Dynamic analysis of multilayered welded aluminum cantilever beams

Welded joints are often used to fabricate assembled structures in machine tools, automotive and many such industries requiring high damping. Vibration suppression in these applications can enhance the dynamic stability significantly. A little amount of work has been reported till date on the damping capacity of welded aluminum structures. The present work outlines the basic formulation for the slip damping mechanism in multilayered and tack welded aluminum beams, vibrating under dynamic conditions. It is observed that there are a number of vital parameters that govern the damping capacity of these structures. The developed damping model is found to be fairly in good agreement with experimental results.     

Effect of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power law profile

In the present paper, an efficient method of damping structural vibrations using the acoustic black hole effect is further investigated experimentally. This method is based on some specific properties of flexural wave propagation in tapered plates (wedges) of power-law profile that have to be partially covered by narrow thin strips of absorbing layers. Ideally, if the power-law exponent of the profile is equal or larger than two, the flexural wave never reaches the sharp edge and therefore never reflects back, which constitutes the acoustic black hole effect. It has been previously established theoretically and confirmed experimentally that this method of damping structural vibrations is very efficient even in the presence of edge truncations. The present work describes the results of the experimental studies of the effects of manufacturing intolerances on damping flexural vibrations in wedge-like structures of power-law profile. In particular, the effect of mechanical damage resulting from the use of cutting tools to wedge tips is investigated, including tip curling and early truncation, as well as the placement of absorbing layers on different wedge surfaces. Also, the effects of welded and glued bonding of wedge attachments to basic rectangular plates (strips) are investigated. The results show that, although the above-mentioned geometrical and material imperfections reduce the damping efficiency by varying degrees, the method of damping structural vibrations using the acoustic black hole effect is robust enough and can be used widely without the need of high precision manufacturing.     

A comment on quantum-mechanical damping

The question of introducing damping into quantum mechanics has come into prominence again. It is argued, from previous experience with the damping of a harmonic oscillator, that it is easy to violate the uncertainty principle, particularly if it is overlooked that absorbers are also emitters. The usual classical equations for a damped system are those for a smoothed variable, with the noise fluctuations subtracted. In the case of a damped harmonic oscillator the process of subtracting the noise and so defining a smoothed variable was examined many years ago, and to some extent can be used to justify present practice.     

Hysteretic damping in rotordynamics: An equivalent formulation

The hysteretic damping model cannot be applied to time domain dynamic simulations: this is a well-known feature that has been discussed in the literature since the time when analog computers were widespread. The constant equivalent damping often introduced to overcome this problem is also discussed, and its limitations are stated, in particular those linked with its application in rotordynamics to simulate rotating damping. An alternative model based on the nonviscous damping (NVD) model, but with a limited number of additional degrees of freedom, is proposed, and the relevant equations are derived. Some examples show applications to the rotordynamics field.     

Estimation of damping from response spectra

In this paper procedures for estimating damping ratio from response spectra are examined. The study is restricted to an evaluation of bias and random errors introduced by signal processing requirements. A second order system is used in the study, and a Gaussian white noise input is assumed. It is shown that, due to bias errors in estimating the response spectra, calculations of damping ratio by the peak response and half-power bandwidth methods give overestimates. The bias errors of the damping ratio estimates are a function of the true damping of the system and the ratio of analysis bandwidth to resonant frequency. The bias error for the half-power bandwidth method is three times that for the peak response method. It is also shown for large ranges of damping ratio and bandwidth ratio that zero bias response occurs at a point where the response is approximately 80% of the peak response. Numerical results obtained by simulation studies are used to verify the expressions for normalized bias error. Expressions for random error associated with damping ratio estimates are also developed. Random error can be minimized by maintaining a high coherence between the system input and response.     

External damping losses in measuring the vibration damping properties in lightly damped specimens using transient time-domain methods

The contaminating effect of external damping sources to the overall measured damping of mechanical structures has always been an issue. Although these sources are qualitatively known, they are often not considered if damping properties are experimentally determined, yielding erroneous results. The aim of this paper is to quantify some of these undesired effects on the overall measured damping value. Free vibrations of steel plate specimens are used to list up several causes of external damping sources. As small modifications to the test setup may lead to totally different results, appropriate actions are offered to design a more accurate test setup. Known observations, such as the damping value’s dependence on the specimen size and the excitation level, are confirmed. Finally, it is shown that the damping capacity of one type of steel alloy can usually not be generalised to other steel alloys.     

Dynamic analysis of slip damping in clamped layered beams with non-uniform pressure distribution at the interface

Slip damping is a mechanism exploited for dissipating noise and vibration energy in aerodynamic and machine structures. Such slip in layered structures can be simulated by applying pressure to hold the members together at the interface. However, while most analyses of the mechanism assume an environment of uniform pressure at the interface, experiments to date have confirmed that this is rarely the case. There have been recent attempts to relax the restriction of uniform interface pressure to allow for more realistic pressure profiles that are encountered in practice. However, such works have mostly been limited to static loading for which it has been established that the interfacial pressure gradient does play a dominant role in modulating the level of energy dissipation. This paper is an attempt to extend such analyses to account for cases of realistic dynamic loading that drive such structural vibration in the first instance. In particular, it is shown that under dynamic loads, frequency variation more than non-uniformity in the interface pressure can have significant effect on both the energy dissipation and the logarithmic damping decrement associated with the mechanism of slip damping in such layered structures.     

Vibration damping material as a means to reduce steel noise barrier cost

A preliminary analysis has been made of the use of vibration damping material as a means to reduce the cost of steel noise barriers in primarily highway applications. For cost-effective barriers, the sound transmission through, as well as over, a noise barrier must be considered. The through-barrier sound transmission characteristics of sample panels from a Toronto noise barrier were measured with and without damping material. It was found that a given through-barrier sound transmission performance could be achieved at less cost with the damping material than without it. Further study is recommended.     

Changing damping parameter to obtain higher output signal-to-noise ratio

The stochastic resonance is investigated by experiments using an electronic circuit simulating a Duffing system. It has been found that a high output signal-to-noise rate can be obtained by varying damping parameter under certain conditions. The deviations between the experimental results and the adiabatic theory are presented. This project is supported by the Educational Commission of Liaoning Province.     

Radiation damping in microcoil NMR probes

Radiation damping arises from the field induced in the receiver coil by large bulk magnetization and tends to selectively drive this magnetization back to equilibrium much faster than relaxation processes. The demand for increased sensitivity in mass-limited samples has led to the development of microcoil NMR probes that are capable of obtaining high quality NMR spectra with small sample volumes (nL-microL). Microcoil probes are optimized to increase sensitivity by increasing either the sample-to-coil ratio (filling factor) of the probe or quality factor of the detection coil. Though radiation damping effects have been studied in standard NMR probes, these effects have not been measured in the microcoil probes. Here a systematic evaluation of radiation damping effects in a microcoil NMR probe is presented and the results are compared with similar measurements in conventional large volume samples. These results show that radiation-damping effects in microcoil probe is much more pronounced than in 5 mm probes, and that it is critically important to optimize NMR experiments to minimize these effects. As microcoil probes provide better control of the bulk magnetization, with good RF and B0 inhomogeneity, in addition to negligible dipolar field effects due to nearly spherical sample volumes, these probes can be used exclusively to study the complex behavior of radiation damping.     

The measurement of damping in large panels

In this paper we consider the problem of measuring the loss factors of large panels, particularly when their damping is high. A method of measurement which may be used over a wide range of damping values is described. It is shown that it is important to measure the damping of panels and walls in situ since the damping can depend critically on the mounting conditions used and is often greater than the internal damping of the wall material itself. It is suggested that a measurement of damping should be made whenever the sound insulation of a panel or wall is measured in the laboratory.     

Practical industrial method of increasing structural damping in machinery,I: Squeeze-film damping with air

There is frequently a need to reduce sound radiation due to resonant flexural motion of stiff machinery panels. This can be achieved by applying squeeze-film damping to the vibrating panel by attaching an auxiliary plate parallel to the surface, thereby trapping a thin layer of air. Relative vibration of the plates pumps this air at high velocities, resulting in energy loss due to the air viscosity. In this study the damping below the critical frequency of the “thick plate” with an “attached plate” and air layer has been investigated by using an impedance approach. This model is incorporated into a two element Statistical Energy Analysis (SEA) model to predict the damping well above the critical frequency of the thick plate. The agreement between the predicted and measured results is remarkably good. Below the critical frequency the damping is pumping controlled, while above critical the plate couplings are the controlling factor.     

Measurement of modal damping by electronic speckle shearing interferometry

A time-average electronic speckle shearing interferometer (ESSI) has been used for modal damping measurement. This is effected by a new fringe enhancement technique. The damping factor of a cantilever measured by using this technique agrees well with the value measured by using the accelerometer method. The study shows that time-average speckle interferometry can be used as a convenient tool for modal damping measurement.     

An analysis of interlaminar stresses in active constrained layer damping treatments

This paper presents an analysis of the interlaminar stresses in active constrained layer (ACL) damping treatments. The primary objective of this study is to provide in-depth understanding of the delamination of ACL damping treatment and, to establish guidelines to lower the risk of delamination without sacrificing performance. Two major issues are addressed in this investigation. First, the effects of feedback control schemes on interlaminar stresses are analyzed. The proportional (P) and the derivative (D) control laws are selected for comparison. It is found that for the system under consideration, for similar vibration reduction, the derivative control scheme introduces lower interlaminar stresses than proportional control. Also, the derivative control scheme has lower voltage requirements. Second, the ACL treatment is compared with the purely active configuration (without the viscoelastic layer). In addition to the damping performance and control effort requirement (which have been analyzed and compared by researchers in the past), the interlaminar stresses are now included in the comparison. It is shown that the ACL configuration could have significantly lower interlaminar stresses than the purely active configuration, for similar levels of vibration reduction. Hence, in applications where system durability is a concern, the ACL treatment should be preferred over purely active configuration because it has lower interlaminar stress as-well-as lower axial stresses in the piezoelectric cover sheet.     

A note on structural damping of ship hulls

Existing information on the structural damping of ships is far from satisfactory. It cannot be calculated and it can only be measured in the presence of hydrodynamic damping, whose nature and magnitude are also somewhat obscure. Yet it is very important.Symmetric responses to wave excitation can be estimated on the basis of existing hydrodynamic theories, with use of rough estimates of hull damping; our limited knowledge of structural damping is then only likely to be a handicap with heavy slender ships and/or fast ships. Much less is known about antisymmetric responses to waves, either as regards the means of estimating them or the appropriate levels of hull damping.Vibration at higher frequencies, due to excitation by machinery (notably propellers), is limited by structural damping to a much greater extent that it is by the fluid actions of the sea. Damping measurements at these frequencies therefore give more accurate estimates of hull damping. Even so, the estimation of ship vibration responses to excitation by machinery remains a matter of considerable difficulty.     

Frequency power law of material damping

The experimental studies often show that the damping in various solid materials increases with frequency over a finite bandwidth, and the increase is weak if the damping is low. A frequency power law is suggested and discussed in this paper to describe this damping behaviour with special respect to the low loss resilient materials used for sound and vibration control. The dynamic modulus as a function of frequency is determined from the loss modulus through the Kramers-Kronig dispersion relations to satisfy the causality requirement. It is proved that the dynamic modulus obeys the frequency power law of the same type as the loss modulus. In addition, it is proved that the weak frequency dependences of damping properties are inevitably associated with the low loss factor. Examples of fitting the frequency power law to experimental data on some materials of acoustical purposes are presented.     

An analytical particle damping model

Particle damping is a passive vibration control technique where multiple auxiliary masses are placed in a cavity attached to a vibrating structure. The behavior of the particle damper is highly non-linear and energy dissipation, or damping, is derived from a combination of loss mechanisms. These loss mechanisms involve complex physical processes and cannot be analyzed reliably using current models. As a result, previous particle damper designs have been based on trial-and-error experimentation. This paper presents a mathematical model that allows particle damper designs to be evaluated analytically. The model utilizes the particle dynamics method and captures the complex physics involved in particle damping, including frictional contact interactions and energy dissipation due to viscoelasticity of the particle material. Model predictions are shown to compare well with test data.     

Effects of hysteretic and aerodynamic damping on supersonic panel flutter of composite plates

The governing equation for the finite element analysis of the panel flutter of composite plates including structural damping is derived from Hamilton's principle. The first order shear deformable plate theory has been applied to structural modelling so as to obtain the finite element eigenvalue equation. The unsteady aerodynamic load in a supersonic flow is computed by using the linear piston theory. The critical dynamic pressures for composite plates have been calculated to investigate the effects of structural damping on flutter boundaries. The effects are dependent on fiber orientation because flutter mode can be weak or strong in the fiber orientation of composite plates. Structural damping plays an important role in flutter stability with low aerodynamic damping but would not affect the flutter boundary with high aerodynamic damping.     

Nonlinear damping calculation in cylindrical gear dynamic modeling

The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.     

Hysteretic damping and causality

It is proven that linear oscillatory systems with hysteretic damping in the form of complex stiffness and/or complex elastic moduli satisfy the causality principle: the response of such a system to an arbitrary external force cannot appear earlier than the onset of the force. The proof, based on a rigorous solution to the problem of forced oscillations, is presented in detail for an oscillator with a complex stiffness, as well as in a brief explanation for a system with N mass. It is also shown that these systems are Lyapunov-unstable. A comparison is made to other linear hysteretic damping models.