Theoretical investigation of interaction between a rectangular plate and fractional viscoelastic foundation

The interaction between plates and foundations is a typical problem encountered in geotechnical engineering. The long-term plate performance is highly dependent on the theological characteristics of ground soil. Compared with conventional linear theology, the fractional calculus-based theory is a more powerful mathematical tool that can address this issue. This paper proposes a fractional Merchant model （FMM） to investigate the time-dependent behavior of a simply supported rectangular plate on viscoelastic foundation. The correspondence principle involving Laplace transforms was employed to derive the closed-form solutions of plate response under uniformly distributed load. The plate deflection, bending moment, and foundation reaction calculated using the FMM were compared with the results obtained from the analogous elastic model （EM） and the standard Merchant model （SMM）. It is shown that the upper and lower bound solutions of the FMM can be determined using the EM. In addition, a parametric study was performed to examine the influences of the model parameters on the time- dependent behavior of the plate-foundation interaction problem. The results indicate that a small fractional differential order corresponds to a plate resting on a sandy soil foundation, while the fractional differential order value should be increased for a clayey soil foundation. The long-term performance of a foundation plate can be accurately simulated by varying the values of the fractional differential order and the viscosity coefficient. The observations from this study reveal that the proposed fractional model has the capability to capture the variation of plate deflection over many decades of time.

Different effect of Li^(+),Na^(+),K^(+)-doping on crystal structure and electrical property of Sr_(0.6)Ba_(0.4)Nb_(2)O_(6)

Ferroelectric Sr_(0.6)Ba_(0.4)Nb_(2)O_(6)(SBN)shows typical unfilled tetragonal tungsten bronze structure where 1/6 A sites and all C sites are unoccupied.The presence of such structural vacancy provides the possibility to further modulate the crystal structure and electrical properties.In this work,alkali ions(Li^(+),Na^(+),K^(+))doped SBN ceramics have been fabricated via solid-solution reaction method.In general,each doping promotes the crystal structure evolves from unfilled toward filled tungsten bronze.However,the different doping ion radius causes the differences in occupying initial structural vacancies,resulting in significantly different electrical properties,Li^(+)doping enhances relaxor characteristic whereas Na+and K^(+)doping lead to normal ferroelectric behavior,accompanying an increase in Curie temperature(TC)from 36℃ of SBN to 40,212,148℃ of Li^(+),Na^(+)and K^(+)doping,respectively.Benefiting from improved relaxor degree and high density,the Li^(+)doped SBN displays a good energy storage performance.Since the ratio of Sr/Ba and(Sr+Ba)/Nb has not been changed,this work presents direct evidence for the effect of structural vacancy on crystal structure and properties,as well as inspiration for further work on unfilled tungsten bronze.

Suppressing longitudinal spatial hole burning with dual assisted phase shifts in pitch-modulated DFB lasers

An equivalent corrugation pitch-modulated （ECPM） distributed feedback （DFB） semiconductor laser with two equivalently assisted phase shifts （EAPS） was theoretically studied and experimentally demonstrated. The simulated results showed that the longitudinal photon density distribution of the ECPM ＋ EAPS DFB lasers was much more uniform than that of a sole ECPM DFB laser without EAPS, and the longitudinal spatial hole burning was therefore suppressed more effectively. The results of experiment showed that good single longitudinal mode operation was achieved, with side mode suppression ratio （SMSR） being over 35 dB, and the wavelength range was from 1,559.64 to 1,563.02 nm when the operation current was from 50 to 160 mA at the temperature of 25 ℃, and the SMSR increased to 46.29 dB when the injection current was 130 mA.