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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Acta mechanica 71 (1988), S. 61-76 
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The dynamic instability of simply supported, finite-length, circular cylindrical shells subjected to parametric excitation by axial loading, is investigated analytically. The shell is taken to be orthotropic, due to closely spaced longitudinal and/or circumferential stiffeners or to many layers of fiber-reinforced composite material either oriented at angles of 0° and 90° (cross-ply) or at +θ and −θ (angle-ply) with respect to the shell axis. The theory used is a general first-order shear deformable shell theory introduced by Hsu, Reddy, and Bert; it can be considered to be the thick-shell version of the popular Sanders-Koiter thin-shell theory. By means of tracers, this theory can be reduced to thick-shell versions of the theories of Love (and Loo) and of Donnell (and Morley). Quantitative results are presented to show the effects of shell geometry, materials, and fiber orientation on the stability boundaries.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions. A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates. It is found that the present method gives good accuracy and is computationally efficient. Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A harmonic differential quadrature (HDQ) method with application to the analysis of buckling and free vibration of beams and rectangular plates is presented. A new approach is proposed for the determination of the weighting coefficients for differential quadrature. It is found that the HDQ method is more efficient than the ordinary differential quadrature (DQ) method, especially for higher order frequencies and for buckling loads of rectangular plates under a wide range of aspect ratios. Also, some shortcomings existing in theDQ method are removed.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of materials science 17 (1998), S. 581-582 
    ISSN: 1573-4811
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved version of the Rayleigh techinique used by Rayleigh and Schmidt for solid mechanics problems is extended to one- and two-dimensional problems of steady heat conduction. Here the technique is applied to the heat-balance integral (HBI) method, the variational method and the square-error method. To determine the most appropriate value of the non-integer exponent, either one of two different criteria is used: the variational or the square-error integral. Thus, four new methods are considered. A comparison with a closed-form solution is made for a one-dimensional fin. It is demonstrated that the error for a one-term trial function is much less for an improved HBI method with the variational integral criterion. Thus, additional terms should not be needed in most instances. Excellent results are also achieved by using one of the new methods in a two-dimensional problem with internal heat generation.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1573-269X
    Keywords: Beam ; gravity effect ; method of multiple scales ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity. The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship. Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios. For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.
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  • 7
    ISSN: 1573-269X
    Keywords: Beams ; free vibration ; nonlinear oscillation ; quadrature method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The quadrature method (OM) has been used in structural analysis only in recent years. In this study, OM is applied to flexural vibration analysis of a geometrically nonlinear beam. The numerical results by OM agree with the results by the finite element method. It is believed that this is the first attempt to solve a nonlinear dynamic problem by the quadrature method.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Significant errors can be present in the isothermal pressure-volume relationships that have been obtained from laterally constrained compression tests of low-strength polymeric materials. Laterally constrained compression tests on PMMA (polymethylmethacrylate) have shown these errors to result from (1) stress gradients in the specimen caused by constraint friction and (2) unknown volume changes resulting from extrusion of the test specimen. Test-specimen geometry was an important parameter.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The applicability of the semidestructive holedrilling technique to the experimental determination of residual stresses in relatively thin rectangularly orthotropic materials was investigated. From the exploratory work, it was determined that the similitudes, for measurements at a particular ratio of hole depth to diameter, which exist for thick materials are not present in relatively thin materials. This implies that calibration tests must be made for each combination of strain-gage size and plate thickness. As a consolation, however, it was found that there is no need to drill to an optimum depth for thin materials. That is, one may simply drill a small hole completely through the material to obtain the desired strain change.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1741-2765
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract One of the most frequently used techniques of determining residual stresses in cylindrical bodies of elastically isotropic materials is the Mesnager-Sachs boring-out method. This method is adequate for many engineering materials; however, certain materials possess elastic properties which vary with direction. Materials having one fairly common kind of directional variation are known as cylindrically orthotropic materials. Heretofore, no means has been available for determining the residual stresses from strain data taken after successive borings of members made of such materials. This paper gives the derivation of equations for this purpose along with graphs depicting the error to be expected if the data had been reduced by the Sachs equations.
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