Characterizing dynamic characteristics of structures with uncertainty is an important task that provides critical predictive information for structural design, assessment, and control. In practical applications, sampling is the fundamental approach to uncertainty analysis but has to be conducted under various constraints. To address the frequently encountered data scarcity issue, in the present paper Gaussian processes are employed to predict and quantify structural dynamic responses, especially responses under uncertainty. A self-contained description of Gaussian processes is presented within the Bayesian framework with implementation details, and then a series of case studies are carried out using a cyclically symmetric structure that is highly sensitive to uncertainties. Structural frequency responses are predicted with data sparsely sampled within the full frequency range. Based on the inferred credible intervals, a measure is defined to quantify the potential risk of response maxima. Gaussian process emulation is proposed for Monte Carlo uncertainty analysis to reduce data acquisition costs. It is shown that Gaussian processes can be an efficient data-based tool for analyzing structural dynamic responses in the presence of uncertainty. Meanwhile, some technical challenges in the implementation of Gaussian processes are discussed.

Film sandwiches, consisting of two outer layers of fluoroethylenepropylene and one middle layer of patterned porous polytetrafluoroethylene, were prepared by patterning and fusion bonding. Contact charging was conducted to render the films piezoelectric. The critical voltage to trigger air breakdown in the inner voids in the fabricated films was investigated. The piezoelectric d 33 coefficients were measured employing the quasistatic method and dielectric resonance spectrum. The results show that the critical voltage for air breakdown in the inner voids is associated with the void microstructure of the films. For the films with patterning factors of 0%, 25% and 44%, the critical values are 300, 230 and 230 kV/cm, respectively. With an increase in the patterning factor, both the piezoelectric d 33 coefficients determined from the dielectric resonance spectra and those determined from quasistatic measurements increase, which might be due to a decrease in Young’s modulus for the films. The nonlinearity of d 33 becomes increasingly obvious as the patterning factor increases.

The thermal stability of piezoelectric d(33) coefficients and charge dynamics in the piezoelectret films with tailored microstructure, made of non-porous polytetrafluoroethylene (PTFE) and fluoroethylenepropylene (FEP) layers, are investigated by the measurements of the isothermal decay of piezoelectric d(33) coefficients at elevated temperatures and the analysis of thermally stimulated discharge (TSD) current spectra in short circuit, respectively. The results show that the quasi-static piezoelectric d(33) coefficient up to 300 pC/N is achieved and its Young's modulus is about 0.28 MPa. The d(33) values in the present studied films show improved thermal stability compared with the films without regular microstructure. The drift path for the most of detrapped charges in the films is through the solid dielectric layer.

Laminated fluoropolymer films with regular void structure, fabricated by using a process consisting of the patterning and fusion bonding steps, are polarized to be piezoelectric. The influence of the applied voltage on the piezoelectric d33 coefficient is investigated. The measurements of ferroelectric-like polarization-voltage hysteresis loops are taken to further understand the capability of polarization in the laminated films. The compressive Young’s moduli of the films are determined from the dielectric resonance spectra. The results show that the laminated fluoropolymer films are piezoelectric after proper charging. The maximum d33 coefficients of the five-layer laminated piezoelectrets are achieved at the applied voltage of 5 kV. The remnant charge density of 0.3 mC/m2 is obtained from the polarization-voltage hysteresis loop at a bias voltage of 4 kV. The measured anti-resonance frequency and calculated compressive Young’s modulus for the five-layer laminated films are 112 kHz and 0.48 MPa, respectively.

Laminated polytetrafluoroethylene (PTFE) films, which are made of compact and porous PTFE layers, are prepared through the process of sintering. The corona charging technique is utilized to make the laminated PTFE films piezoelectric, thus transforming them into piezoelectrets. The crystallinity, Young's modulus in compression mode, stress-strain behavior, charge dynamics, and thermal stability of the fabricated films are investigated by particular techniques, such as differential scanning calorimetry (DSC), dielectric resonance spectra, dynamic mechanical analysis (DMA), thermally stimulated discharge (TSD) spectra, and isothermal annealing, respectively. The results reveal that the crystallinity of the fabricated PTFE films with three and five-layer systems are 79.5 and 59.8 %, respectively. The compressive and tensile moduli at room temperature are 7.4 and 167 MPa for the three-layer system samples. The resulting temperature peak increases by 20°C as the heating rate increases from 2 to 4°C in TSD measurement. Two charge drift mechanisms exist in the films when the samples are thermally stimulated and discharged. With the increase of corona charging voltage from -10 to -25 kV, more and more detrapped charges from the deeper traps in the laminated PTFE films are released, corresponding to the current peaks identified in the temperature range from 130 to 140°C, which prefer to drift through the solid PTFE layers. However, charges also escaped from the relevant shallow traps, corresponding to the current peaks identified in the temperature that range from 80 to 95°C. The charge drift along the surface of the PTFE fibers is always a dominant mechanism, showing resistance of the corona charging voltage under the experimental-study conditions. The sample shows a stable piezoelectric d 33 coefficient of 50 pC/N at 120°C after one day annealing at the same temperature.

Fluorocarbon polymer films with regular void structure are prepared by using a patterning-fusion bonding process. The critical voltage necessary for the build-up of the 'macro dipoles' in the inner voids observed in the experiments agrees well with the calculated value. The fabricated films show improved thermal stability of the d33 coefficients.

The charging capability and Young's modulus of XPP films can be modified by a hot-stretching process. The results show that the onset of piezoelectricity occurs at an elongation ratio of 70% and enhances with the increase of this ratio. A quasistatic piezoelectric d33-coefficient of 308pC/N is achieved for samples with an elongation ratio of 200% and a Young's modulus of 0.54MPa. An improved piezoelectric d33-coefficient is obtained for samples with a rough surface exposed to the corona during charging.

In this work, to improve the electret properties of cellular polypropylene films, they were fluorinated and post-treated with nitrous oxide and by isothermal crystallization. Surface electret properties of the samples were investigated by thermally stimulated discharge current measurements, and their compositions and structures were analysed by attenuated total reflection infrared spectroscopy and wide angle x-ray diffraction, respectively. Time-dependent deterioration of surface electret properties was observed for the fluorinated samples without the nitrous oxide post-treatment. However, deterioration did not occur for the fluorinated samples post-treated with nitrous oxide, and time-invariant excellent surface electret properties or deep surface charge traps were obtained by the combined post-treatments of the fluorinated samples with nitrous oxide and by isothermal crystallization. Based on the analyses of composition and structure of the treated samples, the deterioration was clarified to be due to a trace of oxygen in the reactive mixture, which led to the formation of peroxy radicals in the fluorinated surface layer. The time invariability of surface electret properties was owing to the rapid termination of the peroxy radicals by nitrous oxide. And the deep surface charge traps resulted from the isothermal crystallization treatment which led to an increase in the efficient charging interface between the crystallite and amorphous region and its property change.

Suitable thermal treatments can be used to modify the microstructure of polymer electrets, which in turn may lead to better electret properties. In this paper, non-porous and porous PTFE films are subjected to a thermal treatment consisting of heating at 320°C for 2 min followed by quenching in liquid nitrogen. The influence of such a treatment on the charge stability of the film electrets is studied by means of thermally stimulated surface-potential decay (charge-TSD) measurements. It is found that the charge stability is slightly reduced by the thermal treatment of non-porous PTFE film electrets, while better electret-charge stability is observed after the thermal treatment of porous PTFE film. The microstructural origin of the observed behavior is investigated and analyzed by means of differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD) and scanning electron microscopy (SEM).

Laminated fluoroethylenepropylene (FEP) and porous polytetrafluoroethylene (PTFE) films with patterned void structure were successfully fabricated. An improved model taking into account of both the mechanical structure and charge distribution was used to describe the behavior of the fabricated films. The Young's modulus of the three-layer FEP/PTFE film is ~0.5 MPa. Maximum quasi-static piezoelectric d33 coefficient up to 500 pC/N is achieved. Compared to the PP piezoelectrets, which loose their piezoelectric activity completely at the annealing temperature of 150 °C within 60 min, the laminated FEP/PTFE films show significantly improved thermal stability. For example, the d33-coefficient retains ~22% of the initial value for samples annealed at 150 °C for 4500 min.

The laminated fluoroethylenepropylene (FEP) and porous polytetrafluoroethylene (PTFE) films with regular void structure are prepared by using a rigid template with a periodic-structured surface. The porous PTFE film is firstly patterned with the rigid template surface by applying force on the stack of porous PTFE film and the template, then followed by the fusion bonding process to bond the FEP and patterned porous PTFE together. The corona charging technique is used to make the laminated film piezoelectric, i.e., to become piezoelectrets. The Young’s modulus of the laminated FEP/PTFE films is determined by dielectric resonance spectra. The thermal stability of the piezoelectric d33 coefficients are characterized by measuring the decay of d33 at elevated temperatures. The charge dynamics in such FEP/PTFE piezoelectrets is investigated by analying the thermally stimulated discharge current spectra in short circuit. The results show that laminated FEP/PTFE films with very regular void structure can be made by using rigid template and fusion bonding process. The Young's modulus of such films is about 0.53 MPa. The maximum quasi-static piezoelectric d33 coefficient up to 500 pC/N is achieved. The laminated FEP/PTFE films show improved thermal stability. For example, the remnant d33value is around 22% of the initial value for the sample annealed at 150 ℃ for 5000 min. For the samples after annealing treatment, the main drift path of the detrapped charges is through the solid dielectric layer.

Fluorocarbon films with regular void structure, made of compact fluoroethylenepropylene (FEP), or skived polytetrafluoroethylene (PTFE), and patterned porous PTFE layers, are successfully fabricated by using a rigid template and fusion bonding process. A corona charging technique is used to make the films piezoelectric, i.e., to be piezoelectrets. The results show that the typical Young’s moduli of the films are in the range of 0.45–0.80 MPa. A maximum quasistatic piezoelectric d33 coefficient up to 500 pC/N is achieved. Compared to the laminated FEP/porous PTFE piezoelectrets without regular void structure, the presently fabricated films show significantly improved thermal stability. Furthermore, when the films are designed, fabricated, and corona charged such that positive charges are deposited in the porous PTFE layers, the thermal stability of d33 coefficients can be further improved. For example, after annealing at 90 °C for 4500 min, these samples have a remaining d33 value of 86% compared with 77% for samples where positive charges are deposited in both, the porous PTFE and the compact FEP layers.

Polytetrafluoroethylene (PTFE) films with void structure are prepared by a fusion bonding process. Such void PTFE films are piezoelectric after proper corona charging. The maximum quasi-static piezoelectric d 33 coefficients of 220 pC/N are achieved. The applied pressure dependence of piezoelectric d 33 coefficients for the void films is associated with the structure of the films. The piezoelectric response of the films is dependent on the duration of the applied force, which is apparently due to the creep of the material.

On the basis of the measurement of open-circuit thermally stimulated discharge current and isothermal charge decay, the influence of isothermal crystallization conditions on charge stability of fluorinated cellular polypropylene (PP) film was systematically investigated. The results indicate that the time and temperature of isothermal crystallization of the fluorinated PP film have significant influences on its charge trap structure and charge stability. Charge traps and charge stability can be significantly deepened or improved even by isothermal crystallization at 90 ℃ for 0.5 h. And with the increase of crystallization temperature and time, charge traps are deepened further, presenting further improved charge stability, as observed in the case of isothermal crystallization at 130 ℃ for more than 2 h. Attenuated total reflection infrared analysis and wide angle X-ray diffraction measurement indicate that the improvement of charge stability results from the changes in chemical composition and structure of the PP film.

Time-dependent change in charge trap of fluorinated cellular polypropylene (PP) films exposed to air is found by thermally stimulated discharge current measurements. It is clarified that the change is due to a trace of oxygen in the reactive gas mixture, which leads to the formations of peroxy RO2* radicals as well as C=O-containing groups in fluorination as indicated by attenuated total reflection infrared analyses. However, time-invariant charge traps of fluorinated PP films can be formed by the post-treatment of fluorinated PP films with nitrous oxide which can effectively terminate the peroxy RO2* radicals. And the combined post-treatments of the fluorinated films with nitrous oxide and by isothermal crystallization generate the time-invariant deep charge traps.

A hard template process for preparing piezoelectret films with ordered void structure was described. By using the fabrication process, fluorocarbon polymer piezoelectret film was prepared. The scanning electron microscope (SEM) images showed that the fluorocarbon polymer film piezoelectret has very regular void structure as expected. The piezoelectricity of the fluorocarbon polymer film was investigated by measuring the quasi-static piezoelectric d33 coefficient using positive piezoelectric effect. The thermal stability of d33 was studied by taking the measurement of d33 decay at elevated isothermal temperatures. The results showed that a piezoelectric d33 coefficient of 300 pC/N was achieved. Compared with the fluorocarbon polymer film with disordered void structure, the film with ordered void structure has much improved thermal stability of d33, which can be further improved by pre-ageing treatment. The piezoelectric d33 coefficient is dependent on the applied pressure considerably in the range of 2—35 kPa, which is probably associated with the enhancement of Young’s modulus of the film with the increasing pressure.

An extremely effective and practical approach is proposed and used for improving charge stability of cellular polypropylene (PP) films. The approach is composed of fluorination and subsequent annealing of the PP films. Surface charge stability is significantly improved by the approach, as revealed by the measurements of open-circuit thermally stimulated discharge (TSD) current, charge TSD and isothermal charge decay at 90°C. As an example, after 7h at 90°C, the amount of surface charge of the treated PP film by the approach still remains about 72% of its initial value, while the corresponding value is only 27% for the virgin PP film. The improvement of charge stability is attributed to chemical composition change and structure modification of the PP films due to the fluorination and annealing treatments, as indicated by attenuated total reflection infrared analyses and wide angle X-ray diffraction measurements. The treatments eliminate the shallow charge traps almost completely and produce much deeper ones.

The piezoelectrets made of porous polytetrafluoroethylene (PTFE) and nonporous fluoroethylenepropylene (FEP) layers are prepared by using a hot-pressing method. The dependence of the quasi-static piezoelectric d(33)-coefficients of such films on the grid voltage during the corona charging is investigated. The thermal stability of d(33)-coefficients for the films is characterized by the isothermal method. The Young's Modulus and dynamic d(33)-coefficient are obtained by analyzing the dielectric resonance spectra of the films. The results show that the Young's modulus is around 2.4 MPa and the quasi-static piezoelectric d(33)-coefficient is about 300 pC/N for the laminated PTFE/FEP films. The d(33) value retains 40% of the initial value when the sample was annealed at 90 degrees C for 20 h. For the samples pre-aged at the temperature of 120 degrees C for 5 h, the remained d(33) value is improved to 75% of the initial value in the same conditions. The d(33) value determined by dielectric resonance spectra is smaller than the quasi-static d(33) value, which is properly due to the enhanced Young's modulus with the increase of frequency.

Piezoelectret film made by cross-linked polypropylene foam sheet was prepared by hot-stretching process.The microstructure of stretched films was observed by SEM technique.The piezoelectric d33-coefficients of the samples,with various degrees of elongation,were determined by a quasi-static method.The applied pressure dependence of piezoelectric d33-coefficients was investigated.The influence of surface structure on piezoelectric activity was discussed also.The results show that the piezoelectricity begins at the degree of elongation 70%.The piezoelectric d33-coefficients are enhanced with the increases of elongation degree.The d33 value of 35 pC/N is obtained for the sample stretched to elongation degree of 150%.All the samples show good linearity in the range of applied pressure up to 30 kPa.Improved piezoelectric activity is obtained for the stretched XPP films when the rough surfaces were exposed to corona.