In-plane vibrations of slightly curved beams: two models compared

Linear and nonlinear free vibration analysis of functionally graded porous nanobeam using stress-driven nonlocal integral model

Axially moving materials can represent many engineering devices such as power transmission belts, elevator cables, plastic films, magnetic tapes, paper sheets, textile fibers, band saws, aerial cable tramways, and crane hoist cables @1–3#. Energetics of axially moving materials is of considerable interest in the study of axially moving materials. The total mechanical energy associated with axially moving materials is not constant when the materials travel between two supports. It is a fundamental feature of free transverse vibration of axially moving materials, while the total energy is constant for an undamped non-translating string or beam. Chubachi @4# first discussed periodicity of the energy transfer in an axially moving string. Miranker @5# analyzed energetics of an axially moving string, and derived an expression for the time rate of change of the string energy. Barakat @6# considered the energetics of an axially moving beam and found that energy flux through the supports can invalidate the linear theories of both the axially moving string and beam at sufficiently high transporting speed. Tabarrok, Leech and Kim @7# showed that the total energy of a travelling beam without tension is periodic in time. Wickert and Mote @8# pointed out that Miranker’s expression represents the local rate of change only because it neglected the energy flux at the supports, and they presented the temporal variation of the total energy related to the local rate of change through the application of the onedimensional transport theorem. They also calculated the temporal variation of energy associated with modes of moving strings and beams. Renshaw @9# examined the change of the total mechanical energy of two prototypical winching problems, which provided strikingly different examples of energy flux at a fixed orifice of an axially moving system. Lee and Mote @10,11# presented a generalized treatment of energetics of translating continua, including axially moving strings and beams. They considered the case that there were nonconservative forces acting on two boundaries. Renshaw, Rahn, Wickert and Mote @12# examined the energy of axially moving strings and beams from both Lagrangian and Eulerian views. Their studies indicated that Lagrangian and Eulerian energy functionals are not conserved for axially moving continua. Zhu and Ni @13# investigated energetics of axially moving strings and beams with arbitrarily varying lengths. Although both the Eulerian and Lagrangian functionals for the total mechanical energy of axially moving materials are generally not constant, there do exist alternative functionals that are con-

Linear and nonlinear transient vibration analysis of stiffened plate structures

Linear and nonlinear vibration of non-uniform beams on two-parameter foundations using p-elements

In this paper, a forced vibration model of composite beams under the action of periodic excitation force considering geometric nonlinearity is proposed. For the strain–displacement relationship, Timoshenko beam theory is used, and the element and system matrices are developed using the differential quadrature finite element method. Each node has 3 degrees of freedom. The incremental harmonic balance method is used to solve the nonlinear forced vibration equation. In order to prove the validity of the proposed model, the solution of the Duffing equation is calculated using the analytical method and the proposed method. Next, linear forced vibration analysis of the beam made of isotropic material is performed and compared with the result of ABAQUS. The results are very close. Based on these comparisons, nonlinear vibration phenomena of composite beams are studied under the action of periodic forces.

This study deals with the geometrically non-linear vibration analysis of concrete shallow funicular shells of rectangular plan with four clamped edges under impulse loads. The shape of a concrete funicular shell is such that the shell is subjected to pure compression under its dead weight. Following the existing method presented for the linear vibration analysis, the geometrically non-linear vibration analysis is considered through the use of non-linear shallow shells theory. Each displacement component is expanded in a double Fourier series and the kinetic energy, the elastic strain energy and the virtual work done by external forces are calculated in terms of the displacement components. Then, the equations of motion are obtained using the Lagrangian approach and are solved with the Runge–Kutta fourth-order method. The solution is verified against the results obtained with the finite-element method. The difference between the results of the linear and non-linear vibration analyses has been considered. Furthermore, it is indicated that under the considered dynamic loads, internal moments and consequentially tensile stresses are formed in the funicular shell and the shell does not behave purely as a funicular element. Finally, the plan aspect ratio effect on the time response of funicular shells has been shown.

Theoretical analyses have been carried out on the nonlinear hydroelastic vibration of a cylindrical tank with an elastic bottom. In this report, a linear axisymmetric free vibration analysis of the bottom plate coupled with the liquid contained is presented. In the analysis, the effect of the static deflection of the bottom plate due to the static liquid pressure was taking into account. Numerical calculations were carried out for kind kinds of bottom plates with different thickness and made of different kinds of materials. The effect of the liquid contained on the bulging-type natural frequency, as well as the influence of the bottom plate motion on the sloshing-type natural frequency, was investigated.

Linear and non-linear vibration and frequency response analyses of microcantilevers subjected to tip–sample interaction

Experimental analysis of the linear and nonlinear vibration behavior of flax fibre reinforced composites with an interleaved natural viscoelastic layer

In this study, different alternatives to detect, localize damage from linear and nonlinear vibration responses are investigated. These alternatives are compared on two concrete slabs which were subjected to two different damage types and extents. Linear and nonlinear modal test configurations were conducted. The change of linear resonant frequencies and the nonlinear behavior with damage are compared. Then, the modal shapes are leveraged for localizing the damage position in three different ways. First, the coordinate modal assurance criterion was used. Second, a local damage index is defined as the difference between the maximum principal curvatures (before and after damage) of a set of resonant modes. Third, a nonlinear based localization is proposed by weighting the modal shape curvature differences by its corresponding nonlinear parameter. The results show that linear based techniques were able to localize the damage position in the first slab (severe damage), but failed in the second one (subtle damage). The proposed nonlinear localization technique was able to detect and localize the damage position in both investigated cases.

In this article, based on the Euler-Bernoulli hypothesis, the linear and nonlinear free vibration analysis of a microbeam subjected to a symmetric electrostatic field is investigated by using the differential quadrature method (DQM). In the analysis, the geometric nonlinearity of the microbeam, which performs as a midplane stretching effect, and the fringing field effect are considered simultaneously. In the numerical calculation, the amplitude frequency response curves of the nonlinear free vibration for the microbeam are obtained. The effects of the fringing field and some related parameters on the linear and nonlinear free vibration of the microbeam are discussed.

In the framework of transduction, nondestructive testing, and nonlinear acoustic characterization, this article presents the analysis of strongly nonlinear vibrations by means of an original numerical algorithm. In acoustic and transducer applications in extreme working conditions, such as the ones induced by the generation of high-power ultrasound, the analysis of nonlinear ultrasonic vibrations is fundamental. Also, the excitation and analysis of nonlinear vibrations is an emergent technique in nonlinear characterization for damage detection. A third-order evolution equation is derived and numerically solved for extensional waves in isotropic dissipative media. A nine-constant theory of elasticity for isotropic solids is constructed, and the nonlinearity parameters corresponding to extensional waves are proposed. The nonlinear differential equation is solved by using a new numerical algorithm working in the time domain. The finite-difference numerical method proposed is implicit and only requires the solution of a linear set of equations at each time step. The model allows the analysis of strongly nonlinear, one-dimensional vibrations and can be used for prediction as well as characterization. Vibration waveforms are calculated at different points, and results are compared for different excitation levels and boundary conditions. Amplitude distributions along the rod axis for every harmonic component also are evaluated. Special attention is given to the study of high-amplitude damping of vibrations by means of several simulations. Simulations are performed for amplitudes ranging from linear to nonlinear and weak shock.

Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient

Re-examination of nonlinear vibration, nonlinear bending and thermal postbuckling of porous sandwich beams reinforced by graphene platelets

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.