Dynamic Strain Response Research Articles

Characterization of the dynamic strain response of lead magnesium niobate based ferroelectric relaxor using a fiber optic interferometer

A high resolution optical technique is described which allows for the direct measurement of the dynamic strain response of ferroelectric relaxors. A fiber optic interferometer with strain resolution ≤10-11 (1Hz bandwidth) is utilized to probe the small strain effects in a (Pb(Mg1/3Nb2/3)O3)0.859-(PbTiO3)0.137-(SrTiO3)0.004 ferroelectric relaxor. The total macroscopic strain in the material is assumed to depend both linearly (piezoelectric term) and quadratically (electrostrictive term) on the applied electric field thereby allowing for the characterization of the material as a function of both ac and dc fields. The strain response of the material is monitored at the fundamental (f = 22kHz) and at the second harmonic. The effective piezoelectric and electrostrictive coefficients are computed as a function of temperature from the ac and dc scans and compared to the ones obtained from the low frequency sideband technique (LFST). The maximum value of the dynamic (f = 22 kHz) effective electrostrictive coefficient measured at T = 48°C was found to be 6.4 × 10-16 (m2/V2). The effective piezoelectric coefficient is found to decrease as the temperature increases while the effective electrostrictive coefficient has a maxima near 48°C. At room temperature the material is found to contain a remnant field which decreases as the temperature increases.

Inhomogeneous dynamic strain characteristics of ferroelectric relaxors

Abstract We utilize a high resolution fiber optic (FO) interferometer to measure the dynamic small strain effects in relaxor ferroelectrics. The dynamic strain response of both a PZT and PMN based relaxor ferroelectric is characterized as a function of the applied electric field containing both ac and dc components. Using this technique we have found that relaxor ferroelectrics ferroelectrics exhibit a residual strain signal which cannot be understood by the scalar strain-polarization relationship (e = QP2). The effects of large residual strain signal on the performance of high resolution low frequency fiber optic voltage sensors are discussed.

Observation of residual strain in dynamically excited electrostrictors

We measured the dynamic small strain effects in electrostrictive ceramics with a high resolution fiber optic interferometer. The dynamic strain response of both a lead magnesium niobate (PMN) and a lead zirconate titanate (PZT)-based electrostrictive ceramic exhibited a residual signal which cannot be understood by the simple scalar strain-polarization relationship, e+QP2. The magnitude of the residual signal decreased as a function of increasing temperature indicating that the residual strain signal has origins in the remnant electric polarization of the material. The magnitude of the residual strain was generally higher for the PZT-based electrostrictor than for the PMN based sample. The observed residual strain signal represents a novel phenomenon previously unseen in the dynamical strain response of electrostrictive ceramics.

Observation of stochastic resonance near a subcritical bifurcation

A hysteretic Subcritical period-doubling bifurcation is observed in the nonlinear strain dynamics of a magnetostrictive oscillator. The dynamic strain response of the magnetostrictive oscillator was observed with a high-resolution fiber optic interferometer. The effects of low-frequency modulation and band-limited stochastic fluctuations on such a bifurcation are investigated. Power spectral density measurements show that for an optimal value of externally injected noise the signal-to-noise ratio of a low-frequency modulation signal is enhanced by greater than 14 dB, thus indicating the first experimental observation of stochastic resonance near a bistable period-doubling bifurcation.

Acoustic testing of high-temperature panels

Results are presented of a series of thermal-acoustic tests conducted on the NASA Langley Research Center Thermal-Acoustic Test Apparatus to (1) investigate techniques for obtaining strain measurements on metallic and carbon-carbon materials at elevated temperature; (2) document the dynamic strain response characteristics of several superalloy honeycomb thermal protection system panels at elevated temperatures of up to 1200 F; and (3) determine the strain response and sonic fatigue behavior of four carbon-carbon panels at both ambient and elevated temperatures. A second study tested four carbon-carbon panels to document panel dynamic response characteristics at ambient and elevated temperature, determine time to failure and faliure modes, and collect continuous strain data up to panel failure. Strain data are presented from both types of panels, and problems encountered in obtaining reliable strain data on the carbon-carbon panels are described. The failure modes of the carbon-carbon panels are examined.

Direct observation of dynamic strain bifurcations and chaos in magnetostrictive amorphous ribbons

Period doubling, quasiperiodicity, phase locking, and chaos are observed in the strain dynamics of a magnetically driven magnetostrictive ribbon (Metglas 2605S-2). The dynamic strain response of the ribbon was measured with a fiber-optic Mach–Zehnder interferometer. The predicted universal behavior was characterized with power spectral density measurements and by phase-space flow. The nonlinearity responsible for observing universal behavior in the system does not involve the ΔE effect.

Application of boundary element method to elastodynamic inverse problems. In case of using dynamic strain responses as additional information.

In this paper the boundary element method for steady-state elastodynamics is applied to defect shape identification of structural components. It is assumed that the structural component under consideration has an internal defect and the strain responses measured on the boundary are available as additional information. This inverse problem is reduced to a typical optimum problem, in which the objective function is the square sum of residuals between the strains given as reference data and those computed for an assumed defect by the boundary element method. Numerical experiment is carried out for several example problems in two dimensions to demonstrate the usefulness of the proposed method.

Theoretical and experimental kineto elastodynamic analysis of high speed linkage

A simple method is employed here for the dynamic strain analysis of the high speed mechanism. Formulation of the problem is a linear ordinary second order differential equation with the variable coefficients. Spectrum analysis of the dynamic strain response is obtained theoretically representing the steady state solution by Fourier series. A four bar mechanism is selected here for the experimental investigation as it is the commonly used linkage in industry. Strain gauge technique is used to get the dynamic strain response and its spectrum analysis is obtained using frequency spectrum analyzer. There is favourable comparison between the theoretical and experimental results.

Dynamic strain response of lake and sea ice to moving loads

The results from two experiments to measure the strains due to a vehicle moving over ice are discussed in the context of theoretical work derived from existing solutions in the literature. The experiments took place on two very different types of ice; the lake ice of Femund in Norway, and sea ice near Scott Base in the Antarctic. In both cases, strain was measured directly by means of strainmeters developed specifically for use on ice. The existence of a critical velocity at which the strain is resonant is discussed, and using values derived from the data, a dispersion equation for free waves is solved in the super-critical domain to provide wavelength estimates. At subcritical speeds a moving static load calculation provides the equivalent theory. The experimental results for lake ice and sea ice are similar, although some differences do exist. The magnification factor of the critical strain over static strain is, for example, larger for lake ice (2.25) than for sea ice (1.45). A critical velocity of 15.2 ms −1 was observed for lake ice, for sea ice the value was 19.6 ms −1; both are associated with the minimum phase velocity of free wave propagation.

The effects of large vibration amplitudes on the dynamic strain response of a clamped-clamped beam with consideration of fatigue life

The effects of large vibration amplitudes on the dynamic strain response, near to the fundamental resonance, of a clamped-clamped, thin beam is examined. Complementary theoretical and experimental studies showed that the harmonic distortion of the induced total strain, due to sinusoidal excitation at mid-span, is mainly due to the axial strain component. A limited set of fatigue experiments showed the considerable decrease in fatigue life, which occurs due to non-linear vibration, compared to that of a cantilevered beam of the same material. The statistical approach to the analysis of non-linear vibration induced by random loading is examined theoretically and experimentally, good correlation being achieved between predicted and measured fatigue lives.

Dynamic photoelastic and dynamic finite-element analyses of dynamic-tear-test specimens

The transient response of the dynamic-tear-test specimen of a brittle material, Homalite-100, was investigated by dynamic photoelasticity and dynamic finite-element method. The dynamic stress-intensity factors obtained from dynamic photoelasticity and dynamic finite-element analyses were in reasonable agreement with each other. The dynamic finite-element analysis also showed that the dynamic-fracture-initiation toughness could be determined from the dynamicstrain response of a strain gage located near the crack tip in conjunction with a simple static analysis. Dynamic-fracture-toughness vs. crack-velocity relation was also obtained.