Cantilever Beam Design Research Articles

Optimal Cantilever Dynamic Vibration Absorbers by Timoshenko Beam Theory

A double‐ended cantilever beam as a distributed parameter dynamic vibration absorber has been applied to a single‐degree‐of‐freedom system subjected to harmonic forces.In this investigation, the beam has been analyzed under the well known model of Timoshenko and the computation of best parameters is based on the Chebyshev’s optimality criterion.This is somewhat novel in the field since: The design of cantilever beams as dynamic vibration absorbers is usually made under the hypotheses of the Euler‐Bernoulli theory; It is the first time that the Chebyshev’s criterion is applied to the design of a double‐ended cantilever beam used as a dynamic vibration absorber. For a ready use of the results herein presented, design charts allow a quick choice of optimal parameters such as tuning ratio and mass ratio.

顎関節突起骨折に対する各種骨内固定法の生体力学的評価

The purpose of this study was to evaluate the biomechanical stability of various rigid internal fixation systems for subcondylar fractures.Fifteen identical synthetic polyurethane mandibles with a cancellous bone structure (Synbone (R), Switzerland) were used. The left condylar processes were cut with a band saw to mimic subcondylar fractures directed perpendicularly to the long axis of the ramus, and the right sides were cut to mimic oblique fractures to the ramus. The fixation systems used were a single 4-hole titanium mini-adaptation plate (Synthes), double fixation with the same plates, a single 5-hole titanium mini-dynamic compression plate (Synthes), an Eckelt lag screw (R) system (Martin), and a Wurzburg lag screw plate (R) system (Leibinger). Biomechanical testing was done as described by Haug et al.(1996). The bone models were held with a custom-made jig to keep the occlusal plane horizontal. The canine region was pressed with a cantilever beam design using a servohydraulic testing machine (Autograph, Shimadzu) at a rate of 1mm/sec. The force-displacement curve, maximum load for breakage, and stiffness were measured.In perpendicular fractures, double mini-plate fixation and Eckelt lag screw fixation provided the best stability. The maximum loads of the former and the latter were 46.7±9.5N and 44.7±11.6N, respectively. Their stiffness was 4.1±1.1N/mm and 4.7±1.9N/mm, respectively. Single mini-plate fixation was weakest, i. e., 13.2±2.4N maximum load and 1.3±1.0N/mm stiffness. In oblique fractures, double mini-plate fixation also had the best tolerance for load and stiffness, i.e., 55.1±11.6 N and 5.2±2.7N/mm, respectively. The Eckelt lag screw, however, showed considerably less fixation strength than that for perpendicular fractures, i.e., 22.8±11.3N for load tolerance and 1.0±0.2N/mm for stiffness.In this laboratory setting, double mini-plate fixation proved superior in both types of fractures with regard to resistance to movement and breakage strength. The Eckelt lag screw showed good stability for perpendicular fractures; however, stability was weak for oblique fractures. Not only single mini-plate fixation but also minidynamic compression plate fixation or a Wurzburg lag screw plate system may provide insufficient fixation strength for this type of fracture on early functional loading.

Experimental evaluation of MEMS strain sensors embedded in composites

Micromechanical in-plane strain sensors were fabricated and embedded in fiber-reinforced laminated composite plates. Three different strain sensor designs were evaluated: a piezoresistive filament fabricated directly on the wafer; a rectangular cantilever beam; and a curved cantilever beam. The cantilever beam designs were off surface structures, attached to the wafer at the root of the beam. The composite plate with embedded sensor was loaded in uniaxial tension and bending. Sensor designs were compared for repeatability, sensitivity and reliability. The effects of wafer geometry and composite plate stiffness were also studied. Typical sensor sensitivity to a uniaxial tensile strain of 0.001 (1000 /spl mu//spl epsi/) ranged from 1.2 to 1.5% of the nominal resistance (dR/R). All sensors responded repeatably to uniaxial tension loading. However, for compressive bending loads imposed on a 2-3-mm-thick composite plate, sensor response varied significantly for all sensor designs. This additional sensitivity can be attributed to local buckling and subsequent out of plane motion in compressive loading. The curved cantilever design, constructed with a hoop geometry, showed the least variation in response to compressive bending loads. All devices survived and yielded repeatable responses to uniaxial tension loads applied over 10 000 cycles.

Simultaneous Optimum Design of Structure and Control Systems based on Closed Loop Pole Assignment.

This paper aims at proposing a new simultaneous optimum design method of structure and control system: such as several types of mechanical systems equipped with vibration control system in order to suppress the structural vibration of the mechanical system. When the proposed method is applied to the design of a structure-control combined system, the closed loop pole assignment of the lower order model of the combined system is specified in advance as a design requirement. Proposed method is constructed from two steps: in the first step, output feedback control system is designed for the initial structure in order to realize the specified closed loop pole assignment; and next step, structure and control system design parameters are simultaneously optimized to minimize the objective function subject to constraints on the pole assignment. Scalar objective function is defined as a linear combination of several measures of the optimality of structure design and control system design. According to the proposed method, the closed loop pole assignment of the lower order model is preserved through the iterative optimum design process. The effect of the proposed method will be shown by the numerical simulation results of the cantilever beam design example. Not only structural configuration but also control system are successfully optimized under the objective function minimization.

Maximum Stiffness Solutions of Elastic Beam as the Bolza Problem.

We establish a general theory of maximum stiffness design of elastic beams subject to a given volume. Determination of the maximum stiffness of a beam, with the height taken as an independent variable can be treated as the Bolza problem. The beam is taken to be symmetrical about its center line. The theory thus obtained can easily be extended to take account of variable width or section area of the beam, by defining a control vector u. An illustrative application is presented in cases of cantilever and simple beam designs subjected to a restriction of the lower bound under an arbitrary external load.

A comparison of mandibular angle fracture plating techniques

Objective The purpose of this investigation was to compare the conventional technique of mandibular angle fracture plating with two biomechanically dissimilar techniques in their abilities to resist vertical loads similar to masticatory forces. Study design Three groups of five synthetic hemimandibles with simulated fracture repairs were compared for their capabilities to resist vertical deformation. The conventional group was stabilized with a thin tension band system at the superior border and thick stabilization plate system at the inferior border. The nontraditional group was stabilized with a thick tension band system at the superior border and thin stabilization plate system at the inferior border. The two miniplate group was stabilized with a thin tension band system at the superior border and thin stabilization plate at the inferior border. A cantilever beam design was used. Testing was performed with an Instron 8511.20 (Instron Corp., Canton, Mass.) mechanical testing device. The three groups were compared with a two way analysis of variance. Results The forces resisted by the conventional group (167.6±18.2 N), the nontraditional group (156.3±33.9 N), and two miniplate group (154.0±18.4 N) were not statistically different (F=0.44, p>0.66). All failures occurred at the tension bands secured with monocortical screws. Conclusions Under the conditions described in this in vitro investigation, plate thickness or pattern made no difference. All failures in this experiment occurred with monocortical screws in the superior border tension band system.

Optimal design of a cantilever subjected to dissipative and non-conservative forces

The design of a cantilever beam of a given structural weight subjected to a linearly distributed tangential load is investigated with the intention of maximizing the critical flutter load intensity, Qf. The effects of internal and external damping are included in the partial differential equation of motion. An adjoint variational principle is introduced, the optimality condition is derived, and a variational method is applied to determine approximate values of Qf with respect to certain design parameters. Numerical results are obtained for uniform and smoothly tapered beams of rectangular and circular cross-section, and the optimal values of Qf were determined by a numerical procedure that automatically computes the maximum value of a function of several parameters. For the same weight, it was found that the optimally designed beam has a significantly larger critical flutter load intensity, depending upon the values of the internal and external damping parameters, than has the corresponding uniform beam.