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Solid viscoelastic cylinder bonded to thin elastic casing, analyzing normal and tangential stresses for stress and displacement frequency responses in forced transverse vibration
A theoretical investigation was made of the behavior of a cantilever beam in rotational motion about a transverse axis through the root determining the stresses, the deflections, and the accelerations that occur in the beam as a result of the arrest of motion. The equations for bending and shear stress reveal that, at a given percentage of the distance from root to tip and at a given trip velocity, the bending stresses for a particular mode are independent of the length of the beam and the shear stresses vary inversely with the length. When examined with respect to a given angular velocity instead of a given tip velocity, the equations reveal that the bending stress is proportional to the length of the beam whereas the shear stress is independent of the length. Sufficient experimental verification of the theory has previously been given in connection with another problem of the same type.
The term multicyclic control describes a blade pitch control technique used by helicopter designers to alleviate vibration in rotorcraft. Because rotor-induced vibrations are periodic, a multicyclic system, synchronized to the main rotor's azimuth position, is suitable. Many types of rotors - ranging from the jet-flap and circulation-control rotors to the conventional full-blade feathering rotors - have utilized multicyclic control. Multicyclic control systems may be designed to reduce blade-bending stresses, to reduce rotor-induced vibration, and to improve rotor performance. Rotor types are reviewed, primarily to highlight their differences. The increased use of composites in blade construction is seen to indicate that vibration alleviation will be the prime focus of multicyclic control. Adaptive feedback control systems, which also incorporate gust alleviation, are considered to be the ultimate application of multicyclic control.
A scale model of a VSTOL tilt nacelle with a 0.508 m single stage fan was tested in a low speed wind tunnel to ascertain inlet aerodynamic and fan aeromechanical performance over the low speed flight envelope. Fan blade stress maxima occurred at discrete rotational speeds corresponding to integral engine order vibrations of the first flatwise bending mode. Increased fan blade stress levels coincided with internal boundary layer separation but became severe only when the separation location had progressed to the entry lip region of the inlet.
A scale model of a VSTOL tilt nacelle with a 0.508 m single stage fan was tested in the NASA Lewis 9x15 Low Speed Wind Tunnel to ascertain inlet aerodynamic and fan aeromechanical performance over the low speed flight envelope. Fan blade stress maxima occurred at discrete rotational speeds corresponding to integral engine order vibrations of the first flatwise bending mode. Increased fan blade stress levels coincided with internal boundary layer separation occurring but became severe only when the separation location had progressed to the entry lip region of the inlet. The inlet/fan system could operate within the low speed flight envelope without incurring fan blade stress limits although boundary layer separation did occur for certain operating conditions.
Across many industries and engineering disciplines, components and systems are designed and deployed into their operational environment of intended use. It is the desire of the design agency to be able to predict whether their component or system will function in its shock and vibration environments or if it will fail due to mechanical stresses. One method to determine if the component will survive the shock and vibration environments is to expose the component to the operational environment in a laboratory. One difficulty in executing a representative laboratory test is that the component may not have the same boundary condition in the laboratory as in the operational configuration. This paper examines the use of parameterized optimization to design the test fixture in order to better match the operational configuration. Several frequency and modal-based objective functions are examined for the optimization. The study shows that the Modal Projection Error objective function performs the best of the functions studied. The efficacy of the Modal Projection Error is demonstrated with respect to dynamic test fixture design on several analytical and experimental exemplars.
The effects of various combinations of space flight stresses are discussed. Included are weightlessness, acceleration, vibration, ionizing radiation, hypoxia, and ambient temperature. The problem of constructing mathematical models to describe the dynamics of biological systems, including those to analyze and predict adaptation and restoration processes following combined stresses, is also considered.
High cycle fatigue of metals typically occurs through long term exposure to time varying loads which, although modest in amplitude, give rise to microscopic cracks that can ultimately propagate to failure. The fatigue life of a component is primarily dependent on the stress amplitude response at critical failure locations. For most vibration tests, it is common to assume a Gaussian distribution of both the input acceleration and stress response. In real life, however, it is common to experience non-Gaussian acceleration input, and this can cause the response to be non-Gaussian. Examples of non-Gaussian loads include road irregularities such as potholes in the automotive world or turbulent boundary layer pressure fluctuations for the aerospace sector or more generally wind, wave or high amplitude acoustic loads. The paper first reviews some of the methods used to generate non-Gaussian excitation signals with a given power spectral density and kurtosis. The kurtosis of the response is examined once the signal is passed through a linear time invariant system. Finally an algorithm is presented that determines the output kurtosis based upon the input kurtosis, the input power spectral density and the frequency response function of the system. The algorithm is validated using numerical simulations. Direct applications of these results include improved fatigue life estimations and a method to accelerate shaker tests by generating high kurtosis, non-Gaussian drive signals.
Coupled differential equations of motion are given for application to a rotating, pretwisted and heated beam under the effects of thermal stresses and gas bending loads. The circumferential modes of the multi-blade vibration of a bladed-disk rotor stage were studied. A finite element method was developed for the dynamic and static deformation analysis of the blade. The deformations of a bladed disk and a shrouded-bladed disk were studied by introducing a special bladed-disk element and a special shrouded-blade element. Some features of the vibration of part-span-shrouded, bladed-disk rotor stages are discussed. The static deformation, thermal stress and gas bending effects on the blade vibration were presented previously.
The exact mathematical treatment of the problem is possible by replacing the propeller blade by a homogeneous prismatic rod. Conclusions can them be drawn as to the behavior of an actual propeller, since tests on propeller blades have indicated a qualitative agreement with the homogeneous rod. The natural frequencies are determined and the stressing of the systems under the various vibration modes are discussed.
A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.
Silicon solar cell array interconnector design based on analysis of stresses caused by thermal expansion and vibrational motion
The unveiling of the first reusable space shuttle vehicle by the National Aeronautics and Space Administration is discussed. The role of orbiter 101 as a test vehicle is stressed. Approach and landing tests, ground vibration tests, crew are among the topics included.
A general set of finite-element equations is developed for treating the nonlinear dynamic response of membranes consisting of complex nonlinear materials. The approach proposed by Key (1974) for a most complete treatment of the finite-element method to the nonlinear dynamic analysis of solids is used in developing the nonlinear equations of motion for membranes with cubic quadrilateral finite elements. The computations are kept general with respect to material modeling by computing the deformation gradient and requiring a constitutive subroutine to supply the Cauchy stress. An example calculation of the vibration of a square membrane demonstrates the accuracy of the formulation for small deformation theory and shows the nonlinear effect of large deformations.
A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.
A general purpose methodology for integrated probabilistic assessment of composite structures is demonstrated using aircraft fuselage type structures with rectangular cutouts. The computational simulation took into account buckling loads, vibration frequencies, global displacements, and local stresses. The procedure was embedded into the computer code IPACS (Integrated Probabilistic Assessment of Composite Structures) that calculates the simulated scatter, the sensitivity of the composite structural behavior to all the primitive variables that affect the structural behavior. The probabilistic assessment for the composite structure with rectangular cutouts indicates that the uncertainty in the longitudinal ply stress is mainly due to uncertainty in the laminate thickness.
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