Hinged End Research Articles

On the linear normal modes of planar pre-stressed curved beams

The natural frequencies and mode shapes of planar shear undeformable beams around their curved pre-stressed post-buckling configurations are investigated neglecting rotary inertia effects. Two mechanical models are considered depending on the assumed boundary conditions in the buckling and post-buckling phases. With the first model, the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end, a sliding hinge. In the second case, the beam is assumed inextensible in the pre-stressed phase (same boundary conditions as above), whereas it is extensible in the subsequent free linear dynamic phase because the sliding hinged boundary is changed into a stationary hinged end. Linear vibrations are governed by partial-differential equations with non-constant coefficients and the solutions for the frequencies and mode shapes are found employing two approximate approaches: a fully numerical method based on a finite element formulation and a semi-analytical method based on a weak formulation (Galerkin method). The main results are compared and a close agreement in the outcomes is found. The leading mechanical differences in the linear normal modes of the two pre-stressed curved beam models are discussed.

Elliptic integral solutions of variable‐arc‐length elastica under an inclined follower force

AbstractThis paper presents exact closed‐formed solutions using elliptic integrals for large deflection analysis of elastica of a beam with variable arc‐length subjected to an inclined follower force. The beam is hinged at end but slides freely over the support at the other end. In the undeformed state, the inclined follower force applied at any distance from the hinged end making an angle γ with respect to vertical axis while in the deformed state its direction remains at an angle γ from the normal to the beam axis. The set of nonlinear equations is obtained from the boundary conditions, and solved iteratively for the solutions. The effect of the direction and the position of the follower force on the beam bending behaviour is demonstrated. Comparisons of equilibrium configurations of the beam under non‐follower force and follower force are also given.

Micro-hinges changed flexural rigidity intermittently for micromechanism joints

In order to reduce the output errors of micromechanisms, our study has suggested the use of new micro-hinges with a rigidity that has been made suitable enough to decrease the differences between the hinge end locus and the circular locus. Based on this, we have conducted theoretical analyses, while at the same time creating micro-hinge models using a semiconductor minute processing technique (RIE, etc.) for our experiments. Afterwards, we will discuss and study the effectiveness of the use of the suggested micro-hinges, through comparisons with conventional shaped micro-hinges. The results clarified that the suggested hinge models could reduce errors with the circular locus. This ultimately confirms the effectiveness of our newly reinforced micro-hinge.

NOVEL METHODS FOR CALCULATING NATURAL FREQUENCIES AND BUCKLING LOADS OF COLUMNS WITH INTERMEDIATE MULTIPLE ELASTIC SPRINGS

Numerical methods for calculating both the natural frequencies and buckling loads of columns with intermediate multiple elastic springs are developed. In formulating the governing equations of the column, each elastic spring is modeled as a discrete Winkler foundation of the finite longitudinal length. By using this model, the differential equations governing both the free vibration and buckled shapes of the column are derived, which are solved numerically. The Runge–Kutta method is used to integrate the differential equations, and the determinant search method combined with Regula–Falsi method is used to determine the eingenvalues, namely, the natural frequencies and buckling loads. In the numerical examples, fixed–fixed, fixed-hinged, hinged-fixed and hinged–hinged end constraints are considered. The numerical results including the frequency parameters, mode shapes of free vibrations and buckling loads are presented in non-dimensional forms.

Vibrations of the elasto-plastic pendulum

A numerical strategy for vibrations of elasto-plastic beams with rigid-body degrees-of-freedom is presented. Beams vibrating in the small-strain regime are considered. Special emphasis is laid upon the development of plastic zones. An elasto-plastic beam performing plane rotatory motions about a fixed hinged end is used as example problem. Emphasis is laid upon the coupling between the vibrations and the rigid body rotation of the pendulum. Plastic strains are treated as eigenstrains acting in the elastic background structure. The formulation leads to a non-linear system of differential algebraic equations which is solved by means of the Runge–Kutta midpoint rule. A low dimension of this system is obtained by splitting the flexural vibrations into a quasi-static and a dynamic part. Plastic strains are computed by means of an iterative procedure tailored for the Runge–Kutta midpoint rule. The numerical results demonstrate the decay of the vibration amplitude due to plasticity and the development of plastic zones. The pendulum approaches a state of plastic shake-down after sufficient time.

Detection of Crassostrea virginica hinge lines with machine vision: software development

Shucking (removing the meat from the shell) an oyster requires that the muscle detachments to the two shell valves and the hinge be severed. Described here is the computer vision software needed to locate the oyster hinge line so it can be automatically severed, one step in the development of an automated oyster shucker. Oysters are first prepared by washing and trimming off a small shell piece on the oyster hinge end to provide access to the outer hinge surface. A computer vision system employing a color video camera then grabs an image of the hinge end of the oyster shell. This image is processed by the computer using software. The software is a combination of commercially available and custom written routines that locate the oyster hinge. The software uses four feature variables, circularity, rectangularity, aspect-ratio, and Euclidian distance, to distinguish the hinge object from other dark colored objects on the hinge end of the oyster. Several techniques, including shrink–expand, thresholding, and others, were used to secure an image that could be reliably and efficiently processed to locate the oyster hinge line.

2923 マイクロメカニズムのための剛性を変化させたマイクロヒンジの変位特性

In order to reduce the output errors of micromechanisms, our study has suggested the use of new micro-hinges with a rigidity that has been made suitable enough to decrease the differences between the hinge end locus and the circular locus. Based on this, we have conducted theoretical analyses, while at the same time creating micro-hinge models using a semiconductor minute processing technique for our experiments. Afterwards, we will discuss and study the effectiveness of the use of the suggested micro-hinges, through comparisons with conventional shaped micro-hinges.

Refined theories may be needed for vibration analysis of structures with overhang

The effect of shear deformation and rotary inertia terms on the free vibration of a beam with overhang was investigated. A recently proposed modified Timoshenko-type equations of motion were used to analyze the vibration of the structure. Two different sets of boundary conditions, with either a fixed or hinged end support, were studied. The results were compared with those obtained for the classical Bernoulli–Euler beam theory. The comparison shows that for a hinged end beam with very long overhang, where the span between the supports is less than one tenth of the overall beam length, the classical theory significantly overestimates the values of the fundamental natural frequencies, even for isotropic shear rigidity. On the other hand, the span effect is reversed for the clamped end beam, for which a relatively significant difference between the classical theory and shear theory results may occur only for a long span. For transversely isotropic beams, the refined theory predictions of the fundamental natural frequencies may be much smaller than those obtained through the rigid shear theory, especially for short span hinged end beams and long span clamped end beams.

Exact solutions of variable-arc-length elasticas under moment gradient

This paper deals with the bending problem of a variable-are-length elastica under moment gradient. The variable are-length arises from the fact that one end of the elastica is hinged while the other end portion is allowed to slide on a frictionless support that is fixed at a given horizontal distance from the hinged end. Based on the elastica theory, exact closed-form solution in the form of elliptic integrals are derived. The bending results show that there exists a maximum or a critical moment for given moment gradient parameters; whereby if the applied moment is less than this critical value, two equilibrium configurations are possible. One of them is stable while the other is unstable because a small disturbance will lead to beam motion.

Computer Vision Locating System for an Oyster Hinge Breaker

Removing the oyster meat from the shell requires severing the adductor muscle attachments to each shell valve and severing the oyster hinge. A system, consisting of a computer vision control unit and an air and oil driven oyster hinge severing unit, was developed to sense, locate, and sever the oyster hinge. The oyster hinge severing system consisted of an oyster hinge end trimming unit and a hinge severing unit.

Elastica of Simple Variable-Arc-Length Beam Subjected to End Moment

This paper presents two methods to find the elastica of a bar or a beam of given span length, but unknown arc length. The beam is subjected to a moment at a hinged end that can slide freely over another support. In the first method the differential equation based on large-deflection theory is formulated and solved by using elliptic integrals. The method yields an exact closed-form solution. The critical or maximum applied moment the beam can resist is also obtained by this formulation. Further, the well-known small displacement solution can be obtained from the degeneration of the exact solution by considering small rotations. The second method is based on a variational formulation, which involves the bending strain energy and work done by the end moment. The finite-element discretization of span length instead of bar length is used to solve the problem. Numerical comparisons are given and results from the finite-element method show good agreement with the elliptic integrals solutions.

On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.

Large deflections of an inclined cantilever with an end load

An elastica is weighted on one end and hinged on the other end. The hinged end is then turned by a torque. The solutions depend on the angle turned and a non-dimensional parameter K which represents the relative importance between the end load and flexural rigidity. Approximate solutions for small and large K. and perturbations about the almost vertical cases are found. The results compare well with exact numerical integration. For given K the torque is an extremely non-linear function of the angle turned. Non-uniqueness and hysteresis loops occur when K#62;π/2. The slightly inclined column is also studied.

Derivation of tensile strength ratio by second-order theory

Tension members with edge knots or edge knotholes deflect laterally when they are loaded by a tensile force. In order to consider this behavior for determination of tensile strength ratio (TSR), second-order theory is applied. A matrix displacement method of structural analysis developed from the slope deflection method is used to implement the second-order theory. The method reveals that in a member with a single edge knot the lowest TSR is obtained when the lateral deflection is negligible, and when the ends are hinged. For a stiffness value (EI/L) that is small, both end conditions (hinged and fixed) yield the same TSR; for large stiffness value, fixed end condition always gives a higher TSR than a hinged end condition because the moment is reduced at the defect as a result of the fixed ends. The method further reveals that the maximum moment for two edge knots on the same edge is lower than when they are on opposite edges.

Fatigue Tests of Wire under Progressive Stress

In order to clarify the relations between the progressive stress and fatigue strength of steel wires, a fatigue testing machine was devised and constructed, utilizing the buckling which was produced when one end of the wire was rigidly fixed and the other was hinged without friction.This machine has several advantages. It has but small resistance at the hinged end, and it is fit to perform the test under progressive stress by application of a simple device.The fatigue tests were carried out under the logarithmically increased stress and it has been found that the rupture stress is approximately expressed by the following formula:logσR=logσw+K(σR/NR)1/4where σR: rupture stress, σw: fatigue limit, K: constant and NR: the number of cycles to failure.