Nonlinear vibration and buckling of circular sandwich plate under complex load

The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory,and then accordingly exact solution of static load and its numerical results were given.Based on time mode hypothesis and the variational method,the control equation of the space mode was derived,and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method.Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated.When circumjacent load makes the lowest natural frequency zero,critical load is obtained.     

Nonlinear dynamical characteristics of piles under horizontal vibration

The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So,the effect of the axis force on the pile is considered.     

Nonlinear vibration of circular sandwich plate under the uniformed load

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Nonlinear vibration absorption of laminated composite beams in complex environment

Nonlinear Dynamics - Nonlinear vibration absorption of a laminated composite beam is investigated with the account of complex environment (moisture and temperature). A passive efficient nonlinear...     

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.     

Nonlinear vibration of corrugated shallow shells under uniform load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells     

Nonlinear vibration modes of an elastic panel under periodic loading

The dynamic instability and nonlinear behavior of a nonshallow thin elastic cylindrical panel with simply supported rectilinear edges under uniformly distributed periodic load is studied. The regions of regular and chaotic dynamics are determined for symmetric and nonsymmetric bending modes of the panel. It is shown that depending on the external load frequency, the nonsymmetric buckling. which occurs when the load amplitude reaches a critical value, can lead to two different dynamic modes. Institute of Mechanics and Mechanical Engineering, Kazan' Science Center, Russian Academy of Sciences, Kazan' 420111. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 186–191, January–February, 2000.     

Nonlinear vibration of viscoelastic sandwich plates under narrow-band random excitations

The effect of the narrow-band random excitation on the non-linear response of sandwich plates with an incompressible viscoelastic core is investigated. To model the core, both the transverse shear strains and rotations are assumed to be moderate and the displacement field in the thickness direction is assumed to be linear for the in-plane components and quadratic for the out-of-plane components. In connection to the moderate shear strains considered for the core, a non-linear single-integral viscoelastic model is also used for constitutive modeling of the core. The fifth-order perturbation method is used together with the Galerkin method to transform the nine partial differential equations to a single ordinary integro-differential equation. Converting the lower-order viscoelastic integral term to the differential form, the fifth-order method of multiple scale is applied together with the method of reconstitution to obtain the stochastic phase-amplitude equations. The Fokker–Planck–Kolmogorov equation corresponding to these equations is then solved by the finite difference method, to determine the probability density of the response. The variation of root mean square and marginal probability density of the response amplitude with excitation deterministic frequency and magnitudes are investigated and the bimodal distribution is recognized in narrow ranges of excitation frequency and magnitude.     

Nonlinear vibration of fluid-conveying single-walled carbon nanotubes under harmonic excitation

In this paper, the nonlinear vibration of a single-walled carbon nanotube conveying fluid is investigated utilizing a multidimensional Lindstedt–Poincaré method. Considering the geometric large deformation of the single-walled carbon nanotube and external harmonic excitation force, based on nonlocal elastic theory and Euler–Bernoulli beam theory, the nonlinear vibration equation of a fluid-conveying single-walled carbon nanotube is established. Analyzing the equation through the multidimensional Lindstedt–Poincaré method, and from the solvability condition of the nonlinear vibration equation, the cubic algebraic equation which indicates the amplitude–frequency relation is obtained. Based on the root discriminant of the cubic equation, the first order primary response of the pinned–pinned carbon nanotube is discussed. The relations among internal resonance, the amplitude and frequency of the external excitation force are analyzed in detail. When the external excite force frequency is around the first mode natural frequency, the first mode primary resonance occurs. If simultaneously the first two modes natural frequency ratio is around 3, internal resonance occurs and the internal resonance region depends on the amplitude of external excitation force.     

Nonlinear vibration response of shear deformable FGM sandwich toroidal shell segments

Meccanica - The nonlinear vibration investigation of toroidal shell segment (TSS) with an analytical approach is presented in this paper. The TSS is considered as a sandwich structure with FGM core...     

Nonlinear vibration isolation of a viscoelastic beam

In this paper, the transmissibility of a viscoelastic beam supported by vertical springs is defined by proposing a new vertical elastic support boundary. By contrasting with the viscoelastic beam with rigid vertical supports and the rigid rod with vertical elastic support ends, the necessity of the transmissibility of an elastic structure with vertical elastic supports is proved. In order to approximately solve the steady-state responses of the nonlinear transverse vibration of the viscoelastic beam under periodic excitation, the harmonic balance method in conjunction with the pseudo arc-length method is adopted. The numerical results are calculated to confirm the approximate analytic results. The comparison between the rigid rod and the elastic beam shows that neglecting the bending vibration of the structures will underestimate the frequency range in which the elastic support produces an effective vibration isolation. On the other hand, the comparison between the rigid support and the spring support demonstrates that ignoring the elasticity of the support ends will create a false understanding of the force transmission of elastic structures. In general, this paper presents the necessity of studying the force transmission of elastic structures with elastic supports. Moreover, this paper will become the beginning of the study of the vibration isolation of the elastic structure.     

Nonlinear vibration of beamplates with a delamination

The problem of beam-plates with a delamination located at an arbitrary site undergoing non-linear free vibration without damp is investigated. For this problem, nonlinear governing equations as well as the continuity, equilibrium and compatibility conditions are established. The Galerkin method and harmonic balance method are employed to find solutions. Finally, in some examples amplitude-frequency curves of the delaminated structure are presented in order to reveal some special dynamic features. Supported by the National Natural Science Foundation of China (No. 19872024).     

Nonlinear free vibration of orthotropic shallow shells of revolution under the static loads

I.Intr0ducti0nThenon1inearvibrationprob1emsofshellsofrevolutionarealwaysofgreatdifficultyandofgreatvaluetostudyfortheircomplexityinmathematicsandmechanicsaswellasinwideapplications.ManyinvestigatorshavemaderesearchontheseinoneWayoranother,butfewinvolvedth…     

Nonlinear dynamic response and active vibration control of the viscoelastic cable with small sag

IntroductionCablesareveryefficientstructuralmembersandhencehavebeenwidelyusedinmanylong_spanstructures,includingcable_supportbridges,guyedtowersandcable_supportroofs.Sincecablesarelight,veryflexibleandlightlydamped ,structuresutilizingcables,i.e .,cable_structuresystems,usuallyhavevariousdynamicproblems.Theirmodelsarethereforeverimportantinpredictingandcontrollingtheirresponses.Inthelastdecade,thenonlineardynamicvibrationandstabilitybehaviorofcablesandcable_structureshavedrawntheattentionofman…     

Nonlinear response of vibrational conveyers with non-ideal vibration exciter: primary resonance

Vibrational conveyers with a centrifugal vibration exciter transmit their load based on the jumping method. The trough is oscillated by a common unbalanced-mass driver. This vibration causes the load to move forward and upward. The motion is substantially related to the vibrational parameters. The transition of the vibratory system for over resonance excited by rotating unbalances is important in terms of the maximum vibrational amplitude and the power requirement from the drive for the cross-over. The mechanical system depends on the motion of the DC motor. In this study, the working ranges of oscillating shaking conveyers with a non-ideal vibration exciter have been analyzed analytically for primary resonance by the method of multiple scales with reconstitution, and numerically. The analytical results obtained in this study have been compared with the numerical results, and have been found to be well matched.     

Experiments on the parametric vibration response of plates under tensile loading

Results of an experimental investigation of the parametric vibration response characteristics of plates subjected to tensile edge loads are presented. Two distinct types of parametric instability behavior are observed: principal resonance and secondary resonance. The principal resonance zones are found to be more dominant. It was observed that the natural frequencies and the boundaries of the instability regions of the plate are considerably influenced by the nature of the edge loading.     

Nonlinear harmonic vibration analysis of a plate-cavity system

Nonlinear harmonic oscillation of a plate-cavity system is analytically studied in this paper. Von-Karman theory is used to model a rectangular plate backed by an air cavity. Coupled nonlinear differential equations of system are analytically derived using Galerkin’s approach. The Multiple Scales Method (MSM) is then employed to solve the corresponding nonlinear equations. Primary, secondary, and combinational resonance conditions are taken into account and the corresponding closed-form frequency-amplitude relationships are derived. A parametric study is carried out and effects of different parameters on the frequency responses are investigated.     

Nonlinear vibration of a lumped system with springs-in-series

Meccanica - The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping...