Imperfect Beam Research Articles

Dynamic stability analysis for rotating pre-twisted FG-CNTRC beams with geometric imperfections restrained by an elastic root in thermal environment

This paper deals with the problems of free vibration, buckling, and dynamic stability of rotating pre-twisted functionally graded carbon nanotube reinforced composite (FG-CNTRC) imperfect beams in thermal environment. The imperfect beam contains different modes of geometric imperfections such as sine, global, and local modes, and it is restrained by an elastic root. Three types of CNTs distributions including FG-X, UD, and FG-O distributions are considered and the material is temperature-dependent. First, bending–bending coupled governing equations are established through the Hamilton’s principle based on the Euler–Bernoulli beam theory. By setting different parameters, the governing equations can solve the problems of free vibration, buckling, and dynamic stability of the beam. Then, the differential quadrature method (DQM) is employed to get the discrete equations and numerical solutions of the natural frequency, critical buckling load, and instability region. Finally, parametric studies are carried out to present the effects of hub radius, rotating speed, material properties, geometric imperfections, and rigidity of the elastic root on the natural frequencies, critical buckling load, and instability regions. Results show that the elastic root and imperfection mode have obvious influence on the instability regions.

Performance Analysis of Millimeter Wave Wireless Power Transfer With Imperfect Beam Alignment

In this paper, the impact of imperfect beam alignment (IBA) on millimeter wave (mmWave) wireless power transfer (WPT) is investigated. We consider a mmWave WPT network, where the location of the energy transmitters follows a Poisson point process. Instead of the mostly used flat-top antenna model, we adopt the Gaussian antenna model suggested by the 3 rd Generation Partnership Project (3GPP) for better accuracy. Two beam alignment error (BAE) models, i.e., truncated Gaussian and uniform models, are introduced to represent different BAE sources. We derive the probability density functions (PDFs) of the cascaded antenna gain with both BAE models and then provide the approximated PDFs for tractability. With the help of Fox's H function, the analytic expression for the energy coverage probability with nonlinear energy harvesting model is derived. Besides, we deduce a closed-form expression of the average harvested radio frequency (RF) energy. The simulation results verify our theoretical results and demonstrate the performance degradation incurred by BAE. It also shows that in the imperfect beam alignment scenario, the Gaussian antenna model can accurately represent the performance of mmWave WPT networks with actual beam pattern, while the flat-top antenna model cannot always provide accurate performance evaluation.

Effects of Staggered Undulator Magnetic Field Contributions on Inverse Free Electron Laser Accelerator

In this paper, we include the important effects of sextupolar field contributions on saturation gain and length of a linear polarized undulator driven inverse free electron laser (IFEL) that arise when the electrons are injected off axis. The modified IFEL equations are derived and analyzed. Both the accelerating gradient and the saturation length of the IFEL are influenced by the imperfect beam trajectory. For a fixed laser wavelength, the effects are more pronounced in the case of short period undulator in comparison with a larger period undulator IFEL. A useful empirical fit is prescribed to estimate the tolerance of the IFEL for imperfect beam trajectory.

Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading

An investigation of the nonlinear thermal buckling behavior of a nano-sized beam constructed from intelligent materials called piezo-magnetic materials has been presented in this article. The nano-sized beam geometry has been considered based on two assumptions: an ideal straight beam and an imperfect beam. For incorporating nano-size impacts, the nano-sized beam formulation has been presented according to nonlocal elasticity. After establishing the governing equations based on classic beam theory and nonlocal elasticity, the nonlinear buckling path has been obtained via Galerkin's method together with an analytical trend. The dependency of buckling path to piezo-magnetic material composition, electro-magnetic fields and geometry imperfectness has been studied in detail.

Extreme Raman red shift: ultrafast multimode nonlinear space-time dynamics, pulse compression, and broadly tunable frequency conversion

Ultrashort high-energy pulses at wavelengths longer than 1 µm are now desirable for a vast variety of applications in ultrafast and strong-field physics. To date, the main answer to the wavelength tunability for energetic, broadband pulses still relies on optical parametric amplification (OPA), which often requires multiple and complex stages, may feature imperfect beam quality, and has limited conversion efficiency into one of the amplified waves. In this work, we present a completely different strategy to realize an energy-efficient and scalable laser frequency shifter. This relies on the continuous red shift provided by stimulated Raman scattering (SRS) over a long propagation distance in nitrogen-filled hollow-core fibers (HCF). We show a continuous tunability of the laser wavelength from 1030 nm up to 1730 nm with a conversion efficiency higher than 70% and high beam quality. The highly asymmetric spectral broadening, arising from the spatiotemporal nonlinear interplay between higher-order modes of the HCF, can be readily employed to generate pulses ( ∼ 20 f s ) significantly shorter than the pump ones ( ∼ 200 f s ) with high beam quality, and the pulse energy can further be scaled up to tens of millijoules. We envision that this technique, coupled with the emerging high-power Yb laser technology, has the potential to answer the increasing demand for energetic multi-TW few-cycle sources tunable in the near-IR.

Finite element based post-buckling analysis of refined graphene oxide reinforced concrete beams with geometrical imperfection

The present paper researches post-buckling behaviors of geometrically imperfect concrete beam resting on elastic foundation reinforced with graphene oxide powders (GOPs) based on finite element method (FEM). Distribution of GOPs are considered as uniform and linearly graded through the thickness. Geometric imperfection is considered as first buckling mode shape of the beam, the GOP reinforced beam is rested in initial position. The material properties of GOP reinforced composite have been calculated via employment of Halpin-Tsai micromechanical scheme. The provided refined beam element verifies the shear deformation impacts needless of any shear correction coefficient. The post-buckling load-deflections relations have been calculated via solving the governing equations having cubic non-linearity implementing FEM. Obtained findings indicate the importance of GOP distributions, GOP weight fraction, matrix material, geometric imperfection, shear deformation and foundation parameters on nonlinear buckling behavior of GOP reinforced beam.

Impact of Intra-Cluster Angular Spread on the Performance of NLoS Millimeter Wave Links With Imperfect Beam Alignment

Beam misalignment is an unavoidable occurrence in millimeter wave (mmWave) wireless communication systems which causes a drop in achievable spectral efficiency (SE) and adversely affects the link-level performance. Spatial parameters of the mmWave propagation channel, especially angle distributions of multi-path components are vital in assessing the loss in achievable capacity due to imperfect beam alignment in such systems. In this paper, we present a tractable approach to quantify the achievable SE of beamformed Non-Line-of-Sight (NLoS) links in mmWave fading channels with intra-cluster angular spread. We derive the expression for achievable SE of a point-to-point mmWave NLoS link after accounting for random beam misalignment errors at the transmitter as well as receiver end. Using analytic approximations, we consider the impact of antenna beam pattern parameters, and use a comprehensive mmWave channel model for performance evaluation. The analysis provides realistic bounds on achievable SE since the intra-cluster angular spread of rays at both ends is taken into account. We provide insights into the interplay between antenna half power beam width, the degree of misalignment, channel fading coefficient, channel coherence parameter and the angular spread of rays to demonstrate the decisive impact of intra-cluster spread on the performance of mmWave point-to-point NLoS links.

Exact solutions for second-order effect of imperfect beams and frames based on matrix structural analysis

Initial member imperfections play important roles in the second-order effect of structures, and thus it is helpful to find ways for engineers to easily model the member imperfections in the analysis. Based on the matrix structural analysis (MSA), this paper presents a method for the exact second-order solutions of imperfect frame structures, which allows the use of one element per member for the exact solution. To develop the second-order MSA method, the fixed-end force vector is formulated in simplified forms to account for the effect of the member initial imperfections and the intermediate loads. Based on the equilibrium analysis of an imperfect axial-loaded beam–column, the element-end displacements and forces are solved exactly from the governing differential equation. The equilibrium relationship between the element-end displacements and forces is developed in a matrix form, which includes a second-order element stiffness matrix and the fixed-end force vector. Some intuitive plots of the fixed-end force vector are presented for convenient applications to typical engineering situations. The established formulations and the intuitive plots are readily coded in an easy-to-use computer program given in the Appendix for analyzing the exact second-order effect of general frames with initial imperfections and intermediate loads. Two illustrative examples are presented to demonstrate the simplicity of the developed second-order MSA approach for a systematic analysis of imperfect frames.

Beam Misalignment Aware Hybrid Transceiver Design in mmWave MIMO Systems

In this letter, we design a beam misalignment aware hybrid analog-digital transceiver to minimize the performance loss owing to imperfect beam alignment in millimeter-wave (mmWave) communication systems. Specifically, we consider the inclusion of the ‘error statistics’ into the precoder and combiner design, where the array response that incorporates the distribution of the misalignment error is first derived. The derived array response spreads the directivity of the beam pattern around the desired direction, thereby minimizing the loss in the array gain under beam misalignment. Accordingly, based on the derived array response, we design the hybrid precoder and combiner approach by approximating their fully-digital design using the gradient projection method. Numerical results show that the proposed hybrid precoder and combiner design can effectively alleviate the performance degradation incurred by beam misalignment.

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations

• Periodic and Nonperiodic Modes on Postbuckling and Nonlinear have been studied. • Closed from solutions for cosine and sine imperfection have been derived. • Effect of non-periodic imperfection has been investigated. • Numerical differential-integral quadrature method is compared by analytical method. • Numerical solution is adopted to investigate the effect of nonlinear elastic foundation. This manuscript presents the influence of periodic (sine and cosine) and nonperiodic imperfections modes on buckling, postbuckling and dynamics of beam rested on nonlinear elastic foundations. The geometric von Kármán nonlinear strains induced by mid-plane stretching is considered. So, the generated equation of motion of imperfect beam is obtained as nonlinear integro-partial-differential equation. Elastic cubic nonlinear and linear springs and shearing layer are proposed to model elastic medium around the imperfected beam. Numerical differential-integral quadrature method (DIQM) in combination with Newton's method are used to find buckling loads and modes of imperfect beam that described by nonlinear integro-differential equation. In linear vibration analysis, the problem is discretized by DIQM and solved as a linear eigenvalue problem. The closed form solutions for static response and linear vibration problem of imperfect beam are obtained. Excellent agreement is observed between proposed numerical and analytical solutions. The numerical results indicate that imperfection modes and its amplitude have a weighty influence on the buckling load, postbuckling configurations and natural frequencies. Finally, numerical results for clamped-clamped (C-C) and simply supported (SS-SS) beams with local (nonperiodic) imperfection modes are presented.

Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams

A Timoshenko functionally graded (TFG) imperfect microscale beam is considered and the coupled viscoelastic mechanics is analysed in a nonlinear regime. Based on the Timoshenko beam theory, incorporating geometric imperfections, the Kelvin-Voigt method is used for internal viscosity, the rotary inertia is automatically generated due to the Timoshenko theory, and the Mari-Tanaka scheme is used for the mixture. After utilising the constitutive stress/strain relations, Hamilton’s principle is used giving three sets of coupled motion equations. A discretisation is performed using Galerkin’s method and numerical simulations, for mechanical behaviour analysis, are built upon a continuation method.

Investigation of Broadband Characteristics of Multi-Frequency Piezoelectric Micromachined Ultrasonic Transducer (MF-pMUT)

Multi-frequency ultrasonic transducers are highly promising devices in biomedical applications for providing both good imaging resolution and large detection depth. However, most conventional multi-frequency ultrasonic transducers are designed through integrating multiple single-frequency transducers, with complicated fabrication process, imperfect beam profiles, and limited bandwidths. In this paper, a single-element multi-frequency piezoelectric micromachined ultrasonic transducer (MF-pMUT) is proposed and investigated in terms of broadband property. Three rectangular-diaphragm MF-pMUTs with different length-to-width aspect ratios are fabricated with the microelectromechanical system (MEMS) technology and characterized both in air and underwater. All MF-pMUT samples exhibit at least two broad bands. After optimization of the aspect ratio, two smooth bands with comparable sound pressure level are achieved, providing -6 dB bandwidths of 112%/38% and corresponding central frequencies of 0.615 MHz/1.63 MHz. Benefited from such broadened multi-frequency property and simple structure design, the proposed MF-pMUT shows a great potential in ultrasonic detection, diagnosis, and imaging applications as well as wireless acoustic energy transmission.

Viscoelastic dynamics of axially FG microbeams

A viscoelastic axially functionally graded (FG) imperfect microbeam is considered and the complex nonlinear dynamics is analysed for the first time. The distribution of the material properties from beam's left end to the right one is of an exponential form. The small nature of the system is incorporated using the couple stress theory (CST) in a modified form. The viscosity between microbeam's infinitesimal elements is incorporated through the Kelvin-Voigt scheme. The elastic part of the energy is formulated via the elastic component of the stress and its couple; the viscous parts are incorporated via a negative work. The energy of kinetic type is also formulated. Without ignoring the axial displacement/inertia, Hamilton's principle of energy is used to formulate the viscoelastic mechanical model of the microsystem. A high-dimensional truncation/discretisation is conducted and numerical simulations are performed based upon it. The complex nonlinear dynamics of the axially FG imperfect beam is analysed in the presence/absence of viscosity.

Coverage Analysis for Millimeter Wave Cellular Networks With Imperfect Beam Alignment

Millimeter wave (mmWave) communications is a promising approach to satisfy the increasing high data rate requirement of next generation mobile communications. This paper studies the downlink coverage performance of mmWave cellular networks with imperfect beam alignment. An enhanced antenna model is adopted to model the directional antenna beamforming pattern, in which the mainlobe beamwidth and directivity gain can be expressed as functions of the number of elements in the antenna array. After deriving the probability density function of the distance between mobile station and its serving base station (BS), the directivity gain with imperfect beam alignment is obtained as a discrete random variable. Then, a computationally tractable expression is obtained for the coverage probability of mmWave cellular networks. This generalized expression can be applied in different blockage regimes, e.g., general blockage regime, full-blockage regime, and nonblockage regime with or without beam alignment errors. Numerical results show that small beam alignment errors will not deteriorate the coverage performance significantly, and the antenna array with the less number of elements provides higher robustness against the beam alignment errors. Moreover, when the beam alignment error is small enough, the coverage performance can be improved by increasing the BS intensity and the number of elements in the antenna array.

Vibration analysis of shear-deformable AFG imperfect beams

The vibrations of axially functionally graded (AFG) beams is examined incorporating shear deformation and an imperfection. A coupled nonlinear model is developed in the Hamiltonian framework for an AFG imperfect beam. Different sources of displacement nonlinearities are involved in this problem, namely, the geometrical nonlinearities due to the large deformations, and the nonlinearities due to the presence of a geometrical imperfection along the length of the beam. Expressions for the virtual work of external excitation and damping as well as formulas for the motion and elastic energies of the system are inserted into Hamilton’s energy/work principle. The equations are truncated employing Galerkin’s technique while incorporating symmetric as well as asymmetric modes. It is shown that the nonuniform material properties along with the tapered geometry of the beam as well as the presence of geometric imperfections results in the contribution of both asymmetric and symmetric vibration modes. Hence, a well-optimised scheme on the basis of a continuation method is developed to solve the high DOF nonlinear problem. Numerical simulations are performed to investigate the influences of the gradient index, the imperfection and the taper values.

Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection

ABSTRACTThermal post-buckling analysis of a geometrically imperfect nanoscale piezoelectric beam under closed circuit condition is performed accounting for the flexoelectricity and surface effects. The flexoelectricity is due to the coupling between electrical polarization and strain gradient. Applying Hamilton's principle, the governing equations and related boundary conditions are derived. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. Obtained results indicate that both the flexoelectricity and surface effects possess notable impact on the post-buckling behavior of the system. Only flexoelectricity yields a considerable difference between the present model and previous investigations on conventional piezoelectric nanobeams. A parametric study has been performed to examine the effects of surface elasticity, flexoelectricity, applied electric voltage, geometrical imperfection, foundation parameters and boundary conditions on post-buckling load of piezoelectric nanobeams.

Free vibration of thermo-electro-mechanically postbuckled FG-CNTRC beams with geometric imperfections

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

Algebra of Classical and Quantum Binary Measurements

The simplest measurements in physics are binary; that is, they have only two possible results. An example is a beam splitter. One can take the output of a beam splitter and use it as the input of another beam splitter. The compound measurement is described by the product of the Hermitian matrices that describe the beam splitters. In the classical case, the Hermitian matrices commute (are diagonal) and the measurements can be taken in any order. The general quantum situation was described by Julian Schwinger with what is now known as “Schwinger’s Measurement Algebra”. We simplify his results by restriction to binary measurements and extend it to include classical as well as imperfect and thermal beam splitters. We use elementary methods to introduce advanced subjects such as geometric phase, Berry-Pancharatnam phase, superselection sectors, symmetries and applications to the identities of the Standard Model fermions.

Sub-ppb nitrogen dioxide detection with a large linear dynamic range by use of a differential photoacoustic cell and a 3.5 W blue multimode diode laser

A sub-ppb level photoacoustic spectroscopy (PAS)-based sensor for nitrogen dioxide (NO2) detection was developed by means of a 3.5W CW multimode diode laser emitting at 447nm. A differential photoacoustic cell was designed to match the imperfect laser beam and reduce the external acoustic as well as the electromagnetic noise. The diode laser power, gas flow and pressure of the sensor were optimized, which resulted in a NO2 sensor system with a detection limit of 54 pptv with a 1-s averaging time and an excellent linear dynamic range over>three orders of magnitude. The impact of water vapor as the catalyst on the photoacoustic signal amplitude was also investigated. Continuous measurements covering an eight-day period were performed to demonstrate the stability and robustness of the reported PAS-based NO2 sensor system.