scholarly journals Explicit Determination of Pinned–Pinned Beams with a Finite Number of Given Buckling Loads

2018 ◽  
Vol 18 (02) ◽  
pp. 1850018 ◽  
Author(s):  
Antonino Morassi ◽  
Martina Pressacco ◽  
Anastasia Vrech
Keyword(s):  
Analytical Procedure ◽  
Natural Frequencies ◽  
Explicit Construction ◽  
Buckling Loads ◽  
End Conditions ◽  
Vibrating String ◽  
Sturm Liouville ◽  
Explicit Determination ◽  
Liouville Operators

We present an analytical procedure for the exact, explicit construction of Euler–Bernoulli beams with given values of the first [Formula: see text] buckling loads. The result is valid for pinned–pinned (P–P) end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm–Liouville operators with prescribed natural frequencies.

Natural Frequencies of Nonuniform Beams on Multiple Elastic Supports

1958 ◽  
Vol 25 (1) ◽  
pp. 57-63
Author(s):  
R. A. Di Taranto
Keyword(s):  
Natural Frequencies ◽  
Forced Vibrations ◽  
Moment Of Inertia ◽  
Elastic Supports ◽  
Mass Moment ◽  
End Conditions ◽  
Mass Moment Of Inertia ◽  
Gyroscopic Effects

Abstract A method is presented for the determination of the natural frequencies of nonuniform beams on two or more torsionally and linearly elastic supports, including the effect of rotary mass moment of inertia. The method employed is an extension of the Myklestad method. The cases of two supports with varied end conditions and three supports with a torsional and linear restraint at each support are formulated. It is indicated how this method may be used for problems concerning forced vibrations of beams on multiple elastic supports and for the determination of critical rotor speeds including gyroscopic effects.

On the location of the essential spectra and regularity fields of complex Sturm—Liouville operators

1980 ◽  
Vol 85 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
David Race
Keyword(s):  
Essential Spectrum ◽  
Essential Spectra ◽  
Linearly Independent ◽  
Complete Determination ◽  
Associated Operators ◽  
Sturm Liouville ◽  
Selfadjoint Extensions ◽  
Complex Valued ◽  
Liouville Operators

SynopsisIn this paper the Sturm-Liouville expression τy= −(py′)′ +qy, with complex-valued coefficients is considered, and a number of results concerning the location of the essential spectrum of associated operators are obtained. Some of these are extensions or generalizations of results due to Birman, and Glazman, whilst others are new. These lead to criteria for the non-emptiness of the regularity field of the corresponding minimal operator—a condition which is needed in the theory ofJ-selfadjoint extensions. A complete determination of the regularity field is made when the equation τy= λ0yhas two linearly independent solutions inL2[a,∞) for some complex λ0.

Vibration of Thin Cylindrical Shells

1965 ◽  
Vol 7 (4) ◽  
pp. 399-407 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cylindrical Shell ◽  
General Solution ◽  
Mode Shape ◽  
Shell Length ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Factor ◽  
Thin Cylindrical Shell ◽  
End Conditions

Starting from Flügge's three equations of motion for a uniform thin cylindrical shell, the paper gives a general solution, from which the dependence of natural frequencies on shell dimensions and mode number can be investigated for any end conditions. This solution requires the assumption of a natural frequency and the determination of the corresponding shell length for the prescribed end conditions. Numerical results are given for shells with clamped ends and for shells with free ends; the variation of frequency factor and of mode shape with dimensional and mode parameters is shown and the accuracy of approximate theories assessed.

Explicit half-range expansions for Sturm–Liouville operators

1999 ◽  
Vol 10 (5) ◽  
pp. 447-475 ◽  
Author(s):  
P. S. HAGAN ◽  
M. M. KŁOSEK
Keyword(s):  
Complex Variable ◽  
Range Expansion ◽  
Eigenfunction Expansion ◽  
Explicit Construction ◽  
Green Functions ◽  
Explicit Formulas ◽  
Expansion Formula ◽  
Sturm Liouville ◽  
Expansion Coefficients ◽  
Liouville Operators

Boundary value problems for linear transport equations sometimes require the explicit construction of solutions when boundary conditions are prescribed only on parts of the boundary and thus necessitate the construction of half-range expansions. In contrast to the standard eigenfunction expansion, a half-range expansion of a given function must be reconstructed just over half the domain, using just half of the eigenfunctions. The difficulty of such expansions arises because the eigenfunctions are not orthogonal, though they are complete, over half the domain, and there is no obvious method of obtaining the expansion coefficients. Here we use complex variable techniques to find explicit formulas for the coefficients of half-range expansions for regular, negative definite Sturm–Liouville operators. We prove that the half-range expansion formula is unique, and find the corresponding half-range Green functions.

On the determination of differential pencils with nonlocal conditions

2018 ◽  
Vol 26 (5) ◽  
pp. 577-588
Author(s):  
Chuan-Fu Yang ◽  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Nonlocal Conditions ◽  
Weyl Function ◽  
Uniqueness Theorems ◽  
Type Function ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

Abstract Inverse problems for differential pencils with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl function and Borg’s inverse problem for the classical Sturm–Liouville operators.

A novel method for the determination of linting propensity of paper

TAPPI Journal ◽  
2012 ◽  
Vol 11 (10) ◽  
pp. 9-17
Author(s):  
ALESSANDRA GERLI ◽  
LEENDERT C. EIGENBROOD
Keyword(s):  
Ash Content ◽  
The Novel ◽  
Offset Printing ◽  
Excellent Correlation ◽  
End Conditions ◽  
Bottom Side ◽  
Novel Method ◽  
Total Fraction

A novel method was developed for the determination of linting propensity of paper based on printing with an IGT printability tester and image analysis of the printed strips. On average, the total fraction of the surface removed as lint during printing is 0.01%-0.1%. This value is lower than those reported in most laboratory printing tests, and more representative of commercial offset printing applications. Newsprint paper produced on a roll/blade former machine was evaluated for linting propensity using the novel method and also printed on a commercial coldset offset press. Laboratory and commercial printing results matched well, showing that linting was higher for the bottom side of paper than for the top side, and that linting could be reduced on both sides by application of a dry-strength additive. In a second case study, varying wet-end conditions were used on a hybrid former machine to produce four paper reels, with the goal of matching the low linting propensity of the paper produced on a machine with gap former configuration. We found that the retention program, by improving fiber fines retention, substantially reduced the linting propensity of the paper produced on the hybrid former machine. The papers were also printed on a commercial coldset offset press. An excellent correlation was found between the total lint area removed from the bottom side of the paper samples during laboratory printing and lint collected on halftone areas of the first upper printing unit after 45000 copies. Finally, the method was applied to determine the linting propensity of highly filled supercalendered paper produced on a hybrid former machine. In this case, the linting propensity of the bottom side of paper correlated with its ash content.

Improved Method for the Determination of Ethylenebisdithiocarbamate Residues in Plants, Fruits, and Vegetables

1967 ◽  
Vol 50 (5) ◽  
pp. 1102-1108
Author(s):  
Charles F Gordon ◽  
Richard J Schuckert ◽  
William E Bornak
Keyword(s):  
Sulfuric Acid ◽  
Fruits And Vegetables ◽  
Analytical Procedure ◽  
Improved Method ◽  
Modified Method ◽  
Fungicide Residues ◽  
Crop Types ◽  
Large Representative

Abstract A modified method for the determination of dithiocarbamate fungicide residues on crops is presented. A large representative subsample of the frozen crop is blended in ice-cold deaerated water and an aliquot of the homogenate is added to the analytical apparatus containing hot 5 0% sulfuric acid. Dithiocarbamates are decomposed to evolve CS2 which is removed by a continuous gentle air-sweep from the digestion flask. Variations in technique allow the analysis of dithiocarbamate fungicide residues in several ranges, 1-10, 10-200, and 200-1000 /ig maneb. Recoveries from a wide variety of crops averaged 70 to 103%. Certain crop types present low recoveries and/or high apparent control values, but modifications in the analytical procedure are successful in solving these problems.

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