Abstract This study describes a new finite element method that can be used to analyse transverse and axial vibrations of a Functionally Graded Material (FGM) beam under an accelerating / decelerating mass. The differential equations of the FGM beam are obtained using First-order Shear Deformation Theory (FSDT). In these equations, the interaction terms of mass inertia are derived from the second-order exact differentiation of displacement functions with respect to mass contact point. The FGM beam is made of two different materials (Steel and Alumina Al2O3), which vary in thickness with a power law. Including the effects of neutral axis shift and mass inertia, the proposed method can be used when the dynamic behaviour of the FGM Timoshenko beams is to be analysed in transverse and axial directions, depending on the interaction with the acceleration of the moving loads. After validating this work with literature studies, new investigations and findings are presented for both moving load and mass assumptions. In addition, the obtained results of Timoshenko Beam (TBT) and Euler Bernoulli beam theory (EBT) are compared for FGM beams with various speeds and accelerations of moving mass.

Abstract In this paper, dynamic analysis of two different weapon systems (35 mm Anti-Aircraft Barrel (AAB) and 120 mm Grooved Tank Barrel (GTB)) under the effect of statically unbalanced projectile has been performed with a new 12 DOF 3-D element technique using Finite Element Method (FEM). The muzzle deviations, which negatively affect the barrel shooting accuracy at firing, are calculated in a time dependent manner using Newmark β algorithm with high accuracy at both axes (y and z) considering the Coriolis centripedal and centrifugal forces. The effect of such fundamental physical parameters as shift from rotating center and angular velocity belonging to the unbalanced projectile on barrel dynamics are analyzed with this new and affective FEM. As a result, it was found out that 1% of a millimeter shift from projectile belonging to a weapon system leads to excessive vibration on both axes and compromises the shooting accuracy of the barrel.

Abstract In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, the classical finite element of the beam is modified by the inclusion of the inertial effects of the moving mass. This modification is made using the relations between nodal forces and nodal deflections and shape functions of six DOF beam element. The mass, stiffness, and damping matrices of the modified finite element are determined by forces caused by the corresponding transverse and lateral accelerations and jerks, and transverse Coriolis and centripetal accelerations and jerks, respectively. This method was first applied on a simply supported beam plate to provide a comparison with the previous studies in literature, and it was proved that the results were within acceptable limits. Secondly, it was applied on a CNC type box-framed beam to analyse the dynamic response of the beam in terms of variable acceleration and jerk as well as constant velocity and mass ratios.

Abstract For realistic applications, design and control engineers have limited modelling options in dealing with some vibration problems that hold many nonlinearity such as non-uniform geometry, variable velocity loadings, indefinite damping cases, etc. For these reasons numerous time consuming experimental studies at high costs must be done for determining the actual behaviour such nonlinear systems. However, using advantages of multiple computational methods like Finite Element Method (FEM) together with an Artificial Intelligence (ANN), many complicated engineering problems can be handled and solved to some extent. This study, proposes a new collective method to deal with the nonlinear vibrations of the barrels in order to fulfil accurate shooting expectancy. Using known analytical methods, in practical, to determine dynamic behaviour of the barrel beam is not possible for all conditions of firing that include numerous varieties of ammunition for different purposes, and each projectile of different ammunition has different mass and exit velocity. In order to cover all cases this study proposes a new method that combines a precise FEM with ANN, and can be used for determining the exact dynamic behaviour of a barrel for some cases and then for precisely predicting the behaviour for all other possible cases of firing. In this study, the whole nonlinear behaviour of an antiaircraft barrel were obtained with 3.5% accuracy errors by ANN trained by FEM using calculated analysis results of ammunitions for a particular range. The proposed FEM-ANN combined method can be very useful for design and control engineers in design and control of barrels in order to compensate the effect of nonlinear vibrations of a barrel for achieving a higher shooting accuracy; and can reduce high-cost experimental works.

AbstractIn this study, the dynamic interaction between a 120 mm smoothbore tank barrel modeled as an Euler-Bernoulli cantilever beam and an accelerating projectile during firing is presented. The interaction was modelled using a new FEM approach that took into account the projectile's inertia, Coriolis, and centripetal forces and the horizontal and inclined positions of the barrel. The mass, exit velocity and acceleration effects of the projectile on the dynamics of the barrel were investigated. The effects of the projectile's inertia, and Coriolis and centripetal forces were evaluated as well. Furthermore, the tip displacements at different firing angles were determined by transferring the mass, stiffness and damping matrices of the barrel with the addition of the instantaneous property matrices of the projectile from a local coordinate to the global Cartesian coordinate with the aid of transformation matrices. Finally, the barrel vibrations caused by the successive firings were evaluated under different firing scenarios. To demonstrate the validity of the current study, comparisons were made with the results of previous studies and a good agreement was achieved. By using the method recommended in this study, it is possible to determine the accurate dynamic behavior of any barrel with sufficient sensitivity, without any costly or time-consuming tests being necessary.

A combined plate element is presented for the analysis of transverse and longitudinal vibrations of a thin plate which carries a load moving along an arbitrary trajectory with variable velocity. Depending on the acceleration of the point load on its trajectory on the plate surface, the combined element, which is a combination of the 24 DOF plate element and an equivalent mass element, represents transverse (z) inertia, Coriolis and centripetal and longitudinal (x, y) inertia effects of the moving load. In order to obtain the combined element, mass, damping and stiffness matrices of the equivalent mass element representing the mass are first derived by using the relations between nodal forces, nodal deflections and deflection-shape functions of the plate element and the inertia and other forces of the moving mass according to the global coordinates on the plate and local coordinates on the plate element. Then, the obtained property matrices of the equivalent mass element and property matrices of the plate element were added together in order to obtain the combined plate element. For verification, the suggested technique was applied on a simply supported beam-plate under a moving load, and agreements were obtained with existing literature. In addition, intensive analysis and simulations were conducted at different dimensionless mass rates (mass of the load/mass of the plate) and angular velocities for a circular motion on a CCCC plate, and the results are provided. Furthermore, analysis results are provided for moving force condition which neglects the inertia, Coriolis and centripetal effects of the load, and it was shown that the moving mass assumption generated very different results with moving load assumption especially at high mass ratio and velocity values. Analysis results made it clear that the dynamic behaviour of the plate was differently affected by an orbiting mass depending on its mass ratio, orbiting radius and angular velocity