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A method is developed or drawing ground resonance stability boundaries in the (?1, ?) plane for arbitrary values of the parameters ??, A1 and Aa. The current values of ?1 and ? are expressed simply and directly in terms of the co‐ordinates (Y, Z) of points lying on a parabola whose equation involves ??, A1 and A3. The position of the intersections of this parabola with a certain unique curve in the (Y, Z) plane determines into which of three classes each stability boundary falls. All stability boundaries split up into two separate branches, and only in one class of boundaries do the branches align themselves in such a way as to permit the possibility of stability for all rotor speeds ?. A method is given showing how ??, A1 and A3 may be determined to achieve this effect.

An examination is made of the way in which the ground resonance properties of a helicopter depend on the fuselage damping, blade damping, drag hinge offset, inter‐blade spring stiffness, blade mass and angular velocity of the rotor as specified by the parameters λƒ, λβ, Λ1, Λ2, Λ3 and Ω respectively. A direct method of drawing stability boundaries in the (Ω, λβ) plane is developed, and the geometry of these boundaries as the remaining parameters vary is studied theoretically at length. Arising out of the geometry, the validity of Coleman's criterion for stability is examined, and it is shown that the requirement that the product λƒ,λβ should have a certain minimum value is not itself sufficient to ensure stability for all Ω. The condition can be made sufficient by a proper and unique choice of the individual values of ?f and ??, and these values are found in terms of Λ1, Λ2, and Λ3. All other cases of stability require a larger value of the product λƒ, λβ. An alternative criterion for stability is developed which gives the minimum value of λƒ capable of ensuring stability for all Ω. This, and the preceding criterion, are mathematically exact, and follow from Coleman's equations of motion as applied to the case of a helicopter on isotropic supports. A brief account is also given of the case of a rotor having inter‐blade friction damping as against the viscous damping previously assumed.

The purpose of this paper is to contribute to the solution of the buckling and resonance stability problems in inelastic beams and wooden plane trusses, taking into account geometric and material defects.

Two sources of non-linearity are analyzed, namely the geometrical non-linearity due to geometrical imperfections and material non-linearity due to material defects. The load-bearing capacity is obtained by the rheological-dynamical analogy (RDA). The RDA inelastic theory is used in conjunction with the damage mechanics to analyze the softening behavior with the scalar damage variable for stiffness reduction. Based on the assumed damages in the wooden truss, the corresponding external masses are calculated in order to obtain the corresponding fundamental frequencies, which are compared with the measured ones.

RDA theory uses rheology and dynamics to determine the structures' response, those results in the post-buckling branch can then be compared by fracture mechanics. The RDA method uses the measured P and S wave velocities, as well as fundamental frequencies to find material properties at the limit point. The verification examples confirmed that the RDA theory is more suitable than other non-linear theories, as those proved to be overly complex in terms of their application to the real structures with geometrical and material defects.

The paper presents a novel method of solving the buckling and resonance stability problems in inelastic beams and wooden plane trusses with initial defects. The method is efficient as it provides explanations highlighting that an inelastic beam made of ductile material can break in any stage from brittle to extremely ductile, depending on the value of initial imperfections. The characterization of the internal friction and structural damping via the damping ratio is original and effective.

Of the parameters that may be adjusted to give the helicopter freedom from ground resonance, that which is ignored most frequently is Λ3 (ratio of effective rotor mass to effective fuselage mass). This is because it is usually impractical to change it on an existing helicopter. However, if it is considered sufficiently early in the design of the fuselage, the ground resonance problem can be greatly reduced or even eliminated by the consideration of this parameter alone. The paper investigates the effects of fuselage dynamic properties on Λ3 and also gives results for the effect of Λ3 on the stability boundaries for some simple helicopter configurations.

The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.

The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.

The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.

The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

(i) The Position of the Vertical Asymptotes Vertical asymptotes of the (X, y) curve are given by those values of X which make y infinite. Taking the curve in the form given by Eq. (10), viz.:

THE TABLES I, II and II which have to be read in conjunction with figs. 4, 5 and 6, show the structure of each class of stability boundary regarded as a function of the parameter Y. The end column marked ‘N’ indicates the number of real points of the boundary arising from each value of Y in the range considered. On each boundary the arrows indicate the way in which the curve is traced out as Y increases from zero to infinity.

The supercritical design of tail rotor drive shaft has attracted more attention in helicopter design due to its high power–weight ratio and low maintenance cost. However, there exists excessive vibration when the shaft passes through the critical frequency. Dry friction damper is the equipment applied to the drive shaft to suppress the excessive vibration. In order to figure out the damping mechanism of the dry friction damper and improve the damping efficiency, the dynamic model of the shaft/damper system is established based on the Jeffcott rotor model.

The typical frequency response of the system is studied through bifurcation diagrams, amplitude-frequency characteristic curves and waterfall frequency response spectrum. The typical transient responses under frequency sweeps are also obtained.

The results show that the response of the system changes from periodic no-rub motion to quasi-periodic rub-impact motion, and then to synchronous full annular rub-impact, and finally, back to periodic no-rub motion. The slip of the rub-impact ring improves the stability of the system. Besides, the effects of the system parameters including critical dry friction force, rub-impact friction coefficient, initial clearance on the stability and the vibration damping capacity are studied. It is observed that the stability changes significantly varying the three parameters respectively. The vibration damping capacity is mainly affected by the critical dry friction force and the initial clearance.

Presented results provide guidance for the design of the dry friction damper.

The frequencies of the bursting events associated with the streamwise coherent structures of spatially developing incompressible turbulent boundary layers were predicted. The structures were modeled as wavelike disturbances associated with the turbulent mean flow using a direct‐resonance theory. Global numerical solutions for the resonant eigenmodes of the Orr‐Sommerfeld and the vertical vorticity equations were developed. The global method involves the use of second and fourth order accurate finite difference formulae for the differential equations as well as the boundary conditions. The predicted resonance frequencies were found to agree very well with previous results using a local shooting technique and measured data.

This paper aims to provide detailed information on the dynamic model and closed‐loop control theory for a resonant accelerometer based on electrostatic stiffness, which is important for the design of this type of resonant accelerometer.

After analysing the principles of the resonant accelerometer based on electrostatic stiffness, a dynamic model was built. According to the requirements of the closed‐loop control, the control equations based on phase‐locked technology were also built for the system. With the help of the averaging method, the system behaviour was analysed, and the equilibrium for the vibration amplitude was achieved.

The theoretical analysis and simulation show that integral gain is critical to system stability. When it is larger than the critical point, the system stable time is shorter, but the frequency‐tracking process fluctuates; if it is smaller than the critical point, the system stable time is longer, and the frequency‐tracking process stabilizes a resonant accelerometer was fabricated with a bulk‐silicon‐dissolved process. With the above conclusions, the accelerometer was driven and tested with a sensitivity of 47 Hz/g for a single vibration beam.

The dynamic model and the control theory for the resonant accelerometer based on electrostatic stiffness were presented in this paper. The simulation and experiment results agree well with the theoretical analysis.