Frequency Dependent Loss Factor Research Articles

Complex mode superposition method of non-classically damped systems based on hysteretic damping model with frequency-dependent loss factors

For non-classically damped systems, it is easy to construct a damping matrix based on a hysteretic damping model. However, the damped natural frequency is non-physical, and the frequency response function is non-causal. These two drawbacks can be overcome by the hysteretic damping model with frequency-dependent loss factors. In this paper, a complex mode superposition method for non-classically damped systems based on the hysteretic damping model with frequency-dependent loss factors is proposed. Frequency-dependent loss factors of the natural frequencies are considered in the transient vibration response, while frequency-dependent loss factors of the external excitation frequencies are considered in the steady state vibration response. By decoupling complex modes in state space and physical space, non-proportional damping characteristics of hybrid structures can be effectively considered. Therefore, the proposed method can be used to calculate the time-domain dynamic responses of hybrid structures, whose loss factors are sensitive to frequency variation and have strong non-proportional damping characteristics. The time-domain dynamic responses of numerical examples are compared based on different mode superposition methods. Shaking table tests are performed on cantilever plates with different damping characteristics. The numerical and test results validate the proposed method. Moreover, the proposed method has a wide range of applications.

Time-domain calculation method of improved hysteretic damped system based on frequency-dependent loss factor

Hysteretic damping model is consistent with experiment results within a wide frequency range, and is usually employed in structural dynamic analysis. However, hysteretic damping time-domain model has the two shortcomings, namely damped natural frequency increases with the increase of structural loss factor and the vibration response is non-causal. In order to overcome the two shortcomings, an improved hysteretic damping time-domain model based on frequency-dependent loss factor (IHDT) is proposed. Combined with strain energy method, a mode superposition method based on IHDT is further proposed, then an approximately linear time-domain calculation method (RIHDT) can be realized for multi-degree-of freedom hysteretic damped system. Shaking table test is conducted for cantilever plates composed of host and damping layers to validate the proposed method. Structural vibration responses under random excitations are obtained in the test, which are compared with the corresponding simulation results obtained by RIHDT and the time-domain method based on Rayleigh damping model (RT), respectively. The calculation results of RIHDT and RT are both similar to the test results under external excitation within low vibration frequencies. However, compared with RT, the calculation results of RIHDT are unique and the problem of choosing reasonable modes is avoided. For the test results of external excitation within high vibration frequencies, the computational accuracy of RIHDT is higher than the corresponding one of RT, since the contributions of higher vibration modes are not underestimated by RIHDT. Besides, RIHDT is based on the damping properties of materials, which makes the calculation process simple.

An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures

Owing to their ability to block propagating waves at certain frequencies, phononic materials of self-repeating cells are widely appealing for acoustic mitigation and vibration suppression applications. The stop band behavior achieved via Bragg scattering in phononic media is most commonly evaluated using wave propagation models which predict gaps in the dispersion relations of the individual unit cells for a given frequency range. These models are in many ways limited when analyzing phononic structures with dissipative constituents and need further adjustments to account for viscous damping given by complex elastic moduli and frequency-dependent loss factors. A new approach is presented which relies on evaluating structural intensity parameters, such as the active vibrational power flow in finite phononic structures. It is shown that the steady-state spatial propagation of vibrational power flow initiated by an external disturbance reflects the wave propagation pattern in the phononic medium and can thus be reverse engineered to numerically predict the stop band frequencies for different degrees of damping via a stop band index (SBI). The treatment is shown to be very effective for phononic structures with viscoelastic components and provides a clear distinction between Bragg scattering effects and wave attenuation due to material damping. Since the approach is integrated with finite element methods, the presented analysis can be extended to two-dimensional lattices with complex geometries and multiple material constituents.

Experimental study on energy dissipation factors of wheelset node oscillations

Wheelsets directly subjected to a force impact under the interaction of wheels and rails are intense noisemakers when moving, including overhead cranes and railway rolling stock. Despite the design and functional differences, the calculation of vibroacoustic characteristics can be made from the unified positions. It should be noted that the calculation accuracy of the sound pressure levels and vibrations is in large part determined by the precision of setting the frequency-dependent loss factors of the vibration energy. Theoretical studies of this physical and mechanical value are rather complicated. Therefore, the regression curves obtained on the basis of the mathematical treatment of the experimental coefficient values of the wheelset assembly losses and the approximation dependencies by the exponential polynomials of various degrees should be used for the engineering analysis of the sound pressure levels and vibrations.

Damping: Some often overlooked facts

Damping - dissipation of mechanical energy - has significant effects on only some types of vibrations. Damping can result from many mechanisms, many of which cannot readily be modeled, but prediction of details of motions requires correct representations of the dominant mechanisms. The assumption of viscous damping permits one to analyze vibrations via relatively easily solved linear differential equations, but can lead to results that do not represent reality. Several measures of damping are based on simple models involving frequency-independent viscous damping, but realistic damping behavior often may be better represented by a frequency-dependent loss factor. The chemical properties of plastics and elastomers generally are not known well enough to permit assessment of the behavior of such materials without dynamic measurements. Structural configurations with relatively high damping may be obtained by combining high-damping polymeric materials with efficient structural materials only if the configurations are such that for a given deformation the high-damping material stores a considerable fraction of the total mechanical energy. This is manifest in the behavior of free-layer and constrained-layer damping treatments and in their design equations, which also indicate that a damping material that is very good for one of these types of treatments may not be good for the other.

Comparison of Transformer Detailed Models for Fast and Very Fast Transient Studies

The fast and very fast transient overvoltages can endanger the insulation of transformer windings. Therefore, it is necessary to develop models, to study these transients. This paper compares the two well-known multiconductor transmission line (MTL) and lumped parameter detailed (RLC ladder network) models. The high-voltage (HV) winding of a 220/35-kV, 50-MVA transformer has been modeled using these models. The simulation results of the MTL and the RLC ladder network models have been compared with the measurements results in the frequency domain, by application of the Pearson's correlation coefficients. It is shown that the RLC Ladder Network model should be used for fast transient overvoltage (FTO) studies, i.e. frequency range of 10 kHz < / < 1 MHz and the MTL model with frequency dependent loss factor, demonstrates a better agreement with the measurement results for very fast transient overvoltage (VFTO) studies, i.e., in the frequency range of 1 MHz les / les 5 MHz.

On the Application of Shunted Piezoelectric Material to Enhance Structural Damping of a Plate

In this work the application of resistively shunted piezoelectric material for reducing vibration amplitudes of a plate is studied. The ability to tailor the frequency-dependent loss factor is a consequence of the applied passive electrical network. To predict the damping performance of resistively shunted piezoelectrics, an approach based on the effective strain energy fraction is proposed. A finite element model may be used to accurately determine the effective modal strain energy fraction. However, for placing purposes of the piezoelectric elements, an analytical model, which does not account for local stiffening due to the piezoceramics, can be used. Design considerations include the frequency dependence of piezoceramic properties as well as the effect of stiff piezoceramic material on mode shapes. Experimental results are presented for a rectangular plate with eight pairs of resistively shunted piezoelectric elements.

Acoustic radiation from a 3-D truss: Direct global stiffness matrix modeling results

This study was initiated to evaluate the normalized sound power level radiated by a driven truss. The coincidence frequency for the beam elements was sufficiently high that global truss modes are not a concern. Radiation from local beam modes dominate the field. Acoustic radiation was modeled using a combination of the direct global stiffness matrix (DGSM) method and models based on radiation efficiency of cylindrical beams. Use of a nominal structural loss factor of 10−4 for the beam material (aluminum) overestimates the measured field by an order of magnitude. Earlier studies suggest that a combination of structural loss in the joints and multipath wave-type conversion in the truss leads to a loss factor of order 10−3. For this study experimental data were inverted to estimate a frequency-dependent loss factor, which confirms the prior estimate of order 10−3. When the DGSM based model was run with the estimated frequency-dependent loss factor, the model results match the measured data closely. A power balance shows that the structural loss factor dominates the total power dissipated in the system, as one might expect for a lightly fluid-loaded structure. [Research sponsored by ARPA/ONR.] a)E-mail: fricke@mit.edu

Measurement of losses in five piezoelectric ceramics between 2 and 50 MHz

Approximate formulas including losses to predict the electrical impedance of a thin unloaded piezoelectric plate around antiresonant frequencies of the thickness modes have been derived. To do so, a total loss factor is defined that includes both mechanical and electrical losses. Complex electrical impedance measurements on a lead metaniobate and four PZT-type materials between 2 and 50 MHz have been performed. The total loss factors were deduced from both the peak real impedance and from the -6 dB bandwidth of the real impedance peak. Results for fundamental and harmonic thickness modes on thin plates are discussed and the five materials are compared. It is found that for these piezoceramics the total loss factor is well approximated by a linear function of frequency. Finally, a frequency-dependent loss factor is included in the KLM equivalent circuit and it is shown that the theoretical impedance curves obtained with this model are in good agreement with measurements.

Theory of ultrasonic resonances in a viscoelastic layer

We present a resonance theory for the acoustic transmission and reflection coefficients of an elastic plate imbedded in a fluid medium, which includes the effects of plate viscosity. This formulation provides a direct means for determining the material parameters of the plate from the measured acoustic resonances of the Rayleigh and Lamb waves in the plate (i.e., their positions in frequency or angle, their widths, and their heights) which are given in our formalism by explicit analytic expressions that depend on the material parameters. Viscosity is seen to manifest itself in a decrease of the resonance peaks and in a broadening and frequency dependence of the resonance widths, which may be used to determine the frequency-dependent loss factor of the plate.

Determination of a dynamic model for urethane prosthetic compounds

A frequency-response testing technique for determining the dynamic behavior of urethane prosthetic compounds is discussed. Experimental preparation of strip specimens and test results are presented. Sinusoidal response data of the tested strips are compared with three computer synthesizers (viscoelastic, viscous and complex modulus) of the one-dimensional wave equation for deciding on a model which best represents the material and subsequently calculating the value of a dynamic loss factor. The closed form solutions for the three mathematical models subject to sinusoidal boundary conditions are expressed in terms of functions which can be easily programmed for machine computation in FORTRAN IV language involving complex arguments. Dynamicloss factors are required for experimental and finite-element studies of prosthetic left ventricle of animal and human hearts. For the test strips, the loss factor, δ, is found to be dependent on the frequency.f. The results presented show that a viscoelastic model with a frequency-dependent loss factor of the form δ=c/f n is an excellent representation for analyzing the dynamic behavior of urethane compounds subjected to a range of frequencies corresponding to heart-beat rates. Derivation of the model parametersc andn is explained in detail.

Electrical Conduction in 3-Percent Carbon-Filled Polyethylene Part I: Low-Field Results

The electrical conduction properties of polyethylene filled with 3-percent carbon have been investigated. Detailed step response measurements have been performed as a function of temperature in a range of electric fields below 104 V/cm where conduction is essentially ohmic. Using a Fourier transform technique a frequency-dependent loss factor was calculated from the resorption current data. Thermaliy activated relaxation-type peaks are found at very low frequencies and interpreted tentatively as arising from interfacial polarizations at the various crystalline-amorphous interfaces. Results of measurements of the residual dc conductivity are also discussed.

Computer analysis of vibration of linear chain of atoms lying in a double minimum potential

Computer analyses have been performed of the vibration of monatomic linear chains where each atom is in double minimum potential and is connected to nearest neighbor atoms by springs. It has shown that the increase of spring constant induces many low frequency vibrations in the small wave number region and then the system seems to become overdamped, with a frequency dependent loss factor.