Sinusoidal Mode Research Articles

Reversible wrinkles of monolayer graphene on a polymer substrate: toward stretchable and flexible electronics.

The surface instability of monolayer graphene supported by a soft (polymer) substrate under equal-biaxial compression has been explored through large scale coarse-grained molecular simulations. Regardless of the interfacial adhesion strength between the graphene and the substrate, herringbone wrinkles have always been observed due to their lowest energy status, compared with the checkerboard, hexagonal, triangular and one dimensional sinusoidal modes. Moreover, the graphene-polymer substrate interaction energy has a negligible effect on the critical strain for the onset of these wrinkles. Yet, if the graphene is bonded to a rigid (non-deformable) substrate, the critical strain increases with increasing graphene-substrate interfacial strength. The surface wrinkles of graphene are delayed and suppressed by the strong bonding of graphene to the rigid substrate. Besides, only localized folds and crumples have been observed on the surface of graphene, when graphene-substrate interaction energy is strong enough. All these observations signal that the deformability (stiffness) of the substrate plays an essential role in determining the morphology of supported graphene under compression. In addition, when a flat graphene is attached on a highly pre-strained (50%) polymer substrate, wrinkles will be formed on its surface during the relaxation of pre-strain within the polymer substrate. The wrinkled graphene could be stretched up to 50% without fracture, accompanied by the diminishing of surface wrinkles. Therefore, it opens a new avenue to enhance the stretchability of graphene materials, and enables the future applications of graphene and other 2D materials in stretchable and flexible electronics.

Effects of mode profile on tunneling and traversal of ultracold atoms through vacuum-induced potentials

We consider the resonant interaction of an ultracold two-level atom with an electromagnetic field inside a high-Q micromaser cavity. In particular, we study the tunneling and traversal of ultracold atoms through vacuum-induced potentials for secant hyperbolic square and sinusoidal cavity mode functions. The phase time which may be considered as an appropriate measure of the time required for the atoms to cross the cavity, significantly modifies with the change of cavity mode profile. For example, switching between the sub and superclassical behaviors in phase time can occur due to the mode function. Similarly, negative phase time appears for the transmission of the two-level atoms in both excited and ground states for secant hyperbolic square mode function which is in contrast to the mesa mode case.

Controlled generation of nonlinear resonances through sinusoidal lattice modes in Bose–Einstein condensate

We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state.

Antisymmetric Post-Buckling Localization of an Infinite Column on a Nonlinear Foundation with Softening

Field observations reveal that very long members such as railway tracks and pipelines which are subjected to axial compression, induced usually by temperature and/or pressure increases, experience localized buckling. This paper presents a solution for the antisymmetric post-buckling of such members when restrained by a nonlinear foundation that includes softening effects. The principle of minimum total potential is invoked in order to develop the governing differential equations of buckling, as well as the non-linear equations of equilibrium in the post-buckled range of structural response. In order to solve these equations, a semi-analytical solution is proposed based on a perturbation technique, as well as a numerical technique based on a single shooting procedure for the solution of boundary value problems. The results of the analysis show that the post-buckling configuration of the column changes from a lengthwise periodic mode at the initial stages of loading to an isolated sinusoidal mode at the later stages of post-buckling, which represents a localization in the post-buckling range. This response is typical of that observed often in practice. Comparisons between the results of the perturbation technique and those of the numerical approach indicate that the semi-analytical perturbation solution predicts the initial post-buckling response of a column on a nonlinear foundation quite accurately.

Non-linear reduced-order model for parametric excitation analysis of an immersed vertical slender rod

A unidirectional three-mode reduced-order model (ROM) for the lateral motion of a slender and immersed rod subjected to harmonic and axial top motion was derived from the continuum equation of motion. Simple trigonometric functions were employed as approximations for the vibration modes and projection functions in Galerkin׳s method. The non-linear character of the ROM comes from the extensibility of the rod axis and the quadratic hydrodynamic damping. The focus of this investigation is the principal Mathieu׳s instability with respect to the first vibration mode, i.e., the condition in which the top-motion frequency is twice the structural first natural frequency. Time histories of modal amplitude, as well as maps of post-critical steady-state vibration amplitudes were obtained and discussed. It is seen that, within the principal parametric instability region of the first mode, the time history corresponding to the second classic (sinusoidal) mode oscillates with dominant frequency of the first classic (sinusoidal) mode. Another finding is that, besides the principal Mathieu׳s instability region, there are also other regions of instability, but with considerably smaller amplitudes. This aspect is due to the non-linear character of the coupled system of equations that defines the ROM.

The electric power generation characteristics of a lead zirconate titanate piezoelectric ceramic under various cyclic loading conditions

The electric power generation properties of lead zirconate titanate (PZT) ceramic have been studied under various cyclic loading conditions. The maximum electric voltage increases with an increase in the frequency under the triangular and sinusoidal wave modes, whereas the voltage decreases with an increase in the frequency for the square wave mode. The maximum electric voltage for all wave modes is saturated at around 15Hz, namely, the electric voltage for the three wave modes is almost constant even if the frequency increases by more than 15Hz. With an increase in the loading frequency (50Hz) under the square and triangular wave modes, the electric voltage generates a sinusoidal-like curve formation, which is not reflected by the loading wave mode. The electric voltage increases with an increase of the frequency for the triangular and sinusoidal wave modes, because of the high kinetic energy. For the square wave formation especially at high frequency, a low electric voltage is obtained, which is caused by the switching back of the electric generation arising from the rapid loading speed. The electric voltage increases non-linearly with increasing loading value, and the voltage values become almost constant when loaded with more than 10N because of the limitation of the amount of electrons in the PZT ceramic. In the early loading stage, the electric voltage values do not increase with high efficiency, in which case the weak fitting of the PZT ceramic plate to the test fixture is affected.

Displacement estimation of bridge structures using data fusion of acceleration and strain measurement incorporating finite element model

Recently, an indirect displacement estimation method using data fusion of acceleration and strain (i.e., acceleration-strain-based method) has been developed. Though the method showed good performance on beam-like structures, it has inherent limitation in applying to more general types of bridges that may have complex shapes, because it uses assumed analytical (sinusoidal) mode shapes to map the measured strain into displacement. This paper proposes an improved displacement estimation method that can be applied to more general types of bridges by building the mapping using the finite element model of the structure rather than using the assumed sinusoidal mode shapes. The performance of the proposed method is evaluated by numerical simulations on a deck arch bridge model and a three-span truss bridge model whose mode shapes are difficult to express as analytical functions. The displacements are estimated by acceleration-based method, strain-based method, acceleration-strain-based method, and the improved method. Then the results are compared with the exact displacement. An experimental validation is also carried out on a prestressed concrete girder bridge. The proposed method is found to provide the best estimate for dynamic displacements in the comparison, showing good agreement with the measurements as well.

Evaluation of empirical mode decomposition for quantifying multi-decadal variations and acceleration in sea level records

Abstract. The ability of empirical mode decomposition (EMD) to extract multi-decadal variability from sea level records is tested using three simulations: one based on a series of purely sinusoidal modes, one based on scaled climate indices of El Niño and the Pacific decadal oscillation (PDO), and the final one including a single month with an extreme sea level event. All simulations include random noise of similar variance to high-frequency variability in the San Francisco tide gauge record. The intrinsic mode functions (IMFs) computed using EMD were compared to the prescribed oscillations. In all cases, the longest-period modes are significantly distorted, with incorrect amplitudes and phases. This affects the estimated acceleration computed from the longest periodic IMF. In these simulations, the acceleration was underestimated in the case with purely sinusoidal modes, and overestimated by nearly 100% in the case with prescribed climate modes. Additionally, in all cases, extra low-frequency modes uncorrelated with the prescribed variability are found. These experiments suggest that using EMD to identify multi-decadal variability and accelerations in sea level records should be used with caution.

Rotating thermoelectric device in periodic steady state

We propose a novel rotating thermoelectric device operating in periodic steady state, whether it is possible to achieve better energy conversion performance for rotating device comparing to conventional stationary steady state. The rotating thermoelectric (TE) cooling device consisting of the single TE conductor is described. It operates in two periodical steady state modes: the switching periodical mode (P-mode) when hot and cold ends of the TE conductor are periodically instantly reversed and the continuous sinusoidal mode (S-mode) when the temperature of TE conductor edges varies continuously according to a sine wave. Cooling and power generation regimes of rotating (TE) device in the periodic steady state was studied analytically. The efficiency and the cooling temperature of rotating TE device was found to depend not only on the dimensionless TE figure of merit, but also upon an additional dimensionless parameter comprising of the rotation period, the size and the thermal diffusivity of the TE conductor. The proposed analytical method can be generalized to even more complex rotating cooling modes and allows us to solve the optimization problem for cooling TE device parameters. The S-mode was shown to demonstrate deeper cooling at certain times.

211 PZT圧電セラミックスの繰返し曲げ応力が及ぼす発電特性の影響

The electric power generation properties of lead zirconate titanate (PZT) ceramic have been studied under various cyclic loading conditions. The maximum voltage increases with an increase in the frequency under the triangular and sinusoidal wave modes, whereas the voltage decreases with an increase in the frequency for the square wave mode. The maximum electric voltage for all wave mode is saturated at around 15Hz, namely, the electric voltage for the three wave modes is almost constant even if the frequency increases by more than 15Hz. The maximum electric voltage increases with an increase in the frequency under the triangular and sinusoidal wave modes, because of the high kinetic energy. For the square wave mode especially at high frequency, a low electric voltage is obtained, which is caused by the switching back of the electric generation arising from rapid loading speed.

Toward the Design of Multi Asymmetric Surface Dielectric Barrier Discharge (ASDBD) Actuators

This paper investigates the electrical and mechanical behaviors of a single-ASDBD actuator and a two-ASDBD one supplied in sinusoidal mode (1–10 kHz). The main objective of our research is to determine the optimum frequency values for the function of these actuators with a given power supply. For this purpose, we determine the electrical power density input to the actuators versus frequency through two methods: i) a semi-theoretical method, based on an impedance calculation, and ii) an experimental method, based on direct electrical measurements. These methods show that the addition of a second ASDBD changes the resonance frequency value of the actuator by moving it towards low frequencies. After characterizing the aerodynamic mobile layer structure induced by the single-ASDBD actuator, we analyze experimentally the mechanical response of a two-ASDBD actuator as a function of the inter-ASDBD distance. The experiments demonstrate that the induced electric wind velocity and the electro-mechanical yield of a two-ASDBD actuator reach a maximum value for an optimum inter-ASDBD distance, which is a useful value for the design of highly efficient multi-ASDBD actuators.

Dielectric Properties Measurement of Biological Materials Using Non-Destructive Sensors

The authors' research work has for objective the study of a sensor with planar resonator for applications in the non-destructive control. In this context, two approaches were defined. In a first part, a conception, a modeling, a simulation with commercial software (HFSS, CST), a realization and measurements were treated on Rectangular Patch Resonators (RPR). The proposed theoretical analysis is based on the Moment Method (MoM) via the Galerkin's approach, in which three types of entire domain basis functions are used to expand the patch currents. While, the first two types of basic functions involve a set of sinusoidal cavity modes without edge conditions (sbf-wo-ec) and with edge conditions (sbf-w-ec), and in order to incorporate the edge conditions (cp-ec), the third one consists of Chebyshev polynomials combinations with weighting factors. These last ones as well as the Green Dyadic spectral functions are efficiently implanted with compact Fortran 90 codes. Two EM commercial software HFSS and CST was used to validate the proposed RPR prototypes. The exactness of the obtained results is estimated using four prototypes operating near 6 GHz, taking into account only the fundamental mode resonant frequency. The theoretical model is compared with the simulations and the measurement results. The second approach of the authors' work which is developed in this paper is focused on the characterization of biological materials in vitro using the RPR prototypes proposed as applicator in the non-destructive control and the medical domain to find the abnormalities of these tissues such as: eczema, psoriasis, cancer, etc. The authors' center of interest will be managed towards the dielectric properties of the biological material to extract the relative permittivity and the loss factor on several samples (liver, fat, chicken, butter, foie gras, etc.).

Multiple bifurcations in wrinkling analysis of thin films on compliant substrates

Wrinkling phenomena of stiff thin films on compliant substrates are investigated based on a non-linear finite element model. The resulting non-linear equations are then solved by the Asymptotic Numerical Method (ANM) that gives interactive access to semi-analytical equilibrium branches, which offers considerable advantage of reliability compared with classical iterative algorithms. Bifurcation points are detected through computing bifurcation indicators well adapted to the ANM. The effect of boundary conditions and material properties of the substrate on the bifurcation portrait is carefully studied. The evolution of wrinkling patterns and post-bifurcation modes including period-doubling has been observed beyond the onset of the primary sinusoidal wrinkling mode in the post-buckling range.

Shear displacement controlled periodic wrinkles in hexagonal boron nitride sheet

The initiation and geometry pattern of wrinkles in a single-layer hexagonal boron nitride sheet induced by in-plane shear displacement are studied. The periodic wrinkles in the central region are parallel to each other with an angle of approximate 50° to the fix edges, and the longitudinal shape of the wrinkle matches the sinusoidal mode shape well. The wrinkle wavelength decreases with an increase in shear loading, while the amplitude is found to initially increase and then become stable. The dependence of the wrinkle geometry on chirality and shear direction is further elucidated. This study theoretically provides a powerful way to produce uniform wrinkles in two-dimensional membranes and to tune their properties in devices.

Optical pulse controlled two mode interference coupler based logic gates

In this paper, an optical pulse controlled 1×2 two mode interference (OTMI) coupler having silicon core and GaAsInP cladding has been introduced as NOT and AND gates. The coupling characteristics of OTMI coupler are analyzed by using a simple mathematical model based on sinusoidal modes. It is seen that the length of OTMI based logic gate is eight times lower than that of existing MMI coupler based logic gates and the effect of power imbalance on fabrication tolerances of the device is also less than that of MMI device.

Toward the Design of Multi Asymmetric Surface Dielectric Barrier Discharge (ASDBD) Actuators

This paper investigates the electrical behaviors of a single-ASDBD actuator and a two- ASDBD one supplied in sinusoidal mode (1-10 kHz). The main objective of our research is to determine the optimum frequency values for functioning of these actuators with a given power supply. For that purpose, we determine the electrical power density transmitted to the actuators versus frequency through two methods: i) a theoretical method, based on an impedance calculation, and ii) an experimental method, based on direct electrical measurements. These methods show that the addition of a second ASDBD changes the resonance frequency value of the actuator by moving it towards the low frequencies.

Extension of indirect displacement estimation method using acceleration and strain to various types of beam structures

The indirect displacement estimation using acceleration and strain (IDEAS) method is extended to various types of beam structures beyond the previous validation on the prismatic or near-prismatic beams. By fusing different types of responses, the IDEAS method is able to estimate displacements containing pseudo-static components with high frequency noise to be significantly reduced. However, the concerns to the IDEAS method come from possible disagreement of the assumed sinusoidal mode shapes to the actual mode shapes, which allows the IDEAS method to be valid only for simply-supported prismatic beams and limits its applicability to real world problems. In this paper, the extension of the IDEAS method to the general types of beams is investigated by the mathematical formulation of the modal mapping matrix only for the monitored substructure, so-called monitoring span. The formulation particularly considers continuous and wide beams to extend the IDEAS method to general beam structures that reflect many real bridges. Numerical simulations using four types of beams with various irregularities are presented to show the effectiveness and accuracy of the IDEAS method in estimating displacements.

Extension of indirect displacement estimation method using acceleration and strain to various types of beam structures

The indirect displacement estimation using acceleration and strain (IDEAS) method is extended to various types of beam structures beyond the previous validation on the prismatic or near-prismatic beams. By fusing different types of responses, the IDEAS method is able to estimate displacements containing pseudo-static components with high frequency noise to be significantly reduced. However, the concerns to the IDEAS method come from possible disagreement of the assumed sinusoidal mode shapes to the actual mode shapes, which allows the IDEAS method to be valid only for simply-supported prismatic beams and limits its applicability to real world problems. In this paper, the extension of the IDEAS method to the general types of beams is investigated by the mathematical formulation of the modal mapping matrix only for the monitored substructure, so-called monitoring span. The formulation particularly considers continuous and wide beams to extend the IDEAS method to general beam structures that reflect many real bridges. Numerical simulations using four types of beams with various irregularities are presented to show the effectiveness and accuracy of the IDEAS method in estimating displacements.

Numerical investigation for effects of actuator parameters and excitation frequencies on synthetic jet fluidic characteristics

Numerical investigation is performed to further address the effects of geometric parameters and excitation frequency of the actuator on the synthetic jet fluidic characteristics by utilizing a two-dimensional unsteady Reynolds-averaged Navier–Stokes model. The vibrating diaphragm is modeled as a movable wall varying in sinusoidal mode. Computations are carried out by using FLUENT software with the coupled user definition function (UDF) describing the diaphragm movement. The results show that the geometric parameters of the actuator, such as the cavity depth and diameter, as well as orifice thickness and diameter, have important influences on the synthetic jet fluidic characteristics. The velocity output could be maximized if the geometric parameters of the synthetic jet actuator are designed to ensure that the cavity acoustic Helmholtz resonance frequency is coincided with the diaphragm excitation frequency. For a fixed actuator cavity, when the diaphragm excitation frequency is consistent with the Helmholtz resonance frequency of actuator cavity, the relative pressure insides the cavity is obviously great during the ejection stroke while low during the suction stroke. In the presented actuator parameters, the synthetic jet is enhanced as the decrease of cavity depth for the fixed orifice. The change of cavity diameter in the vicinity of corresponding cavity acoustic resonance diameter has relatively weaker influence on the synthetic jet. When the diaphragm is excited at high frequency, small orifice diameter will restrict the ejection and suction capacity of the synthetic jet actuator.

Solutions of dynamic and acoustic responses of a clamped rectangular plate in thermal environments

This work presents an investigation of vibration and acoustic response characters of a clamped rectangular thin plate in thermal environments. The general form of governing equation of plate flexural vibration with considering thermal loads is established, and the influence of uniform temperature change on response characters is studied in detail. A set of double sinusoidal mode shape functions for fully clamped boundaries is used to describe the displacement distribution. The governing equation is solved with Fourier series expansion to discuss the natural vibration and dynamic responses of a clamped plate in thermal environments. Accordingly, acoustic radiation characteristics are obtained based on Rayleigh integral. Results show that natural frequencies decrease with the increment of plate temperature, and the first natural frequency is much more sensitive to thermal environment changes. Response curves of plate vibration and radiated sound power shift toward lower frequency range, and the response amplitudes of the first resonant peak of the two responses present opposite variation tendencies. These phenomena are verified with finite element and boundary element simulations. Thermal loads reduce the radiation efficiency of the plate obviously below the critical frequency, but the maximum value almost remains unchanged.