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The problems of inelastic instability (buckling) and dynamic instability (resonance) have been the subject of extensive investigation and have received wide attention from the structural mechanics community. This paper aims to tackle these problems in thin-walled structures, taking into account geometrical and/or material non-linearity.

The inelastic buckling mode interactions and resonance instabilities of prismatic thin-walled columns are analysed by implementing the semi-analytical finite strip method (FSM). A scalar damage parameter is implemented in conjunction with a material modelling named rheological-dynamical analogy to address stiffness reduction induced by the fatigue damage.

Inelastic buckling stresses lag behind the elastic buckling stresses across all modes, which is a consequence of the viscoelastic behaviour of materials. Because of the lag, the same column length does not always correspond to the same mode at the elastic and inelastic critical stress.

This paper presents the influence of mode interactions on the effective stresses and resonance instabilities in thin-walled columns due to the fatigue damage. These mode interactions have a great influence on damage variables because of the fatigue and effective stresses around mode transitions. In its usual semi-analytical form, the FSM cannot be used to solve the mode interaction problem explained in this paper, because this technique ignores the important influence of interaction of the buckling modes when applied only for undamaged state of structure

The paper desribes an energy‐based framework for a simple model with two degrees‐of‐freedom that statically exhibits bifurcations or limit‐points. Dynamically, the equivalent system may respond with small amplitude motion (being dynamically stable) or it may ‘escape’ and move to exhibit ‘large amplitude motion’ (thus becoming dynamically unstable). The energy framework is used to define bounds for these stable and unstable motions. These bounds are used to provide a framework for a set of dynamic finite element computations based on conventional finite element techniques.

To predict the critical flutter load and frequencies of doubly curved panels using first‐order shear deformation theory considering the effects of shear deformation and rotary inertia.Design/methodology/approach – A finite element analysis procedure is based on the extension of dynamic, shear deformable theory initially according to Sanders' theory, which can be reduced to Love's and Donnell's theories by means of tracers.Findings – Flutter is observed to be more common than divergence under follower loading; the magnitude of the flutter load is gradually decreasing with the increasing cut‐out size; load bandwidth and type of load conditions have significant influence on flutter and divergence characteristics of both isotropic and laminated curved panels; damping is perceived to have significant effect on flutter behaviour; the effect of direction control parameter with damping significantly affects the critical load.Practical implications – The practical behaviour of follower forces involving: aerodynamic drag; engine thrust; cantilever pipe conveying fluid; gas turbine rotor; automatic control system application; and automobile disk brakes can be monitored more successfully.Originality/value – Will assist students of elastic systems, both conservative and non‐conservative.

To study the effect of rocket mass and an intermediate mass on the critical flutter load of a free‐free beam (missile‐like structure).

A finite element model of beam considering shear deformation and rotary inertia, based on Hamilton's principle applied to non‐conservative system.

Smaller geometric dimensions of the end rocket assist in the stability. Optimum positioning of the intermediate mass leads to stability.

The stability of free‐free missile structures can be better understood.

Sheds new light on the effect of rocket mass and an intermediate mass on the critical flutter load of a free‐free beam.

Computerising inventory control procedures is usually an attempt to gain better control over stock availability. The effectiveness of the procedures depends on the time delays imparted by such events as order processing and delivery. Through these time delays, much of a finished goods physical distribution system is linked together through the inventory control procedures. Changing the length of any one time element through changes in inventory stocking rules, order processing methods or selected transportation services impacts on the economics of the entire physical distribution system. Little is understood about the effects of time change in such complex systems. In this article, the actual computer inventory control procedures of a chemical company were computer simulated. Physical distribution system design decisions and their associated time delay effects were explored by interrogating the model. Surprising effects were discovered, some of them being counter‐intuitive to what simple theory would predict. Management guidelines were provided as to the system‐wide economic consequences of change in individual elements of a physical distribution system.

Since robot’s structural stiffness is usually less than 1 N/µm, mode coupling chatter occurs frequently during robotic milling process, and chatter frequency is close to the natural frequency of the robot itself. Chatter not only affects the surface quality but also damages the robot and reduces the positioning accuracy. Therefore, it is necessary to predict chatter in robotic machining process.

A three-dimensional dynamic model for robot’s spatial milling plane is established, and a corresponding stability criterion is obtained. First, the cutting force in milling plane is transformed into the coordinate system of the robot principal stiffness direction based on homogeneous transformation matrix. Then the three-dimensional stability criterion under milling process can be obtained by using system stability analysis. Furthermore, the circle diagram of mode coupling chatter stability is drawn. Each feeding direction’s stability under the two processing forms, referred as spindle vertical milling and spindle horizontal milling, is analyzed.

The experimental results verify that the three-dimensional stability criterion can avoid chatter by selecting machining feed direction in stable area.

This paper established a three-dimensional dynamic model in robot’s spatial milling plane and proposed a three-dimensional stability criterion according to the Routh criterion. The work is also expected to be an efficient tool in the development of robotic milling technology.

This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the actual crack detection during welding process.

The paper studied the AE characteristics in welding using thermoelastic theory, which investigates the dynamical displacement field caused by a crack and the welding heating effect. In the calculation model, the crack initiation and extension are represented by moment tensor as the AE source, and the welding heat source is the Gauss heat flux distribution. The extended finite element method (XFEM) is implemented to calculate and solve the AE response of a thermoelastic plate with a crack during the welding heating effect. The wavelet transform is applied to the time–frequency analysis of the AE signals.

The paper provides insights about the changing rule of the acoustic radiation patterns influenced by the heating effect of the moving heat source and the AE signal characteristics in thermoelastic plate by different crack lengths and depths. It reveals that the time–frequency characteristics of the AE signals from the simulation are in good agreement with the theoretical ones. The energy ratio of the antisymmetric mode A0 to symmetric mode S0 is a valuable quantitative inductor to estimate the crack depth with a certain regularity.

This paper mainly discusses the application of XFEM to calculate and analyze thermoelastic problems, and has presented few cases based on a specified configuration. Further work will focus on the calculation and analysis under different plate configurations and conditions, which is to obtain more interesting and general conclusions for guiding practice.

The paper is a successful application of XFEM to solve the problem of AE response of a crack in the dynamic welding inhomogeneous heating effect. The paper provides an effective way to obtain the AE signal characteristics in monitoring the welding crack.

The purpose of this paper is to show how to find the regions of dynamic instability of a beam axially loaded and visco‐elastically constrained at its ends by Kelvin‐Voigt translational and rotational units variously arranged according to different configurations, by using the equation of boundary frequencies.

With respect to visco‐elasticity the time variable is present as a parameter so that the above‐mentioned exact approach is exploited to draw three‐dimensional diagrams of the dynamic component of the periodic load and its frequency, varying with time and with the viscosity parameter μ characterizing the restraints.

For not rigidly constrained configurations a peculiar asymptotic tendency is recognizable in both cases.

The study allows for identifying the influence of visco‐elastic restraints in the response of a beam under a dynamic axial load. Dynamic excitation occurs in several fields of mechanics: dynamic loads are encountered in structural systems subjected to seismic action, aircraft structures under the load of a turbulent flow and industrial machines whose components transmit time‐dependant forces.

Visco‐elasticity accounts for possible vibration control solutions planned to improve the dynamic response of the rod; they can consist of layers of visco‐elastic material within the body of the modelled element or local viscous instruments affecting the boundary conditions; the latter is the application this paper focuses on.

With this paper a calculation procedure to get an exact solution for particular static configurations of the beam is followed in order to define the influence of visco‐elastic restraints under a dynamic axial load; the responses are given in terms of boundary frequencies domains and are supposed to be useful to learn the behaviour in time and in dependence of the intrinsic viscosity of the restraints.

To predict the occurrence of the combination resonances in parametrically excited, simply supported laminated composite plates in contrast to the simple resonances by using first‐order shear deformation lamination theory considering the effects of shear deformation and rotary inertia.

Finite element technique is applied to obtain the equilibrium equation of a plate. Modal transformation is applied to transform the equilibrium equation into a suitable form for the application of the method of multiple scales (MMS). The MMS is applied to obtain the boundaries of the simple and combination resonances.

The combination resonance zones contribute a considerable amount to the local instability region and the widths of combination resonance zones are comparable to those of the simple resonance zones for the loading of the small bandwidth at one end or for the concentrated edge loading.

Aircrafts, spacecrafts and many other structures such as ships, bridges, vehicles and offshore structures use the plate type elements, which are susceptible to dynamic instability.

It will assist the researchers of stability behavior of elastic systems.

The Euler beam theory is used to study the dynamic stability of a composite material slider‐crank mechanism with an elastic connecting rod. The Ritz finite element procedure is applied to derive the governing equations of motion of the mechanism. Based on the assumption that the slider‐crank mechanism is subjected to a sinusoidal input torque and the operation condition is at a steady dynamic state, the governing equations represent a system of second order differential equations with periodic coefficients of the Mathieu‐Hill type. Making use of the Bolotin method, the boundaries between stable and unstable solutions of the elastic connecting rod are constructed. The advantages of using composite materials in the design of mechanisms are demonstrated.