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RESEARCH PAPERS

J. Appl. Mech. 1984;51(3):457-464. doi:10.1115/1.3167657.

The effect of gravity on two-dimensional imcompressible potential nozzle flows has been studied using the method of hodograph transformation coupled with numerical computation. It has been demonstrated that although hodograph transformation is an inverse technique, it has the ability to allow curved walls to be prescribed a priori. Calculations have been performed for flows discharging from symmetric nozzles with horizontal lips. The variation of total head versus discharge rate can only be obtained from detailed consideration of the gravitational effect. Some general features of nozzle flows, including the possibility of early flow separation from the top nozzle wall, have been observed.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):465-469. doi:10.1115/1.3167658.

This paper considers the problem of a body composed of an elastic/perfectly plastic solid that is subjected to constant applied load P and a time-varying cyclic temperature distribution, characterized by a maximum thermoelastic stress σt . For sufficiently large P and σt , in excess of the shakedown limit, the body will begin to suffer incremental growth. A linearized theory is used to obtain a relationship between the increase in displacement Δu per cycle and the increase in ΔP and Δσt , above the shakedown limit. From the result, a simple lower bound is derived for Bree-type problems, which for kinematically determinate structures shows that for moderate thermal loading the displacement increment per cycle is four times the elastic displacement of the body if it were subjected only to the increase ΔP. From a practical point of view the analysis indicates that ratchet rates are always high, in the sense that only a small increase of load above shakedown will produce substantial ratcheting within relatively few cycles.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):470-474. doi:10.1115/1.3167659.

A linearized method of analysis proposed in an accompanying paper [1] is used to obtain the ratchet rate for two types of thermal loading problems where parts of the structure experience reversed plastic straining. For structures that can shakedown plasticially it is found that for a given increment of load beyond the plastic shakedown boundary, the rate of ratchet increases with increasing level of thermal loading. When a structure is unable to shakedown plastically it ratchets at low mechanical loading as the result of a localized mechanism that involves some reversed plasticity. It is shown that the ratchet rate in such situations can be substantial but its value is very dependent on the local curvature of the yield and not the accuracy of the yield surface itself.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):475-480. doi:10.1115/1.3167660.

At high stress levels the creep strain rate for many materials varies as the exponential of stress while at low stresses it varies as stress to some power. An analysis is presented for a sharp notch under antiplane shear loading in a material that deforms by hyperbolic-sine-law creep, ε̇c = ε̇0 [sinh(σ/σ0 )]n . The asymptotic notch-tip stress intensification is weaker and the strain-rate intensification is stronger than for a power-law creeping material.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):481-486. doi:10.1115/1.3167661.

In this work we use a consistent homogenization theory approach to study the overall behavior of a highly porous elastic material at finite levels of strain. Although the matrix material in the problem considered here remains elliptic at all deformations, the resulting “homogenized” material is found to admit a loss of ellipticity at sufficiently high strains, i.e., can fail in a localized shear mode.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):487-493. doi:10.1115/1.3167662.

Within the framework of an existing purely mechanical, rate-type theory of plasticity, detailed calculations are presented for certain types of material response during stress and strain cycling in a uniaxial homogeneous deformation. These features pertain specifically to material response in stress cycling between fixed values of stress in tension and compression (not necessarily equal in magnitude) resulting in ratcheting of strain, and a type of saturation hardening caused by strain cycling between any two fixed values of strain when the mean value of stress (in tension and compression) tends to zero.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):494-500. doi:10.1115/1.3167663.

Modifications of a simple elastic-plastic technique [1-4] are shown which allow estimation of local deformation in the loaded column of a portal frame as well as the side-sway deflections of the frame. A wholly elastic response stage provides input to a simplified rigid-plastic solution, in which velocity patterns first of local and then of modal (side-sway) type occur, and which furnishes estimates of final plastic deflections. Maximum (elastic plus plastic) deflections are estimated by adding displacements corresponding to the elastic strain field defined by the stresses of the closing rigid-plastic mode. The method is described for perfectly plastic and for strain-rate sensitive material, and comparisons are shown here with values computed3 for both types of material by a finite element program. Emphasis in this paper is put on the inclusion of elastic and vicoplastic effects.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):501-504. doi:10.1115/1.3167664.

A rigid-plastic fan blade is subjected to a transverse impact force at the tip in addition to radial centrifugal forces caused by fan rotation. Large and small deflection formulations for inplane bending of the cantilevered blade are calculated and compared. If the effects of centrifugal force are completely considered, the difference between these calculations is shown to be small within the beam. Most of the deflection originates from plastic deformation far from the tip so the large deflection effects near the tip have little influence. The largest curvature is inversely proportional to the centrifugal force, directly proportional to the third power of impact force, and always occurs near the point of impact.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):505-509. doi:10.1115/1.3167665.

The title problem is solved by estimating the maximum strain rate field in a circular membrane associated with a modal velocity condition when one-half the kinetic energy in the system has been dissipated. The radial stress may only vary in the radial direction, but is taken as a constant with time at any given location. Internal plastic energy absorbed during the large deformation is found by integrating while accounting for rate sensitivity effects; this absorbed energy is equated to the initial kinetic energy in the system to obtain the final deformed configuration. Correlation of analytically determined results with a series of experiments reported elsewhere is very good. The procedure described here is potentially extendable to any planform membrane shape as well as to axisymmetric shells. The method is applicable to plate problems when membrane effects dominate over bending, that is for deformations of the order of two thicknesses or more. A simple general formula for final plate deformation is devised and also agrees well with experimental results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):510-518. doi:10.1115/1.3167666.

Using a building block approach and starting with a single element, expressions for the energy of various two-dimensional frametype gridwork configurations are derived. These are then used to develop energy equivalent continua for the grid-works. Equations of motion and associated boundary conditions are obtained for the continua. Some dynamic characteristics of these continua are investigated and compared with corresponding results obtained from finite element codes and also with some available theoretical predictions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):519-525. doi:10.1115/1.3167667.

The large deflections of a simply supported beam, one end of which is free to move horizontally while the other is subjected to a moment, are investigated by means of inextensional elastica theory. The linear theory is found to be valid for relatively large angles of rotation of the loaded end. The beam becomes transitionally unstable, however, at a critical value of the bending moment parameter MI L/EI equal to 5.284. If the angle of rotation is controlled, the beam is found to become unstable when the rotation is 222.65 deg.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):526-530. doi:10.1115/1.3167668.

Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):531-535. doi:10.1115/1.3167669.

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):536-539. doi:10.1115/1.3167670.

In Parts 1 and 2, we determined optimal forms of shallow shells with respect to vibration and stability, respectively. In this final part, we consider a given load and find the shell form for which the volume between the base plane and the deflected shell is a maximum. As before, the shell is assumed to be thin, elastic, and axisymmetric, with a given circular boundary that is either clamped or simply supported. The material, surface area, and uniform thickness of the shell are specified. Both uniformly distributed loads and concentrated central loads are treated. In the numerical results, the maximum enclosed volume is on the order of 10 percent higher than that for the corresponding spherical shell.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):540-545. doi:10.1115/1.3167671.

This paper examines upper and lower bounds of the effective elastic modulus of unidirectional short-fiber composites. The short-fibers are modeled by aligned ellipsoidal inclusions of the same aspect ratio but not necessarily the same size. We adopt a perturbation expansion of the composite local strain field by using the Green function tensor. Explicit expressions of the effective elastic modulus are derived up to the third-order term by use of the information on the correlation functions. The variational method is then employed to optimize the bounds of the effective modulus in a closed form. Numerical examples of the bounds as functions of the fiber aspect ratio and the fiber volume fraction are given for a glass/epoxy system. The present approach predicts narrower bounds than those of Hashin and coworkers for the limiting cases of spherical particles and continuous fibers since their bounds corresponds to a model that take the correlation functions up to the second order into account.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):546-550. doi:10.1115/1.3167672.

An elastic potential is proposed that is capable of modeling the reversible portion of the observed nonlinear response of unidirectional graphite fiber composites. The model includes both the stiffening stress-strain behavior as well as the softening Poisson’s response for loading in the fiber direction. The model is compared with experimental results for Celion 6000/PMR-15 graphite-polyimide.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):551-559. doi:10.1115/1.3167673.

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):560-565. doi:10.1115/1.3167674.

Columns, marine risers, pipelines, hydraulic columns, and legs of tension leg platforms can be modeled for customary Euler buckling analysis by a single model which, in its most general form, applies to risers. Previous work has shown that numerical algorithms fail to provide stability boundaries for long risers. Asymptotic analyses for long columns have been developed as early as 1941 but the results are either incomplete or incorrect. The goals of this paper are to develop a long-column buckling theory, indicate errors in holding theories, and complete the numerical data available in the literature.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):566-573. doi:10.1115/1.3167675.

The present paper deals with the design of beneficial geometric imperfections of short, thin-walled columns in order to maximize their energy absorption. The investigation was motivated by the experimental finding that under axial compressive load, the symmetric mode (which has a higher buckling load than the antisymmetric mode) actually has a much higher energy absorption than the antisymmetric mode as measured by the area under the curve of applied load versus end-shortening curve. Thus, an attempt is made to introduce imperfections in the beneficial symmetric mode so that the mode shapes of extremely large deflection in plastic collapse will also be of the symmetric type. The two-mode stability problem is studied using Koiter’s theory of elastic stability.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):574-580. doi:10.1115/1.3167676.

In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is developed for analyzing clamped plates of any shape resting on an elastic foundation. A numerical technique for the solution to the boundary integral equations is presented and numerical results are obtained and compared with those existing from analytical solutions. The effectiveness of the BIE method is demonstrated.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):581-585. doi:10.1115/1.3167677.

An exact solution for the natural frequencies of a thick free circular plate is compared to approximate solutions. The exact solution is a series solution of the general linear elasticity equations that converges to the correct natural frequencies. The approximate solutions to which this exact solution is compared are the Mindlin plate theory and a modification of a solution method proposed by Pickett. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Mindlin plate theory is considered by evaluating the shear coefficient that would make the exact and modified Pickett method match the Mindlin plate solution.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):586-594. doi:10.1115/1.3167678.

The reflection of an oblique plane shock wave from a boundary in a two-dimensional isotropic hyperelastic material is studied. For plane strain deformations, the strain energy function W is a function of two invariants p and q of the deformation gradient. There are, in general, two reflected waves each of which can be a simple wave or a shock wave. For a special class of materials for which the strain energy function W(p, q) represents a developable surface (of which harmonic materials are particular examples), one of the reflected waves is always a shock wave. It is shown that there are materials other than harmonic materials for which the wave speeds are independent of the direction of propagation. Illustrative examples are presented to show how one can determine the reflected waves from a rigid boundary. It is also shown that for certain incident shock waves, there exists only one reflected wave.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):595-601. doi:10.1115/1.3167679.

The propagation of torsional shock waves in a thin circular viscoelastic rod is investigated theoretically. An analysis is carried out based on the approximate equations previously derived. Two typical viscoelastic models are considered, which possess, respectively, the discrete and continuous relaxation spectrum. One is the usual Maxwell- Voigt model and the other is a new model whose relaxation function is given by a power law with weak singularity. The structures of steady shock profiles are presented and compared for both types. Finally a brief discussion is included on the simplified evolution equations for a far field transient behavior.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):602-607. doi:10.1115/1.3167680.

We developed a convenient laboratory procedure to determine forces on projectiles penetrating geological targets. Gas guns were used to accelerate foundry core targets (a simulated soft sandstone) to steady velocities, and the targets subsequently impacted 20.6-mm-dia penetrators instrumented with piezoelectric accelerometers. Rigid-body acceleration data were recorded for one ogival and two conical nose shapes for impact velocities between 0.2-1.2 km/s.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):608-613. doi:10.1115/1.3167681.

Propagation of longitudinal waves in isotropic homogeneous elastic plates is studied in the context of the linear theory of nonlocal continuum mechanics. To determine the nonlocal moduli, the dispersion equation obtained for the plane longitudinal waves in an infinite medium is matched with the parallel equation derived in the theory of atomic lattice dynamics. Using the integroalgebraic representation of the stress tensor and the Fourier transform, the system of two coupled differential field equations is solved in the standard manner giving the frequency equations for the symmetric and antisymmetric wave modes. It is found that the short wave speed in the Poisson medium differs by about 13 percent from the speed established in the classical theory. A numerical example is given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):614-621. doi:10.1115/1.3167682.

A finite element eigenfunction method (FEEM) is formulated for elastic wave scattering by bounded three-dimensional axisymmetric regions (cavity, homogeneous, or inhomogeneous) for harmonic waves incident at arbitrary angles. The solutions are hence three-dimensional and no longer axisymmetric. The scattering region is enclosed within a sphere. The scattered field outside the sphere is expanded in outgoing vector spherical functions. Within the sphere, basis-functions are generated by a finite element technique applying the vector spherical harmonics as boundary conditions. The field inside the sphere is then written as a superposition of these basis functions with unknown coefficients which are then solved by matching with the exterior field. Numerical results are obtained for a variety of scatterers and comparisons made with available results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):622-629. doi:10.1115/1.3167683.

An elastic punch, modeled as a semi-infinite strip, moves with constant speed over the surface of a semi-infinite elastic body. Using the plane strain theory of elasticity, we obtain the resulting stress distribution along the interface of the contacting bodies for different material combinations and a range of sliding velocity and frictional coefficients. It is found that both the stress intensity factor and the order of the singularity depend on sliding velocity as well as on the other parameters. Speed-dependent composite material parameters are defined which determine the orders of the singularities.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):630-635. doi:10.1115/1.3167684.

In the present paper a method of ascent for axisymmetric problems is developed. It is shown that, for problems where the vector or scalar Laplacian operator specifies the space behavior of the potential functions, the three-dimensional axisymmetric problems may be solved by operating on the solution to an associated two-dimensional problem. Hence, the theoretical results presented here may be applied to heat transfer problems, to problems in elastostatics, and to elastic wave propagation problems.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):636-640. doi:10.1115/1.3167685.

A solution is given for the surface displacement and stresses due to a line heat source that moves at constant speed over the surface of an elastic half plane. The solution is obtained by integration of previous results for the instantaneous point source. The final results are expressed in terms of Bessel functions for which numerically efficient series and asymptotic expressions are given.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):641-645. doi:10.1115/1.3167686.

The propagation and scattering of SH-waves of general form is investigated using the boundary element method. Attention is focused on semi-infinite regions containing subsurface cavities. The analysis is carried out within the context of linear elastodynamic theory formulated as an integral equation. Using a time-dependent Green’s function for the half space, the boundary integral equation is developed and is discretized into a finite set of algebraic relations. A time-stepping algorithm is constructed for the solution of general boundary value—initial value problems. Results of this solution technique are presented for the two-dimensional case of transient waves scattering off of buried stress-free cavities.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):646-651. doi:10.1115/1.3167687.

A rigorous theory of the diffraction of time-harmonic elastic waves by a cylindrical, stress-free crack embedded in an elastic medium is presented. The incident wave is taken to be either a P-wave or an SV-wave. The resulting boundary-layer problem for the unknown jump in the particle displacement across the crack is solved by employing an integral-equation approach. The jump is expanded in a complete sequence of Chebyshev polynomials, and, writing the Green’s function as a Fourier integral, a system of algebraic equations is obtained. Numerical results are presented in the form of dynamic stress intensity factors, scattering cross sections, and normalized power-scattering characteristics. Some of them deviate from earlier published results.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):652-656. doi:10.1115/1.3167688.

A study is made of time-harmonic wave modes in an elastic layer in plane strain with traction-free surfaces. It is demonstrated that, at points of the Rayleigh-Lamb frequency spectrum where the group velocity vanishes, there exist nonseparable time-harmonic modes in which the amplitudes of the displacements vary linearly in the direction along the layer. These modes are used to explain the terrace-like structure of the free-vibration frequency spectrum of a circular disk.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):657-663. doi:10.1115/1.3167689.

When structures are excited by random force excitation the circle fits of the data around resonance are usually poor. The structural parameter estimates, which result from this fit, are usually erroneous. No matter how elegant the circle or the multimodal fit, the results will be poor if the frequency response function (FRF) is a poor representation of the actual structural response. In general for the random excitation case, this is the case. The conventional fast Fourier transform (FFT) method which is used to estimate the frequency response function, is given by H1 (f) = Gxy /Gxx . This produces poor results when the coherence of the data falls in the resonance region. A drop in the coherence usually indicates noise at the input of the structure for this case. H1 (f) is quite sensitive to such noise giving erroneous estimates. This paper investigates an alternative method for computing the frequency response function, H2 (f) = Gyy /Gyx , and its impact on the accuracy of the circle fit procedure used in modal analysis. This new estimator is not sensitive to input noise like the currently used H1 (f). H2 (f) provides the best estimate at or around resonance even in the presence of noise on the input signal. If one defines the average percentage fit error in the circle fit operation as 100 times the average radial deviation of the data points from the radius of the statistically fit circle divided by the fit circle radius, one can compute the circle fit accuracy for each of the proposed methods of data treatment. Typically, the percentage fitting error for H1 (f) might be 10 percent while the fitting error for H2 (f) using exactly the same data will be 0.5 percent. Thus, the proposed method eliminates long-standing system analysis errors through the use of a simple revision of the way the data are treated in the FFT processor around the resonance regions.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):664-673. doi:10.1115/1.3167690.

Time histories, phase plane portraits, power spectra, and Poincare maps are used as descriptors to observe the evolution of chaos in an autonomous system. Although the motions of such a system can be quite complex, these descriptors prove helpful in detecting the essential structure of the motion. Here the principal interest is in phase plane portraits and Poincare maps, their methods of construction, and physical interpretation. The system chosen for study has been previously discussed in the literature, i.e., the flutter of a buckled elastic plate in a flowing fluid.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):674-679. doi:10.1115/1.3167691.

The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated. Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):680-686. doi:10.1115/1.3167692.

An analysis of the mechanics and dynamics of a railroad vehicle wheelset during flange contact and wheelclimb derailment is presented. The theoretical model includes wheelset lateral, vertical, roll, yaw, and axle rotation degrees of freedom, plus lateral displacement of the truck frame. The equations of motion are based on the kinematics and dynamics of the wheelset subject to constraints imposed by wheel/rail contact geometry. These constraints are used to compute creepages and normal forces at the wheel/rail contact points, needed as inputs to the Kalker Simplified Theory of rolling contact. Computational methods for simulation of the nonlinear dynamic model are discussed. Results of the simulation demonstrate the significance of the various degrees of freedom on wheelset motion and on predicted values of the derailment quotient (Q/P).

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Appl. Mech. 1984;51(3):687-689. doi:10.1115/1.3167693.
Abstract
Topics: Deformation
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):689-691. doi:10.1115/1.3167694.
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):691-692. doi:10.1115/1.3167695.

An accelerating laminar thin-film flow along a vertical wall is investigated in this paper. Using a cubic polynomial for the velocity profile inside the boundary layer the momentum integral equation is solved by a Runge-Kutta method to determine the boundary layer thickness. The corresponding film-thickness is then calculated for the entrance region. These results are compared with the existing results obtained by using a parabolic velocity profile.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):694-696. doi:10.1115/1.3167697.
Abstract
Topics: Vibration , Rivers
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

BOOK REVIEWS

J. Appl. Mech. 1984;51(3):705. doi:10.1115/1.3167704.
FREE TO VIEW
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):705. doi:10.1115/1.3167705.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):706. doi:10.1115/1.3167706.
FREE TO VIEW
Abstract
Topics: Deformation , Waves
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):706-707. doi:10.1115/1.3167707.
FREE TO VIEW
Abstract
Topics: Elasticity
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):707. doi:10.1115/1.3167708.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):707-708. doi:10.1115/1.3167709.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):708. doi:10.1115/1.3167710.
FREE TO VIEW
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 1984;51(3):708-709. doi:10.1115/1.3167711.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

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