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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 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 detection of H₂ concentrations in concentrations undetectable by the conventional detection method of surface acoustic wave (SAW) sensors based on frequency shift, by correlating analyte presence with Fourier spectra components.

Fast Fourier Transform (FFT) and autocorrelation analysis of phase noise in a SnO2-coated SAW sensor was performed. Fourier spectra were obtained by FFT from the SAW sensor resonance frequency instability, in the absence of analyte, and for H₂ concentrations between 0.08 and 0.4 per cent.

All analyte concentrations are below the sensor limit of detection, which is 0.8 per cent for H₂. Although these analyte concentrations caused no significant change in the resonance frequency of the SAW resonator, the FFT spectra presented several modifications, namely, the appearance of a new peak and the decrease of randomness. The authors consider that the effect is because of the chaotic behavior of the temporal dependence of the SAW resonance frequency. This explanation is substantiated by the decrease observed in the SAW oscillator autocorrelation function, which is an indication for a chaotic behavior.

As chaotic systems are extremely sensitive to perturbation, measurement methods based on chaos diagnosis could potentially greatly improve the SAW detection.

Fourier spectra components were correlated with analyte presence in concentrations undetectable by the conventional SAW detection method based on frequency shift.

The purpose of this paper is to contribute to the solution of the buckling and resonance stability problems in inelastic beams and wooden plane trusses, taking into account geometric and material defects.

Two sources of non-linearity are analyzed, namely the geometrical non-linearity due to geometrical imperfections and material non-linearity due to material defects. The load-bearing capacity is obtained by the rheological-dynamical analogy (RDA). The RDA inelastic theory is used in conjunction with the damage mechanics to analyze the softening behavior with the scalar damage variable for stiffness reduction. Based on the assumed damages in the wooden truss, the corresponding external masses are calculated in order to obtain the corresponding fundamental frequencies, which are compared with the measured ones.

RDA theory uses rheology and dynamics to determine the structures' response, those results in the post-buckling branch can then be compared by fracture mechanics. The RDA method uses the measured P and S wave velocities, as well as fundamental frequencies to find material properties at the limit point. The verification examples confirmed that the RDA theory is more suitable than other non-linear theories, as those proved to be overly complex in terms of their application to the real structures with geometrical and material defects.

The paper presents a novel method of solving the buckling and resonance stability problems in inelastic beams and wooden plane trusses with initial defects. The method is efficient as it provides explanations highlighting that an inelastic beam made of ductile material can break in any stage from brittle to extremely ductile, depending on the value of initial imperfections. The characterization of the internal friction and structural damping via the damping ratio is original and effective.

In Report No. 103 of the Aeronautical Research Institute, will be found the results of experiments in the electrical method of measuring small vibrations with the aid of a triode valve, together with its applications to the measurement of vibrations of airscrew blades.

The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.

The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.

The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.

The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

Vibration monitoring is being increasingly used as a tool for safe operation of machinery and efficient maintenance planning. There are, however, many problems associated with the measurement and interpretation of vibration data. In order to obtain a rapid diagnosis of a machine's health, and to apply condition monitoring results in practice, it is often necessary to consider the machine operating conditions, performance and other factors. These different approaches should be incorporated into one diagnostic technique having the proper balance of emphasis on each approach.

The prediction of critical velocity at instability threshold for shell and tube heat exchangers is important to avoid failure of tubes as a result of flow-induced vibrations due to water cross flow. The flow-induced vibration in finned tube heat exchangers is affected by various parameters such as fin height, fin pitch, fin material, tube array, pitch ratio, fin type, fluid velocity etc. In this paper, an experimental investigation of fluid elastic instability in shell and tube heat exchangers is carried out by subjecting normal square finned tube arrays of pitch ratio 1.79 to water cross flow.

The five tube arrays, namely plain array, two finned tube arrays with 3 fpi and 9 fpi fin density, and two finned tube arrays with 3 mm and 6 mm fin height are tested in the experimental test setup with water flow loop and vibration measurement system. The research objective is to evaluate the effect of fin density and fin height on the instability threshold. The critical velocity at instability threshold is determined to characterize the fluid elastic instability behavior of different tube arrays. The vortex shedding behavior of the tube arrays is also studied by determining Strouhal number corresponding to the small peaks before fluid elastic instability.

The fluid elastic instability behavior of the tube arrays was found to be the function of fin tube parameters. The experimental results indicate that an increase in fin density and fin height results in delaying the instability threshold for finned tube arrays. It is also observed that critical velocity at instability is increased for finned tube arrays compared to plain tube arrays of the same pitch ratio. The design modifications in the outer box have resulted in further reduction in the natural frequency. This enabled to reach clear instability for all the five-tube arrays.

The research data add the value to the present body of knowledge by knowing the effect of fin height and fin density on the fluid elastic instability threshold of normal square finned tube arrays subjected to water cross flow.

The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat source/sink varying in a linear fashion with a vertical height expressed as z was allowed, functioning as a heat sink in an area of the layer and as a heat source in the remainder.

First, the authors present the governing equations of motion and derive the associated perturbation equations. Second, the authors introduce the linear and nonlinear analysis of the system. Third, the authors transform the system to velocity-vorticity-potential formulation and introduce a numerical study of the problem in three dimensions.

First, the linear instability and nonlinear stability thresholds are derived. Second, the linear instability thresholds accurately predict the onset of instability. Third, the required time to arrive at the steady state increases as Ra tends to Ra_L . Fourth, the authors find that the convection has three different interesting patterns.

With the modernday need for heat transfer or insulation devices in industry, particularly those connected with nanotechnology, the usefulness of a mathematical analysis of such resonance became apparent. Thus, this study is believed to be of value.