Somchai Chucheepsakul

Large deflections of an end supported beam subjected to a point load

Treated herein is a class of large deflection beam problems where one end of the beam is being held while the other end portion is allowed to slide freely over a frictionless support fixed at a distance from this end. The elastic beam is subjected to a point load. This highly non-linear problem is solved using both the elliptic integral method and the shooting-optimization technique, thus providing independent checks on the solutions. This kind of problem features: (1) the possibility of two possible equilibrium solutions for a given load magnitude; and (2) a maximum (or critical) load and a maximum deformed arc-length for equilibrium.

Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

This paper presents a model formulation capable of analyzing large-amplitude free vibrations of a suspended cable in three dimensions. The virtual work-energy functional is used to obtain the non-linear equations of three-dimensional motion. The formulation is not restricted to cables having small sag-to-span ratios, and is conveniently applied for the case of a specified end tension. The axial extensibility effect is also included in order to obtain accurate results. Based on a multi-degree-of-freedom model, numerical procedures are implemented to solve both spatial and temporal problems. Various numerical examples of arbitrarily sagged cables with large-amplitude initial conditions are carried out to highlight some outstanding features of cable non-linear dynamics by accounting also for internal resonance phenomena. Non-linear coupling between three- and two-dimensional motions, and non-linear cable tension responses are analyzed. For specific cables, modal transition phenomena taking place during in-plane vibrations and ensuing from occurrence of a dominant internal resonance are observed. When only a single mode is initiated, a higher or lower mode can be accommodated into the responses, making cable spatial shapes hybrid in some time intervals.

Large Amplitude Three-Dimensional Free Vibrations of Inclined Sagged Elastic Cables

The nonlinear characteristics in the large amplitude three-dimensionalfree vibrations of inclined sagged elastic cables are investigated. Amodel formulation which is not limited to cables having smallsag-to-span ratios and takes into account the axial deformation effectis considered. Based on a multi-degree-of-freedom cable model, a finitedifference discretization is employed within a numerical solution of thegoverning equations of three-dimensional coupled motion. Variousnumerical examples of arbitrarily inclined sagged cables with initialout-of-plane or in-plane motions are carried out for the case of aspecified end tension. The major findings consist of highlighting theextent of two-and three-dimensional nonlinear couplings, the occurrenceof nonlinear dynamic tensions, and the meaningfulness of modaltransition phenomena ensuing from the activation of various internalresonance conditions. The influence of cable inclination on thenonlinear dynamic behavior is also evaluated. Comprehensive discussionand comparison of large amplitude free vibrations of horizontal andinclined sagged cables are presented.

Large strain formulations of extensible flexible marine pipes transporting fluid

This paper develops mathematical formulations for large strain analysis of extensible flexible marine pipes transporting fluid in two different coordinates: Cartesian and natural coordinates. Both the virtual work method and the vectorial method are applied to generate the large strain formulations, in which deformation descriptions based upon the total Lagrangian, the updated Lagrangian, and the Eulerian mechanics are taken into consideration. The new ideas used in the model formulations deal with applications of the extensible elastica theory and the apparent tension concept to handle combined action of the effect of axial deformation with large strain and behaviour of flow of transported fluid inside the pipe including the effect of Poissons ratio. The present models cover nonlinear statics and nonlinear dynamics, and provide flexibility in the choice of the independent variables used to define the elastic curves.

Double Curvature Bending of Variable-Arc-Length Elasticas

This paper deals with the double curvature bending of variable arc-length elasticas under two applied moments at fixed support locations. One end of the elastica is held while the other end portion of the elastica may slide freely on a frictionless support at a prescribed distance from the held end. Thus, the variable deformed length of the elastica between the end support and the frictionless support depends on the relative magnitude of the applied moments. To solve this difficult and highly nonlinear problem, two approaches have been used. In the first approach, the elliptic integrals are formulated based on the governing nonlinear equation of the problem. The pertinent equations obtained from applying the boundary conditions are then solved iteratively for solution. In the second approach, the shooting-optimization method is employed in which the set of governing differential equations is numerically integrated using the Runge-Kutta algorithm and the error norm of the terminal boundary conditions is minimized using a direct optimization technique. Both methods furnish almost the same stable and unstable equilibrium solutions. An interesting feature of this kind of bending problem is that the elastica can form a single loop or snap-back bending for some cases of the unstable equilibrium configuration.

Plates on two-parameter elastic foundations with nonlinear boundary conditions by the boundary element method

Abstract A boundary element method is developed for the bending analysis of plates having nonlinear boundary conditions and resting on two-parameter elastic foundations. The nonlinearity of the problem arises from the normal bending moment of plates which is assumed to be nonlinear function of the boundary slope recognized as a support model with nonlinear rotational restraint. Thus, the solution can be treated all cases of the boundary conditions ranging from simple support to completely fixed support. The kernels of the boundary integral equations are conveniently established which the fundamental solution for the linear plate theory is used. The surface integration of the kernels for the foundation pressure is evaluated by using the property of Dirac delta function. The system of nonlinear equations is established and solved by the Newton–Raphson iterative process. The application of high-order elements, i.e. cubic elements, for improving the solution is adopted. Numerical results of several problems are given to demonstrate the accuracy and applicability of the proposed method.

Postbuckling of Unknown-Length Nanobeam Considering the Effects of Nonlocal Elasticity and Surface Stress

The objective of this paper is to study the postbuckling behaviors of an unknown-length nanobeam combined with small-scale effects. The concept of variable-arc-length elastica is firstly applied on the problem of nanobeams. The span length is not changed while the arc length is varied increasingly. The nanobeam is on a clamped support at one end, while the other end is an overhanging part through a frictionless slot subjected to axial compression. At this end, the nanobeam is movable only in a horizontal direction. The governing equation is developed by the moment–curvature relationship based on the classical Euler–Bernoulli beam theory, including the effects of nonlocal elasticity, residual surface stress, and both combined effects. The shooting–optimization technique with two-point boundary condition is employed to solve the differential equations in this problem. The results, including nonlocal elasticity, reveal that nanobeams have decreased structural stiffness; meanwhile, the residual surface tension and both combined effects have increased strength. The postbuckling loads decrease as the arc length of nanobeams is increased. The equilibrium configurations are close to an anti-loop for very large deflections. The friction force at the nanoslot is also considered.

DYNAMIC RESPONSES OF A TWO-SPAN BEAM SUBJECTED TO HIGH SPEED 2DOF SPRUNG VEHICLES

The deflection, bending moment, shear force and acceleration-time histories of a two-span beam subjected to moving sprung vehicles are presented. The vehicle model is a 2DOF system with a constant velocity. The two-span beam with a rough surface is used as structure model. The beam is defined in modal domain by natural frequencies, mode shapes and modal damping values. The rough surface is modeled by filtered white noise. The equations of motion for the coupled vehicle-structure system are formulated, for non-dimensionalized variables in the system equation. The first-order linear stochastic differential equations are solved, and the effects of the span passage rate and other important parameters are studied.

Nonlinear Vibrations of an Extensible Flexible Marine Riser Carrying a Pulsatile Flow

The influence of transported fluid on static and dynamic behaviors of marine risers is investigated. The internal flow of the transported fluid could have a constant, a linear, or a wave velocity. The riser pipe may possibly experience the conditions of high extensibility, flexibility, and large displacements. Accordingly, the mathematical riser models should be governed by the large strain formulations of extensible flexible pipes transporting fluid. Nonlinear hydrodynamic dampings due to ocean wave-pipe interactions implicate the high degree of nonlinearity in the riser vibrations, for which numerical solutions are determined by the state-space-finite-element method. It is revealed that the impulsive acceleration of internal flow could seriously relocate the vibrational equilibrium positions of the riser pipe. The fluctuation of the pulsatile flow relatively introduces the expansion of amplitudes and the reduction of frequencies of the riser vibrations. The pulsatile frequencies of the internal flow in wave aspect could reform the oscillation behavior of the conveyor pipe.

A variational approach for three-dimensional model of extensible marine cables with specified top tension

Abstract This paper presents a variational model formulation that can be used for analyzing the three-dimensional steady-state behavior of an extensible marine cable. The virtual work-energy functional, which involves virtual strain energy due to a cable stretching, and virtual works done by the gravitational, inertial and external drag forces, is formulated. Euler–Lagrange’s equations, obtained by considering the first variation of the functional, are identical to those obtained by equilibrating forces on a cable infinitesimal segment. Two mathematical simulations, namely, the finite element method and the shooting-optimization technique, are employed to solve and evaluate the problems. The numerical investigations are carried out for the case of a specified end tension, whereas the specified cable unstrained length case can be applied in the algorithm procedure. The validity of the present model and the influence of various geometrical parameters on the cable equilibrium configuration are demonstrated. The effects of cable extensibility and the omnidirectionality of current actions are presented and discussed.