Circumferential Bending Strain Research Articles

Distributed flexoelectric modal signals on circular cylindrical shells

Flexoelectricity exhibits both direct effect and converse effect. For direct flexoelectric effect, mechanical strain gradients induce a homogeneous electric polarization in dielectrics. Thus, the induced electric field between the electrodes can be measured. Compared with the piezoelectric sensors, the main advantage of the flexoelectric sensors is that they are not sensitive to the in-plane strains. This paper presents segmented flexoelectric sensors laminated on circular cylindrical shells, and investigates the electromechanical strain-gradient/signal-generation characteristics and distributed modal flexoelectric signals on the cylindrical shells. The dynamic equations of the proposed flexoelectric sensor are derived based on the direct flexoelectric effect and thin shell assumptions. The model of modal signal is derived to investigate the sensing characteristics. In case studies, the effects of design parameters, i.e. size and thickness of the sensors and geometry of the shells, are evaluated and compared. Numerical results indicate that the contribution of longitudinal bending strain gradient is dominant in the total signals of most evaluated modes, except that in modes 1 and 2, where the contribution of the circumferential bending strain gradient is slightly higher. The amplitudes of the modal signals decrease with the shell radius, but increase with the sensor thickness.

Modal signal analysis of conical shells with flexoelectric sensors

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. In this study, a flexoelectric sensor is laminated on conical shells to monitor the natural modal signal distributions. The sensing mechanism of a generic flexoelectric sensor patch is presented first. Then, the spatially distributed microscopic sensing signal with respect to coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the circumferential and longitudinal bending strain components. Analytical results show that the flexoelectric sensing signal induced by the longitudinal bending strain is the dominant contribution to the total signal for lower order modes; the contribution of the circumferential bending strain components increases while increasing the circumferential mode number. In lower modes, the optimal location of flexoelectric sensor is at the minor end and shifts to the middle for shallow shells. In higher modes, the optimal location is at the middle of the shell, but first shifts to the major end and then shifts to the minor end while increasing the semi-apex angle.

Procedures for the strain based assessment of pipeline dents

A criterion for strain-based assessment of dents in gas pipelines has been recently proposed in the ASME B31.8 code. This work initially presents a critical review of the equations for estimating strains presented in Appendix R of that code. Next, a procedure based on B-spline curves is presented that interpolates dent geometry from data measured by in-line inspection (ILI) tools and evaluates strain components. The paper proceeds with studies to assess the influence of the ILI tool resolution and positioning on the estimation of the circumferential bending strain. Finally, the evaluation of longitudinal membrane strains is assessed by taking two alternative definitions for dent length that enters in the formula proposed in Appendix R of the aforementioned code, and comparing with results provided by Finite Element analyses. The comparison suggests that directions on how to measure the dent length might be incorporated in a revision of the ASME B31.8 Code.

A magnetoelastic theoretical model for soft ferromagnetic shell in magnetic field

With the aid of a generalized variational method, in this paper, a theoretical model for soft ferromagnetic shells is derived to describe their magnetoelastic behavior in an applied magnetic field. Having made a quantitative comparison between the numerical predictions given by several theoretical models and the experimental results on strains of a cylindrical shell, we find that the predictions got by our model are in good agreement with the experimental data. It is also found that the Moon’s model is a special case of the model derived in this paper when the relative magnetic permeability μ r>10 4, which confirms that it is reasonable for the Moon’s model to calculate strains of the soft ferromagnetic shells. Having displayed the distribution of the equivalent magnetic force in the length of the cylindrical shell and its circumferential bending strains with different elastic end constraints, we give an explanation for the discrepancy between Moon’s analytical results and his experimental ones.

Corrugated High-Density Polyethylene Pipe: Laboratory Testing and Two-Dimensional Analysis to Develop Limit States Design

Baseline data on buried thermoplastic pipe behavior under biaxial loading have been developed in a controlled laboratory environment. Deflections and local wall strains of a lined corrugated high-density polyethylene pipe were determined. Use of the finite element method and simplified design equations was then evaluated relative to the laboratory measurements. Measurements of soil response during the tests were used to evaluate the constitutive response for the soil. The comparisons reveal that the two-dimensional finite element method can effectively be used to predict pipe deflections and circumferential strains in the corrugation, given that appropriate material parameters are used. Liner strains, however, are influenced by local bending, so that three-dimensional analysis is required. The simplified design methods were shown to be effective tools for pipe design. A strain factor of three in the semiempirical equation for circumferential bending strain appears to be reasonable for pipes buried in uniform ground. The finite element method was then used to study lined corrugated pipe response when the zones of backfill placed beneath the haunches have low density and modulus. These alter the location of the peak strains, may significantly increase the magnitude of the circumferential strains and the strain factor, and induce yield at the extreme fibers.

Modal Sensor for Axial Propagating Waves in an Infinite In-Vacuo Pipe

In an infinite in-vacuo pipe, the radial vibration can be decomposed into an infinite number of circumferential modes. For each mode, there is a right-going and a left-going propagating axial wave. In this paper, a sensor to detect either one of these waves is described. The wave chosen belongs to the first circumferential (n 1/4 2) mode of vibration, and the sensor consists of two PVDF (polyvinylidene fluoride) elements shaped in the form of sine and cosine functions. Two elements are required because the orientation of the wave at some arbitrary point on the pipe is generally unknown. The relationship between the charge generated on the element to the combination of axial and circumferential bending strains, is established for the case of in-extensional deformation. It is found that a practical sensor is sensitive to higher order modes as well as the n 1/4 2 mode, and this cross-sensitivity is dependent upon the width of the modal sensor. It is shown that the cross-sensitivity is small provided that the width of the modal sensor is less than one third of the wavelength of the propagating wave at the ring frequency. Experimental results are presented to validate the sensor sensitivity equation.

Thermal Ratcheting Criteria and Behavior of Piping Elbows

A thermal ratcheting test was performed using an elbow model test specimen subjected to sustained primary load and cyclic thermal transient strains. Under severe loading conditions incremental longitudinal strains are observed in the region where a circumferential angle is around ± π/9 from the side of the elbow, while the elbow cross section was ovalized cycle by cycle causing large circumferential bending strain at around φ = π/2. It was shown by the test and analyses that the maximum primary membrane stress in an elbow is an essential parameter for thermal ratcheting behavior of elbows. Direct application of thermal ratcheting criteria in the ASME Code Case N-47 showed considerable conservative estimation and an improved thermal ratcheting criterion for elbows is recommended.