Internal Damping Research Articles

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

All-round responses and boundaries of a shaft and dry friction damper assembly

A helicopter tailrotor driveline is equipped with dampers to suppress the resonance of transmission shafts. A dry friction damper and a slender shaft form an assembly The comprehensive understanding of different responses of the assembly provides the basis for a more reasonable parameter configuration of the damper. To this end, the assembly is modeled as a dynamic system with rub impact between a rotor with continuous parameter distribution and a suspended elastic stator. Boundaries of rub impact and condition of Hopf bifurcation are derived. Pinned natural frequencies and backward whirl frequencies are solved by analytical deduction. The critical speed for triggering a backward whirl with consideration of eccentric excitation is obtained by the multiple scale perturbation method. Then, all-round responses and boundaries are solved by both analytical and numerical approaches based on the parameters of a helicopter. The effects of friction coefficient, internal damping, suspension stiffness, variable impact stiffness, etc. on the boundaries are presented in detail with the discussion of relationships between physical reasons and analytical conditions. Results show that smaller impact stiffness difference and friction coefficient, a greater mass damping ring, moderate suspension stiffness, greater internal and external damping are the key factors for the damper design. This study has reference significance not only for the assembly in a helicopter but also for similar mechanical systems.

Parametric dynamic analysis of a double-hanger system via rigid cross-ties in suspension bridges

As a key force transmitting and bearing component of suspension bridges, hangers are significant for bridge safety. Due to the characteristics of long length, high flexibility and low internal damping, hangers are prone to produce various vibrations. Cross-tie, as an effective vibration control member, is widely used in suspension bridges built with double-hanger systems. However, as a special cable network, a double-hanger system still lacks a detailed discussion of mechanical and serviceable performances. Therefore, in this paper, the dynamic behavior of a double-hanger system strengthened by a rigid cross-tie (DHS_RCT) is studied by using a theoretical method. First, the system frequency equation considering the hanger bending stiffness, tension and per unit length mass is deduced from the theoretical formula. Then, the accuracy of the system frequency equation is verified by comparison with literature results. Finally, based on the proposed frequency equation, the effects of hanger length, bending stiffness, cross-tie position and asymmetric hanger tension on the dynamic characteristics of DHS_RCT are analyzed. The results demonstrate that the system stiffness is positively related to the single hanger bending stiffness. In addition, the rigid cross-tie does not increase the system stiffness, but the cross-tie position and asymmetric hanger tension have significant effects on the dynamic characteristics of DHS_RCT.

Identification of limiting damping mechanisms in a high quality factor hybrid resonator of space application gyroscope

• Studied hybrid gyroscope resonator damping mechanisms with imperfection sensitivity. • Realized thin film coated high precision resonator with few millions quality factor. • Limiting damping mechanisms are identified at each stage from design to realization. The performance of Hemispherical Resonator Gyroscopes (HRG) is decided by the mechanical resonator’s Quality factor ( Q factor). The Q factor is a measure of energy dissipation. A Q factor of few millions is needed to realize fine resolution millimeter size of the HRG for future interplanetary satellite missions. The objective is to carry out a detailed study of thermoelastic damping (TED), anchor loss, surface loss, material internal friction and fluid damping. A hybrid resonator is designed with very low TED. One of the major contributions of the present work is the study of the effect of thin film coating and different coating configurations on TED. Extensive simulations have been carried out on the effect of different fabrication deviations on anchor loss. A unique sensitivity study of mode interactions and mass unbalance pattern on frequency split and anchor loss mismatch is also done. Based on this, dimensional and geometric tolerances are derived for precision fabrication and the precision hybrid configuration resonator is realized. Surface loss and material internal friction are estimated. Also, surface characterisation has been done using nanoindentation techniques. Q factor of few millions is obtained in a fabricated precision resonator with thin film coating. Based on the estimation of different damping mechanisms and measurements, the limiting mechanisms are identified at each stage from the design to the realization. The Q factor of an uncoated resonator is limited by the surface loss while that of a coated resonator is limited by the coating induced additional TED, the coating material internal friction and the surface loss.

On viscoelastic transient response of magnetically imperfect functionally graded nanobeams

This research focuses on transient response of porosity-dependent viscoelastic functionally graded nanobeams subjected to dynamic loads and magnetic field as well. The material properties of the nanobeams with changing gradually along thickness direction is presented by modified power-law function. In this research, nonlocal strain gradient theory (NSGT) in framework of a quasi-3D beam theory, which is capable of including thickness stretching effect, are employed. In order to capture the internal damping effect in the model, Kelvin-Voigt visco constitutive model is applied. Applying Hamilton's variation, the governing equations are obtained, and Navier as well as inverse Laplace transform methods are utilized to solve them analytically. Eventually, some parametric investigations are conducted to display the sensitivity of transient response to porosity coefficient, internal damping, volume fraction, length to thickness ratio, position of point load, magnetic field as well as small size parameters. It is manifested that by raising the magnetic field and length scale parameter (LSP), the oscillation amplitudes diminish whereas the number of periodic cycles of the nanobeams increases and the systems are damped much faster.

Nonlinear forced vibration analysis of composite beam considering internal damping

Nonlinear forced vibration analysis of composite beam considering internal damping

The lack of exponential stability for a weakly coupled wave equations through a variable density term

<p style='text-indent:20px;'>In this paper, we consider a system of two wave equations coupled through zero order terms. One of these equations has an internal damping, and the other has a boundary damping. We investigate stability properties of the system according to the variable strings densities. Indeed, our main result is to show that the corresponding model is not exponentially stable using a spectral theory which forms the center of this work. Otherwise, we establish a polynomial energy decay rate of type <inline-formula><tex-math id="M1">\begin{document}$ \frac{1}{\sqrt{t}}. $\end{document}</tex-math></inline-formula></p>

On a variational inequality for a beam equation with internal damping and source terms

On a variational inequality for a beam equation with internal damping and source terms

Development of Vibration Apparatus Learning from Sounds

Nowadays, rubber isolators are widely used for the mitigation of vibrations in structures including household appliances and industrial facilities. Rubber isolator are kinds of springs that use rubber elasticity. However, many students don’t understand about rubber isolator’s original characteristics by being too conscious of its internal damping.

A New Method to Restrain Schuler Periodic Oscillation in Inertial Navigation System Based on Normal Time–Frequency Transform

The pure inertial navigation system (INS) contains three inherent periodic oscillations, namely, Schuler periodic oscillation (84.4 min), Foucault periodic oscillation and Earth periodic oscillation (24 h), which can decrease the navigation accuracy, especially in long-term and low-velocity applications, such as ships and submarines. This paper applies the inaction method (IM) to restrain Schuler periodic oscillation. Compared to external damping network technology and integrated navigation technology, the IM is more independent, as it does not require auxiliary reference information. The IM is based on the so-called normal time-frequency transform (NTFT), and its uniqueness lies in recognizing and extracting instantaneous amplitude, frequency and phase from a harmonic/quasi-harmonic signal directly and exactly. In this paper, simulation data and experimental data are analyzed, and both show that the IM is effective. Moreover, the calculation results show that IM has wider applicability and higher stability than internal damping network technology and bandpass filtering. Compared to pure INS, the root mean square (RMS) of the velocity error decreases significantly; the RMSs of the latitude and longitude errors decrease as well. The IM can restrain Schuler periodic oscillation, and Foucault periodic oscillation is also restrained. However, the IM has no effect on the divergence of longitude error, and the edge effect is a drawback that needs to be addressed in the future.

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.

Dynamic Response Analysis of a Forced Fractional Viscoelastic Beam ∗

In this paper, dynamic response analysis of a forced fractional viscoelastic beam under moving external load is studied. The beauty of this study is that the effect of values of fractional order, the effect of internal damping, and the effect of intensity value of the moving force load on the dynamic response of the beam are analyzed. Constitutive equations for fractional order viscoelastic beam are constructed in the manner of Euler–Bernoulli beam theory. Solution of the fractional beam system is obtained by using Bernoulli collocation method. Obtained results are presented in the tables and graphical forms for two different beam systems, which are polybutadiene beam and butyl B252 beam.

Viscoelastic Response of Graphene Oxide‐Based Membranes and Efficient Broadband Sound Transduction

AbstractFreestanding micrometer thick graphene oxide (GO) membranes combine high stiffness, low mass density, and high loss coefficient. This unique combination of properties is ideal for efficient and broadband electro‐acoustic transduction, relying on membrane lightness, stiffness, and internal damping. Here, the viscoelastic response of GO membranes is measured, and the application of ≈100 µm thick GO membranes is demonstrated in dynamic loudspeakers. Using dynamic mechanical analysis and the time‐temperature superposition principle of polymer rheology, it is found that the stiffness of GO membrane increases by more than 50% over 1–20 kHz while damping decreases by less than 20%. GO membranes exhibit 45% higher damping than aluminum membranes in loudspeakers assemblies. Consequently, GO membranes enable the upshift of loudspeaker breakup frequency by octave above speakers assembled with aluminum, polyethylene terephthalate, titanium, and oak wood membranes. GO is thus found to be an exceptional material for electro‐acoustic transduction.

Damping of layered porous composites and an application in machinery

The structured composite can involve the porous materials providing the important internal damping that is usable in mechanical engineering applications. The stiff base material is equipped by layer/s of softer porous material/s covered by constrained layer. Such layered structure is characterized by increased internal damping in vibration process. Paper analyses some either measured or simulated mechanical properties of designed layered porous composites. Novelty provided in paper is a specific application of structured composite for damping the high frequency vibrations in resonance frequency obtaining the beneficial results, e.g. 40-48% of maximum amplitude reduction.

Evolution of epsilon-near-zero plasmon with surface roughness and demonstration of perfect absorption in randomly rough indium tin oxide thin films

Any degree of surface roughness could play a significant role in determining the optical properties of ultra-thin films required for epsilon-near-zero (ENZ) applications. In this report, we have provided a systematic analysis of the evolution of an ENZ mode with increasing surface roughness values and established both experimentally and theoretically that roughness acts as a supporting mechanism for achieving a strong ENZ plasmon resonance response in randomly rough indium tin oxide thin films. For pulsed laser deposited indium tin oxide thin films, ENZ plasmon-mediated absorption is enhanced monotonically with the increasing surface roughness. A value of 99.75%, depicting near-perfect absorption, at a wavelength of 1335 nm for the incidence angle of 50° is demonstrated experimentally via Kretschmann–Raether configuration for the film with the highest surface roughness. A modified transfer matrix method based on the anisotropic Bruggemann effective medium approximation is being used to effectively simulate the experimental spectra, and based on this analysis, an even higher absorption is predicted at lower angles outside the experimentally viable domain. Such a high value of absorption just above the ENZ wavelength is due to the strong electric field enhancement inside the film layer, while in terms of absorption loss, surface roughness leads the way and contributes immensely toward the occurrence of perfect absorption in the collective media. Modification of the ENZ mode dispersion in the presence of a surface roughness layer is also discussed, and observed perfect absorption is recognized as the outcome of the crossover between the internal damping and radiation damping terms.

Analytical approach to the stepped multi-span rotor-bearing system with isotropic elastic boundary conditions

This paper strives to derive the analytical solutions for the dynamic analysis of stepped multi-span rotor system, where the rotating shaft's internal damping effect is also considered. Specifically, the steady-state whirl analysis and free vibration analysis is given herein. For the steady-state whirl analysis, firstly, the stepped shaft is spilt to several uniform segments and their governing equations are established by Hamilton principle. Subsequently, by applying variable separation method and Laplace transform method to each segment's governing equation, their steady-state responses in terms of determinate interpolation functions multiplied by unknown boundary constants are derived. Then based on the transfer matrix method, each segment's boundary constants are determined with consideration of the compatibility conditions of each two adjacent segments and the end boundary conditions. For the free vibration analysis, one only need to remove the forced term in the steady-state form of transfer matrix and the rotor's characteristic equation will be obtained. Through the theoretical derivation, it is found that this analytical approach can be generalized to any isotropic elastic boundary conditions. To validate the proposed method, two case studies are proposed, where the finite element method is used as benchmark method. For the first one, the influence of internal damping on a uniform rotor's damped whirl characteristics and its stability is analyzed. The damped whirl characteristics analysis reveals that viscous internal damping result in the destabilization of forward modes as long as the spinning speed becomes higher than the critical speed. This phenomenon is also demonstrated by the time responses analysis. For the second one, the dynamic responses of a two-span three steps rotor-bearing system with isotropic viscoelastic boundary conditions are determined. All of simulated results show a great agreement between analytical results and FEM results.

Stabilization for Schrödinger Equation with Internal Damping and Boundary Disturbance

Stabilization for Schrödinger Equation with Internal Damping and Boundary Disturbance

Nonlinear dynamical analysis of some microelectromechanical resonators with internal damping

Nonlinear dynamical analysis of some microelectromechanical resonators with internal damping

A novel geometric model of breathing crack and its influence on rotor dynamics

The present research focuses on performing the dynamic study of a cracked, internally damped, composite rotating shaft system with journal bearing end supports. A novel mathematical formulation is proposed to introduce a time-varying stiffness matrix for simulating the breathing behaviour of the crack. The random search algorithm is used as one of the metaheuristic processes to carry out the optimization and generate time-dependent geometric parameters of the cracked surface for one full rotation. The derived stiffness matrix is used in the composite shaft’s higher order motion equation obtained through equivalent modulus theory, whose internal damping properties are incorporated using operator-based viscoelastic model. Eigenanalysis is carried out to perform a thorough study of dynamic characteristics of cracked shaft considering the crack depth and crack position as two important parameters. The effect of crack on stacking sequence as well as mode shapes of the heterogeneous laminated shaft is also studied.

Fault identification in cracked rotor-AMB system using magnetic excitations based on multi harmonic influence coefficient method

On-site estimation of multiple fault parameters has been performed in a rotor integrated with active-magnetic bearing (AMB) with a cracked shaft supported on flexible conventional bearings. In addition to external viscous damping (at flexible bearings), internal damping (at transverse crack) is considered to show its influence on the dynamics of the cracked system. The instability generated in the rotor system due to the effect of internal damping at high speed are reduced with the control action of the AMB. A Multiple Harmonic Influence Coefficient Method (MHICM) has been proposed that requires the full spectrum amplitude and phases of the rotor responses and excitation forces to obtain the fault parameters of the rotor. The additive crack stiffness, residual unbalances, and internal damping can be estimated in the operating condition with less information on the rotor system. The intensity of the fault parameters is required to be monitored periodically to identify the safe operating speed of the system. As the AMB is an integral part of the rotor system, the multi-harmonic excitation can be initiated without changing the physical condition of the system. To check the robustness of the algorithm, different percentages of random noise are added to the rotor responses.