Mechanical Properties of Bamboo And Their Use In Fishing Rods

Bamboo has historically been used in Japan as a structural material and for building tools such as fishing rods owing to its remarkable structural properties. In recent years, the materials used for manufacturing fishing rods have changed greatly owing to the development of composite materials; however, the basic slender tapered hollow cylindrical fishing rod design has remained unchanged throughout the long history of fishing. However, the mechanical rationale behind this structural design has not yet been sufficiently verified, and this study clarifies this. The analysis was performed by solving the nonlinear bending equation of a slender tapered cantilever beam with a concentrated load at the tip, which causes large deflection, using the Runge–Kutta method. The deflection curves and bending stresses were obtained, and the structural design to minimize the stresses was explored. Our results may prove useful for bamboo-inspired bionic design and bring to light our ancestors’ deep knowledge of natural materials and their advanced technological capabilities.

Nonlinear forced vibration analysis of a rotating three-dimensional tapered cantilever beam

In this article, nonlinear forced vibration analysis is carried out for a rotating three-dimensional tapered cantilever beam subjected to a uniformly distributed load. Considering the effects of Coriolis terms, static axial deformation and geometric nonlinearity in modeling process, nonlinear partial motion equations of a rotating tapered Euler–Bernoulli beam are established by using Hamilton’s principle. Galerkin’s procedure is used to discretize the equations to obtain the dynamic response of the beam. Frequency responses, the time-history response, the phase diagram, and the Poincaré map are introduced to study the effects of the taper ratio, rotating velocity, radius of hub, and external excitation on the nonlinear resonances and detailed responses of the rotating three-dimensional tapered beam. Results show that the fundamental natural frequency increases with the increase of the taper ratio, radius of hub, and rotating velocity. Besides, by increasing the taper ratio and excitation amplitude and decreasing the rotating velocity and radius of hub, the nonlinearity and vibration amplitude of the rotating beam intensify.

Derivation and optimization of deflection equations for tapered cantilever beams using the finite element method

This study derived analytical solutions for the deflection of a rectangular cross sectional uniformly tapered cantilever beam with varying configurations of width and breadth acting under an end point load. The deflection equations were derived using a numerical analysis method known as the finite element method. The verification of these analytical solutions was done by deterministic optimisation of the equations using the ModelCenter reliability analysis software and the Abaqus finite element modelling and optimisation software. The results obtained show that the best element type for the finite element analysis of a tapered cantilever beam acting under an end point load is the C3D20RH (A 20-node quadratic brick, hybrid element with linear pressure and reduced integration) beam element; it predicted an end displacement of 0.05035 m for the tapered width, constant height cantilever beam which was the closest value to the analytical optimum of 0.05352 m. The little difference in the deflection value accounted for the numerical error which is inevitably present in the analyses of structural systems. It is recommended that detailed and accurate numerical analysis be adopted in the design of complex structural systems in order to ascertain the degree of uncertainty in design. Keywords: Deflection, Finite element method, deterministic optimisation, numerical error, cantilever beam.

Transverse Vibration of Rotating Tapered Cantilever Beam with Hollow Circular Cross-Section

Problems related to the transverse vibration of a rotating tapered cantilever beam with hollow circular cross-section are addressed, in which the inner radius of cross-section is constant and the outer radius changes linearly along the beam axis. First, considering the geometry parameters of the varying cross-sectional beam, rotary inertia, and the secondary coupling deformation term, the differential equation of motion for the transverse vibration of rotating tapered beam with solid and hollow circular cross-section is derived by Hamilton variational principle, which includes some complex variable coefficient terms. Next, dimensionless parameters and variables are introduced for the differential equation and boundary conditions, and the differential quadrature method (DQM) is employed to solve this differential equation with variable coefficients. Combining with discretization equations for the differential equation and boundary conditions, an eigen-equation of the system including some dimensionless parameters is formulated in implicit algebraic form, so it is easy to simulate the dynamical behaviors of rotating tapered beams. Finally, for rotating solid tapered beams, comparisons with previously reported results demonstrate that the results obtained by the present method are in close agreement; for rotating tapered hollow beams, the effects of the hub dimensionless angular speed, ratios of hub radius to beam length, the slenderness ratio, the ratio of inner radius to the root radius, and taper ratio of cross-section on the first three-order dimensionless natural frequencies are more further depicted.