Lagrangian–Eulerian Formulation of Two-Dimensional Viscoelastic Beams Based on the Consistent Corotational Method

Abstract In this paper, an arbitrary Lagrangian–Eulerian (ALE) formulation based on the consistent corotational method is presented for the geometric nonlinear dynamic analysis of two-dimensional (2D) viscoelastic beams. In the ALE description, mesh nodes can be moved in some arbitrarily specified way, which is convenient for investigating problems with moving boundaries and loads. By introducing a corotational frame, the rigid-body motion of an element can be removed. Then, the pure deformation and the deformation rate of the element can be measured in the local frame. This method can avoid rigid-body motion damping. In addition, the elastic force vector, the inertia force vector, and the internal damping force vector are derived with the same shape functions to ensure the consistency and independence of the element. Therefore, different assumptions can be made to describe the local deformation of the element. In this paper, the interdependent interpolation element (IIE) and the Kelvin–Voigt model are introduced in the local frame to consider the shear deformation, rotary inertia, and viscoelasticity. Moreover, the presented method is capable of considering the arbitrary curved initial geometry of a beam. Numerical examples show that internal damping dampens only the pure elastic deformation of the beam but does not dampen the rigid-body motion. Three dynamic problems of a beam with a moving boundary or subjected to a moving load are investigated numerically by the presented formulation and the commercial software ansys to verify the validity, versatility, and computational efficiency of the presented formulation.

Instability attenuation and bifurcation studies of a non-ideal rotor involving time-delayed feedback

In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time-delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.

Damping and Frequency Response Characteristics of Functionally Graded Fiber-Reinforced Composite Cylindrical Shells

This paper presents research on the modal damping and frequency response of functionally graded fiber-reinforced composite cylindrical shells considering the internal damping. Based on the Love shell theory and energy approach, the dynamical equations of cylindrical shells are established. In the process of variable separation, the Haar wavelet series and trigonometric functions are respectively to represent the axial and circumferential modes. Based on the microscopic damping prediction method and multi-cell model of hybrid materials, the equivalent damping and elastic characteristics of composite materials are determined. Then the damping and frequency response characteristics are solved by the complex modulus method. The present analysis is validated by comparing the results with those in the literature and finite element simulation. The effects of fiber content and distribution, lamination and geometry configuration on damping and frequency response properties are further analyzed. The analysis show that the damping decreases monotonically with the increase of fiber volume fraction. The damping behaviors may be improved by changing the fiber distribution type and stacking sequence. Increasing the internal damping of composites can obviously reduce the vibration amplitude in the resonance region, especially in the high frequency range.

Uniform stabilization for a Timoshenko beam system with delays in fractional order internal dampings

Uniform stabilization for a Timoshenko beam system with delays in fractional order internal dampings

Using a Duffing control approach to control the single risk factor in complex social-technical systems

An approach based on forced Duffing Equation with cubic term is proposed to solve the single risk factor control problem in complex social-technical systems from the micro perspective. The single risk control problem is transformed into a system vibration control problem. Firstly, the relationships among Duffing Equation, system state sudden change and single risk factor control are analyzed. System control point crosses the bifurcation set is an important condition for the system state sudden change, the Duffing Equation can be used to establish the vibration equation of the complex social-technical system, and the risk control method of the complex social-technical system can be deduced based on the vibration equation. Secondly, the interference of the external environment in Duffing Equation is defined as the energy change of risk pulse. Next, we establish the system risk control equation and derive its bifurcation response equation with stable solutions. Under three safety protection measures conditions, including strengthening internal damping of system, reducing external excitation influence, strengthening internal damping of the system while reducing external excitation influence, three system risk control strengthening equations are established and their corresponding bifurcation response equations with stable solutions are derived, respectively. Finally, a real-world case study is conducted.

Bifurcation and vibration resonance in the time delay Duffing system with fractional internal and external damping

Bifurcation and vibration resonance in the time delay Duffing system with fractional internal and external damping