Analytical Solution For Response Research Articles

Study on longitudinal vibration of a pile with variable sectional acoustic impedance by integral transformation

A study on longitudinal vibration of a pile with variable sectional acoustic impedance subjected to arbitrary form of external excitation is conducted. The analytical solution of transfer function is primarily solved by Laplace transform, and then its corresponding impulse response function is solved by residue method of inverse Laplace transformation. With impulse response function, the analytical solution of response at pile top can be obtained by convolution calculation, which overcomes the limit of previous analytical solutions subjected to prescribed time-harmonic load. The accuracy of presented solution is verified by compared with existing solutions subjected to semi-sine excitation and low-strain test of model piles. To take advantage of presented solution, this paper also proposes a case study of imposed excitation considering superimposed high-frequency interference component, and some conclusions derived from this case can provide practical guidance for engineering implementation.

Analytical and numerical solutions on the response of pore pressure to cyclic atmospheric loading: with application to Horonobe underground research laboratory, Japan

During the long-term stability assessment of underground disposal repositories buried in sedimentary formations, one of crucial scientific problems is to determine parameters of site formations. The analysis of response of the pore pressure due to atmospheric loading provides a possible way of accurate estimation of formation parameters. In this paper, an analytical solution of response of the pore pressure to atmospheric loading was derived starting from the Biot’s poroelasticity, and its corresponding numerical solutions were developed by finite element methods for 1D and 2D situations. With comparison to the analytical solution, the experimental results show that the numerical schemes sound reasonable to implement the assessment of response of the pore pressure in horizontal multilayer sedimentary formations. In particular, it is effective for a 2D model over large area with consideration of background horizontal groundwater flow. A highlight of this work is to construct a reasonable approach to capture responses of the pore pressure to atmospheric loading, and at the same time to provide the feasibility of integrated analysis of well monitoring data of pore pressure variance in Horonobe Underground Research Laboratory (URL), Hokkaido, Japan.

Analytical solution for response of ferroelectric thin film to infrared radiation

Abstract Micro-bolometer pixel is an essential element in the infrared focal plane array (IRFPA) of infrared detectors. Its response to infrared radiation is analyzed in this paper. The pixel structure is modeled as a composite laminate thin plate whose sides are measured with the thickness from 0.1-1 μm. Its middle ply is a ferroelectric thin film. Its top surface is covered with a gold or platinum infrared absorber, while the bottom surface is deposited with platinum or lanthanum-nickel. Meanwhile both surfaces are a pair of electrodes. The top surface receives infrared radiation pulses successively. For the very tiny micro bolometer pixel, it is assumed that the infrared radiation is uniformly distributed on the plate. Furthermore, as the ratio of the side length to the thickness of the plate is dramatically large, it is assumed that heat transfer only takes place across the thickness of the plate. The thermal-electric-mechanical coupling governing equations are solved in a form of Fourier series. Results of the displacement, temperature variation and electric output signals of the micro bolometer pixel structure under infrared radiation are obtained, analyzed and compared with experimental data.

Response of an enzyme-modified pH-sensitive ion-selective device; analytical solution for the response in the presence of pH buffer

An analytical solution for the steady-state response of an enzyme-modified pH-sensitive ion-selective device in the presence of pH buffer is derived. The model assumes effective equilibrium is maintained between the buffer and protons and describes the enzyme reaction rate in terms of conventional Michaelis-Menten kinetics, though no account is made for any pH dependence in the kinetics. Theoretical response curves, consistent with those observed experimentally, are derived, illustrating their dependence upon buffer capacity, solution pH and various kinetic parameters. Limitations to the analytical application of the device are considered.