Imperfect Beam Research Articles

Exact shape functions of imperfect beam element for stability analysis

In this paper, a versatile and efficient solution for the displacement function of a geometrical imperfect beam element under high axial load is derived. The initial imperfection is included by a sine curve approximation. The aim of this work is to propose a natural extension of the element by stability functions. For this purpose, exact displacement shape functions are solved from the differential equilibrium equation, by using arbitrary boundary conditions. These shape functions offer the possibility to express the equivalent nodal forces for any arbitrary transverse loads, and are further extended to obtain the equivalent nodal forces relating to the effect of the initial curvature without affecting the boundary conditions of the element. The accuracy of this element makes the convergence rate better than the conventional cubic element or other used elements. Euler’s critical load is computed readily with no more than two iterations for each step loading with a single element per member. By using these exact shape functions in computer software, the second-order analysis and the nonlinear integrated design become reliable and easy to use for practical purposes.

Buckling dynamics of imperfect Elastica subject to various loading conditions

Buckling dynamics of a pinned-pinned flexible imperfect beam attached to a sliding mass is investigated using nonlinear Elastica theory. Initially straight flexible buckling beam having pinned end boundary conditions loaded at one of its end with curved imperfection is considered. Large deflection analysis of flexible beam is studied using nonlinear Elastica theory. Imperfection analysis of the flexible beam is investigated considering the imperfection as an initial curvature. The governing differential equations are expressed in terms of nonlinear functions that are typical of flexible beams, generally leading to highly implicit relationships involving elliptic integrals and functions. Dynamic simulation of the flexible beam is studied using numerical simulation procedures with various types of loading (step, ramp, and sinusoidal) assuming this member buckles in its first mode. Dynamic response of the imperfect buckling Elastica has been obtained by using numerical Runge-Kutta methods. Load deflection characteristics of flexible beams are presented in polynomial curve fits. The polynomial curve fits obtained from nonlinear inextensible exact beam theory may then be used as the nonlinear lumped system stiffness. The buckling Elastica may find applications in compliant mechanism design. The motivation behind this research is not only to present the dynamic behavior of the buckling beam considering the magnitude of the imperfection but also to provide a tool to design new types of compliant mechanisms. Original compliant mechanism designs are presented demonstrating where the buckling dynamics of imperfect Elastica or flexible curved beams might be needed in mechanism design and synthesis.

Precision measurement scheme using a quantum interferometer

We present a scheme that makes use of quantum mechanical entanglement to significantly enhance the measurement precision accessible by interferometers. This is achieved by making use of a special type of interferometer composed of two ``quantum beam splitters,'' which each transform the input particles into a macroscopic superposition at the outputs. We show that this technique not only enables phase measurements to be made with Heisenberg limited precision, but also overcomes the major practical problems of detector inefficiencies and imperfect beam splitters. It may provide a promising route to implementing sub-shot-noise limited measurement schemes in the laboratory.

Betatron contributions to the angular gain spectrum of a free-electron laser with an imperfect beam trajectory

The effect of betatron oscillations on the angular gain spectrum of a free-electron laser is examined in the case of an imperfect beam trajectory. The use of an axial magnetic field is suggested to improve the beam–mode coupling and gain of the laser.

Photoresist line-edge roughness analysis using scaling concepts

We focus on the problem of obtaining and characterizing the edge roughness of photoresist lines by analyzing top-down scanning electron microscope (SEM) images. An off-line image analysis algorithm detecting the line edge, and an edge roughness characterization scheme, based on scaling analysis, are briefly described. As a result, it is suggested that apart from the rms value of the edge (sigma), two more roughness parameters are needed: the roughness exponent and the correlation length . These characterize the spatial complexity of the edge and determine the dependence of sigma on the length of the measured edge. Completing our previous work on the dependencies of the roughness parameters (sigma,,) on various image analysis options, we examine the effect of the type of noise smoothing filter. Then, a comparative study of the roughness parameters of the left and right edges of resist lines is conducted, revealing that the sigma values of the right edges are larger than those of the left edges (due to an imperfect SEM beam alignment), whereas the roughness exponents and the correlation lengths do not show such a trend. Finally, the relation between line width roughness and line edge roughness is thoroughly investigated with interesting conclusions.

Shell Theory Accuracy with Regard to Initial Postbuckling Behavior of Cylindrical Shell

are the normal strains in the prebuckling state. The buckling anal- ysis for the nondebonded imperfect beams is then similar to that presented earlier for the free-vibration problem. In the case of a generally debonded beam, an exact buckling solution cannot be obtained and approximate treatments should be employed. How- ever, if the beam is with through-length delamination at the kth interface, for example, an exact solution can be obtained, just as it can for the nondebonded imperfect beam, but with K (k)

Closed-loop non-linear control of an initially imperfect beam with non-collocated input

A closed-loop non-linear control strategy to reduce the flexural vibrations of a hinged–hinged initially imperfect beam is investigated. The beam is subjected to a harmonic transverse excitation involved in a primary resonance of the first antisymmetric mode. A closed-loop symmetric control action—bending moments imparted by two piezoceramic actuators—although non-collocated, is designed to be non-orthogonal, in a non-linear sense, to the excited mode and be capable of exerting resonant beneficial damping effects onto it. The approximate responses of the controlled and uncontrolled beam are constructed by applying the method of multiple scales directly to the integral–partial differential equations of motion and boundary conditions. The frequency response curve governing the primary resonance of the uncontrolled system is compared with that obtained when the controller is in action. It is shown that, by exerting feasible control efforts, the response of the beam may be reduced by an order of magnitude and is stable in the overall frequency range in contrast with the uncontrolled large-amplitude responses which undergo jumps at the saddle-node bifurcations.

Properties of the linearized quantum optical bus

A formalism is developed that allows one to calculate the propagation of quantum noise, technical noise, and signals through a linearized quantum optical bus, i.e., a complex composite multibeam optical quantum system. General expressions for the output squeezing, the correlation coefficient, and quantum correlation coefficient between output observables and the transfer coefficients are derived and discussed in detail. The total correlation is introduced as a measure of the overall correlation of a set of output quadratures. From its geometric interpretation a multidimensional uncertainty relation is derived. Direct quantum-state preparation (QSP) is introduced as a method complementary to the conventional, indirect QSP. The minimal variance achievable by direct QSP is shown to provide superior noise suppression, including quantum noise suppression, than the conditional variance provided by indirect QSP. As an application we calculate and discuss the properties of a balanced bus of beam splitters with squeezed vacua at the usually unused ports. An important experimental effect is imperfect beam mode match, which is shown to lead to dramatic effects. A theory is derived which quantitatively matches measurements. Analytic expressions for the imperfectly modematched squeezed-light beam splitter including detection losses are given. Finally, a direct method is used to calculate the input-output matrix for the multiport subthreshold degenerate optical parametric amplifier for arbitrary parametric and mirror coupling strengths and detuning.

Adaptive compensation of phase and magnitude aberrations

A new method for aberration correction is presented. Using multiple receive beams reconstructed at each transmit direction, image artifacts due to imperfect beam forming can be identified and greatly reduced. Previous studies have demonstrated the efficacy of such a compensation algorithm for blocked elements. In this study, the algorithm is extended for magnitude and phase aberrations. Experimental results show that substantial improvements are possible for small amplitude and phase errors. The compensation method is less effective for large errors, however. Based on this, a two-step procedure is proposed for general aberration correction. First, cross-correlation processing is used to reduce significant phase errors. Then, the adaptive compensation method is applied to remove remaining artifacts due to blocked elements, amplitude aberrations, and residual phase errors. This two-step procedure is shown to be effective in significantly reducing image artifacts due to amplitude and phase errors.

Polarization characteristics of spontaneous emission and off-axis coherent gain in a free-electron laser.

The polarization characteristics of spontaneous radiation from relativistic electrons moving through helical and planar wiggler fields are evaluated for imperfect beam injection. Maximum coherent gain in free-electron laser systems are seen to occur in optical fields having these polarization characteristics rather than those of the wiggler magnets. Coupling coefficients for an electron beam skewed at an angle to the optical mode are presented.

Custom Beam Profiles in Computer-Controlled Radiation Therapy: International Journal of Radiation Oncology, Biology, and Physics, Vol. 22, No. 1, 1992, pp. 167–174

A computer-controlled radiation therapy technique is demonstrated which uses multiple concurrent boost fields to modify the beam profile of a conventional treatment beam. A principal field, identical to that of a corresponding conventional treatment plan, delivers the major component of the prescribed dose. Dose increments given from boost fields placed within this principal field compensate for variations in patient anatomy, for variations in target volume shape, and/or for imperfect beam characteristics, such as excessive off-axis dose or inadequate beam wedge angle. This concurrent boost field technique is demonstrated for several treatment sites. It produces significant improvement in uniformity of dose delivered to the target compared to conventional treatment. Implementation of these treatments requires a computer-controlled linear accelerator with independently-movable collimator jaws, an automatic beam set-up procedure, and a patient prescription database. Since all fields are delivered under computer control, concurrent boost technique treatment times are not much longer than those of conventional treatments.

Custom beam profiles in computer-controlled radiation therapy

A computer-controlled radiation therapy technique is demonstrated which uses multiple concurrent boost fields to modify the beam profile of a conventional treatment beam. A principal field, identical to that of a corresponding conventional treatment plan, delivers the major component of the prescribed dose. Dose increments given from boost fields placed within this principal field compensate for variations in patient anatomy, for variations in target volume shape, and/or for imperfect beam characteristics, such as excessive off-axis dose or inadequate beam wedge angle. This concurrent boost field technique is demonstrated for several treatment sites. It produces significant improvement in uniformity of dose delivered to the target compared to conventional treatment. Implementation of these treatments requires a computer-controlled linear accelerator with independently-movable collimator jaws, an automatic beam set-up procedure, and a patient prescription database. Since all fields are delivered under computer control, concurrent boost technique treatment times are not much longer than those of conventional treatments.

A LIMIT ANALYSIS OF LATERAL BUCKLING OF SLENDER CONCRETE BEAMS.

Keywords CAIRO AIN SHAMS UNIVERSITY, HERIOT WATT UNIVERSITY LIMIT ANALYSIS, LIMITS, ANALYSIS, LATERAL, BUCKLING, SLENDER, CONCRETE, BEAMS, INCREMENTAL, COMBINED, BENDING, TORSION, STRESS, RESULTANTS, LOADS, GEOMETRIC, IMPERFECT, LINEAR, MOMENTS, NON LINEAR, CURVATURE, SPECIFIC, TWIST, CHARACTERISTICS, INCREMENT, ITERATIVE, PROCEDURE, METHODS, LOADING, RECTANGULAR, I BEAMS, ELASTIC, RANGE, CURVES, INSTABILITY, RELATIONS, EXPERIMENTS, FAILURES, ENERGY, STIFFNESS, COEFFICIENTS, EQUATIONS... Show All

Vibration of geometrically imperfect beam and shell structures

The purpose of this paper is to present a general theory for analysis of the effect of initial geometrical imperfections on vibration frequencies of undamped, conservatively loaded, linear elastic beam and shell structures. The theory will be restricted to single mode vibrations with imperfections in the same shape as the vibration modes. The mathematical tool is a perturbational procedure developed with the aid of the principle of virtual work. The approach is illustrated by applications to beams, plates and axisymmetric shell structures. The examples show that the vibration frequency of these structures may be significantly raised or lowered due to imperfections.

Dynamic response of a rigid-plastic simply-supported imperfect beam subjected to a uniform intense dynamic loading

This paper presents a theoretical analysis for the dynamic response of a rigid-perfectly plastic simply-supported beam with an imperfection in its midspan cross-section under uniform step, pulse or impulsive loading, while the supports are assumed to be free to move inwards. The complete solutions for the entire dynamic response process are obtained, and the dependence of the distribution of energy dissipated upon the imperfection parameter is discussed.

Measurement of 1-μm diam beams

Measurements of beams of ~1 μm in diameter are presented. Three approaches, one using a Ronchi ruling, the other two based on knife-edge scan techniques are compared experimentally. Effects of Ronchi ruling accuracy and nonconstant scan velocity are discussed. Included are results of theoretical studies on the effect of imperfect scanning edges and non-Gaussian beam profiles on measurement results.

A new pseudostatistical time-of-flight spectrometer for quasielastic neutron scattering studies

A new time-of-flight spectrometer with a mechanical correlation chopper is described. The instrument is designed for the measurement of quasielastic neutron scattering from isotropic systems in the low momentum range. It is shown that some inherent experimental difficulties of the correlation technique such as imperfect beam modulation can be avoided by improving the chopper design. A better beam utilization than with the conventional time-of-flight technique can be achieved. As a test, the scattering from CH 4 gas at room temperature is measured.

Theory of the sideband instability in free electron lasers

In a Compton-regime free electron laser a relativistic electron moves in the combined potential (ponderomotive potential) formed by the optical radiation field and the static magnetic field. If the energy of the electron, the wavelength of the light, and the period and strength of the static magnetic field are connected by the well-known resonance condition, the electron may exchange part of its energy with the radiation field during its transit through the interaction region (wiggler magnet). Whether the electron gains or loses energy is determined by the phase of its transverse motion with respect to the phase of the optical field. Satisfaction of the resonance condition implies that the relative phase between the light and the electron will vary slowly during the interaction time, thus allowing the possibility of net energy transfer. Consideration of the detailed dynamics of the electron motion shows that, as the electron's energy slowly changes, so does its phase with respect to the optical field. This motion may be described as an oscillation in the ponderomotive potential (synchrotron oscillation). The occurrence of synchrotron oscillations is a fundamental property of the theory of electron dynamics in a free electron laser at high optical intensities and therefore strongly affects the saturation properties of such a laser. In particular, such oscillations can couple the motion of an electron to light at other wavelengths and thus lead to the generation of sidebands on the frequency spectrum of the laser light. The appearance of such sidebands corresponds to a strong modulation of the temporal profile of the optical pulse and modifies the interaction of the light with the electron beam. A review of the theory of the sideband instability will be presented. Results from analytical and numerical studies on the growth and saturation of the instability will be reviewed. Modifications of the results due to two- or three-dimensional effects will be discussed, as will the effects of an imperfect electron beam. Experimental evidence of this effect will be reviewed.

Effect of imperfect beam modulation in neutron time of flight spectroscopy using mechanical correlation choppers

We discuss the effects of imperfect pseudorandom chopping of a neutron beam arising from practical limitations on achievable chopper perfection. It is known that imperfect modulation produces anomalous structure in decorrelated time of flight data. A method is presented for removing such anomalous structure through use of a suitably derived inverse sequence for decorrelation. An example using actual time of flight data is presented.

Static and Dynamic Stability of an Imperfect Beam

This paper concerns the stability of an imperfect beam resting on a nonlinear elastic foundation, subjected to axial loads. Two types of load are considered: a static load, and a dynamic load in the form of a step function of time. The effect on the critical load of initial geometric imperfections is obtained and comparisons are drawn between the static and dynamic results. Comparisons are also drawn between asymptotic results and extended results, where terms up to cubic in the initial imperfection and deflection are retained. It is shown that the form of the results for static and dynamic loads is very similar. Also, the ratio of the reduction in the dynamic and static critical loads, due to the presence of imperfections, appears to be more or less constant when the asymptotic and extended results are compared.