On Wave Equations for Elastic Rods

Boström, Anders E

doi:10.1002/(sici)1521-4001(200004)80:4<245::aid-zamm245>3.0.co;2-p

Cited by 36 publications

(45 citation statements)

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“…By substituting the power series ansatz (3.1) into the expressions for stresses (2.2) and further substituting these into the the equations of motion (2.1) it is possible to obtain recursion formulas by identifying terms with equal powers of r [2]. In the case of m ≥ 1 two constraint equations are also obtained from the equations of motion.…”

Section: Recursion Formulasmentioning

confidence: 99%

“…The second constraint (3.7) can be obtained by setting k = −1 in (3.3). For the case of m = 0 the constraint equations vanish in accordance with [2] and [3]. The recursion formulas are used to write all coefficients u i , v j and w k as functions of the coefficient with lowest index.…”

Section: Recursion Formulasmentioning

confidence: 99%

“…Another method for analyzing the behavior of elastic bodies and in particular rods was developed by Boström [2]. The method consists of choosing a proper power series ansatz for the displacement fields from which the governing equations can be obtained and consequently other relations such as stresses and dispersion equations.…”

Section: Introductionmentioning

confidence: 99%

“…The method consists of choosing a proper power series ansatz for the displacement fields from which the governing equations can be obtained and consequently other relations such as stresses and dispersion equations. This method was used to investigate the governing equation and dispersion relations for rods [2]. The method was also used to investigate stresses and eigenfrequencies for finite rods [3].…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this thesis is to investigate whether the method described by [2] can be used to analyze beams. In order to examine if the attained governing equations yield acceptable results, the work presents dispersion relations, displacement and stress distributions and eigenfrequencies.…”

Section: Introductionmentioning

confidence: 99%

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Higher Order Beam Equations

Abadikhah¹

Civil-Comp Proceedings

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This thesis considers the analysis of a homogenous isotropic linearly elastic solid cylinder by assuming a displacement field that is a power series expansion in the radial coordinate. The solid cylinder is also referred to as a beam. Governing equations for the beam are obtained by inserting the power series ansatz into the equations of motion for linear elasticity, thereby obtaining recursion formulas which relates the coefficients of the power series with each other. Lateral boundary conditions on the beam's outer surface are expressed with the power series ansatz and the recursion formulas. The lateral boundary conditions form the basis of the governing equations. Dispersion relations and eigenfrequencies for the simply supported case are computed and compared to the exact theory, given by Pochhammer and Chree, and also with classical theories such as the Euler-Bernoulli and the Timoshenko theories. Displacement and stress fields are compared with the classical theories to show the deviancies of the proposed method.

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Section: Recursion Formulasmentioning

confidence: 99%

Section: Recursion Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher Order Beam Equations

Abadikhah¹

Civil-Comp Proceedings

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Two mode Mindlin–Herrmann rod solution based on modified couple stress theory

Güven

2013

Z Angew Math Mech

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In this work, the classical two mode Mindlin–Herrmann rod model is extended by using the modified couple stress theory having the single internal length scale parameter to investigate the propagation of the longitudinal stress waves along a nanorod. This analysis also contains the single mode Rayleigh Bishop rod solution based on the modified couple stress theory. Comparative results for the classical Mindlin–Herrmann and the single mode Rayleigh–Bishop rod models based on the modified couple stress theory are presented and discussed. The present analysis shows that Mindlin–Herrmann rod model is influenced significantly by the internal length scale parameter.

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Torsional surface wave dispersion in pre-stressed dry sandy layer over a gravitating anisotropic porous half-space

Prasad

Kundu

2016

Z. Angew. Math. Mech.

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The present paper discusses the dispersion of torsional surface wave in a pre-stressed dry sandy layer over an anisotropic porous half-space under the influence of gravity. The inhomogeneity has been expected as hyperbolic variation in the sandy layer. The mathematical analysis of the problem has been dealt with the asymptotic expansion of Whittaker function and its derivative. The dispersing mathematical statement acquired is in concurrence with the conventional consequence of Love wave in a homogeneous layer over a homogeneous half space when the upper limit plane is thought to be traction free. The velocities of torsional waves are ascertained numerically as a component of kH and introduced in various graphs, where k is the wave number and H is the thickness of the sandy layer. The numerical expression gives the scaffold between displaying results and field application. The impact of non-homogeneity in modulus of rigidity, stress, density, and porosity have been portrayed by the method for numerical data and graphs. The study reveals that the torsional surface wave propagates in an initially stressed dry sandy layer over a gravitating anisotropic porous half-space. It is additionally watched that the vicinity of gravity field builds the speed of the torsional surface wave. This work may be valuable to comprehend the way of seismic wave proliferation amid quake in the considered media.

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On Wave Equations for Elastic Rods

Cited by 36 publications

References 0 publications

Higher Order Beam Equations

Higher Order Beam Equations

Two mode Mindlin–Herrmann rod solution based on modified couple stress theory

Torsional surface wave dispersion in pre-stressed dry sandy layer over a gravitating anisotropic porous half-space

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