A simple and efficient coupled displacement field method is developed to study the large amplitude free vibration behavior of the moderately thick square plates.A single term trigonometric admissible displacement fiel...A simple and efficient coupled displacement field method is developed to study the large amplitude free vibration behavior of the moderately thick square plates.A single term trigonometric admissible displacement field is assumed for one of the variables,say,the total rotations(in both X,Y directions).Making use of the coupling equation,the spatial variation for the lateral displacement field is derived in terms of the total rotations.The coupled displacement field method makes the energy formulation to contain half the number of unknown independent coefficients,in the case of a square plate,contrary to the conventional RayleighRitz method.The lesser number of undetermined coefficients significantly simplifies the vibration problem.The expressions for the linear and nonlinear fundamental frequency parameters for the all edges simply supported moderately thick square plates are derived.The numerical results obtained from the present formulation are in very good agreement with those obtained from the existing literature.展开更多
The ternary phosphate glass series(50-x)CaO-xCaF_(2)-50P_(2)O_(5)(x=0-20 mol%)were synthesized using melt quench technique.Structural,optical and mechanical properties were investigated with increase in CaF_(2) conten...The ternary phosphate glass series(50-x)CaO-xCaF_(2)-50P_(2)O_(5)(x=0-20 mol%)were synthesized using melt quench technique.Structural,optical and mechanical properties were investigated with increase in CaF_(2) content.Using X-ray diffraction(XRD),synthesized glasses were confirmed to be amorphous in nature.Replacement of oxygen ions by fluorine ions increased the values of density.Decrease in refractive index due to the low polarizability of fluorine ions in the glass matrix was observed.In Fourier transform infrared(FTIR)spectra,the slight variation in v_(as)(PO_(2))band position and intensity could be attributed to replacement of fluorine ions for oxygen ions in phosphate glass structure.These data were well supported by Raman spectra.Optical band gap energy increased from 3.44 eV to 3.64 eV with increase in CaF_(2) content,and Urbach energy decreased suggesting that the fluorine ions reduced the tail energy states in the band gap compared to the oxygen ions.Mechanical parameters such as Vickers hardness,fracture toughness and brittleness were evaluated from the Vickers micro indentation measurements.Increase in Vickers hardness,decrease in fracture toughness and increase in brittleness were observed with increase in CaF_(2) content.展开更多
基金JNTU-Kakinada for sponsoring the necessary economical support for presenting the paper under TEQIP2the support given by Mallareddy college of engineering and Indian national academy of engineering
文摘A simple and efficient coupled displacement field method is developed to study the large amplitude free vibration behavior of the moderately thick square plates.A single term trigonometric admissible displacement field is assumed for one of the variables,say,the total rotations(in both X,Y directions).Making use of the coupling equation,the spatial variation for the lateral displacement field is derived in terms of the total rotations.The coupled displacement field method makes the energy formulation to contain half the number of unknown independent coefficients,in the case of a square plate,contrary to the conventional RayleighRitz method.The lesser number of undetermined coefficients significantly simplifies the vibration problem.The expressions for the linear and nonlinear fundamental frequency parameters for the all edges simply supported moderately thick square plates are derived.The numerical results obtained from the present formulation are in very good agreement with those obtained from the existing literature.
文摘The ternary phosphate glass series(50-x)CaO-xCaF_(2)-50P_(2)O_(5)(x=0-20 mol%)were synthesized using melt quench technique.Structural,optical and mechanical properties were investigated with increase in CaF_(2) content.Using X-ray diffraction(XRD),synthesized glasses were confirmed to be amorphous in nature.Replacement of oxygen ions by fluorine ions increased the values of density.Decrease in refractive index due to the low polarizability of fluorine ions in the glass matrix was observed.In Fourier transform infrared(FTIR)spectra,the slight variation in v_(as)(PO_(2))band position and intensity could be attributed to replacement of fluorine ions for oxygen ions in phosphate glass structure.These data were well supported by Raman spectra.Optical band gap energy increased from 3.44 eV to 3.64 eV with increase in CaF_(2) content,and Urbach energy decreased suggesting that the fluorine ions reduced the tail energy states in the band gap compared to the oxygen ions.Mechanical parameters such as Vickers hardness,fracture toughness and brittleness were evaluated from the Vickers micro indentation measurements.Increase in Vickers hardness,decrease in fracture toughness and increase in brittleness were observed with increase in CaF_(2) content.
