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Li-qun Chen - One of the best experts on this subject based on the ideXlab platform.
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dynamic effect of Internal Resonance caused by gravity on the nonlinear vibration of vertical cantilever beams
Journal of Sound and Vibration, 2020Co-Authors: Guoxu Wang, Hu Ding, Li-qun ChenAbstract:Abstract Although the transverse vibration of the cantilever structure is of great interest, the Internal Resonance of the vertical cantilever structure is always ignored. In this paper, nonlinear free vibration and 1/3 super-harmonic Resonance of a hanging cantilever beam are firstly presented with 3:1 Internal Resonance caused by gravity. By employing the temporal multi-scale method, mode responses in these two vibrations are obtained. The harmonic balanced method is used for solving the excitation component and the whole deflection in super-harmonic Resonance. For nonlinear free vibration, beat phenomenon is found and the effect of mode interaction is determined by gravity, damping and initial perturbation. For super-harmonic Resonance, the amplitude of the first two modes can be quite large and exceed the excitation component if damping is not strong. Besides, the softening-type frequency curves are predominated by the inertia nonlinearity. Compared with the excitation component and the whole deflection, the mode responses are more easily affected by gravity. If the value of gravity parameter is a little bit lower than the one in the condition of strict Internal Resonance, the energy transmission, multiple solutions and bifurcations and three complex types of frequency curves can be found in mode responses. Hysteresis and saturation phenomena in mode responses can be discovered as well. Results from analytical methods are almost identical to those from numerical ways. In summary, the Internal Resonance of slender hanging cantilever structures should be aroused more attention, for hanging cantilevers are common in practical engineering and considerable mode responses can be induced by large initial perturbation in weakly damped free vibration or by low excitation frequency and large excitation amplitude in super-harmonic Resonance. In addition, the complex dynamics can be worthwhile to judge the occurrence of Internal Resonance and its impact on structures. Since gravity has tensile effects on hanging cantilevers, these phenomena may also occur in beams with axial tension.
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Resonance response interaction without Internal Resonance in vibratory energy harvesting
Mechanical Systems and Signal Processing, 2019Co-Authors: Hu Ding, Li-qun ChenAbstract:Abstract Resonance response interaction in nonlinear multiple degrees of freedom vibration systems has always involved Internal Resonance. In this article, bubble shaped response curve is uncovered without pre-designated Resonances relationship that is a necessary condition for Internal Resonance. The objective of this article is twofold: first to explore the connection between the Resonance response interaction and bubble shaped response curve that may appear in the forced response of a nonlinear magnetoelectric coupled system; and, second, to exploit Resonance response interaction to enhance the vibratory energy harvesting bandwidth. A nonlinear magnetoelectric oscillator coupled linearly to an additional oscillator is used to demonstrate the phenomena and the enhanced performance. The lateral springs could produce the geometrical nonlinear stiffness and its stiffness to adjust the two Resonance responses such that the bubble shaped response curve appears in the power-frequency response plot. The method of harmonic balance is well established method for the analysis of such the power-frequency response. The results are also validated by some numerical work. The power-frequency response curves are generated for distinct harvesting mass, manifesting the Resonance response interaction could increase the bandwidth and output power. At last, the Resonance response interaction designed energy harvesting from Gaussian white noise excitation is numerically addressed to illustrate positive effects of geometrical nonlinearity.
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irregular instability boundaries of axially accelerating viscoelastic beams with 1 3 Internal Resonance
International Journal of Mechanical Sciences, 2017Co-Authors: Youqi Tang, Dengbo Zhang, Li-qun ChenAbstract:Abstracts Irregular instability boundaries of axially accelerating beams with 1:3 Internal Resonance are analytically and numerically investigated in this paper. The distributed parameter is due to the small simple harmonic axial speed. The viscoelastic characteristic of the beam is described by the Kelvin–Voigt model in which the material time derivative is used. A linear partial-differential equation with the variable coefficient and the relevant boundary conditions governing the transverse motion is presented. The effects of the nonhomogeneous boundaries are highlighted. By the method of multiple scales, the solvability conditions in summation and principal parametric Resonances are established by some different manipulations in the process of the classical multiple scales method. The Routh–Hurwitz criterion is used to determine the instability boundaries. The effects of viscoelastic coefficient and the viscous damping coefficient are examined on the instability boundaries. Irregular instability boundaries appeared when the 1:3 Internal Resonance is introduced. It is shown that the numerical calculations by the differential quadrature scheme can verify the approximate analytical results.
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forced vibration of axially moving beam with Internal Resonance in the supercritical regime
International Journal of Mechanical Sciences, 2017Co-Authors: Xiao-ye Mao, Hu Ding, Li-qun ChenAbstract:Abstract Local and global Resonances under the condition of 3:1 Internal Resonance of a super-critically axially moving beam, subjected to a harmonic exciting force, are investigated in the present work. The governing equation is derived from the generalized Hamilton's principle and discreted into a multiple-degrees-of-freedom system by the Galerkin's method. In the super-critical regime, the axially moving beam becomes a bistable system with two symmetrical non-trivial equilibrium configurations. Based on the transformation around one of them, natural frequencies and the condition of Internal Resonance are obtained. By employing the method of multiple scales, Resonances for first-two modes and harmonics under the condition of Internal Resonance are discussed analytically. Total displacement at the middle of the beam is composed by them and confirmed by direct numerical method. Internal Resonance is found to have a big effect on the phase angle of and the amplitude. Coupling ship between the first-two modes is verified to be produced by the cubic nonlinearity and the 3:1 commensurability together. The effect of moving speed acting on the Internal Resonance is discussed and an energy transmission region is found. Different with the Internal Resonance in the sub-critical regime, most of the transferred energy is absorbed by the quadratic nonlinearity in the super-critical regime. The critical excitation of the local response is predicted by the analytical method and certified by simulations. The global response for the primary Resonance has two stable focal points. However, the global response for the secondary Resonance only has one stable focal point for the non-trivial equilibrium configuration is counteracted.
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primary Resonance of traveling viscoelastic beam under Internal Resonance
Applied Mathematics and Mechanics-english Edition, 2017Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:Under the 3:1 Internal Resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the Internal Resonance, the energy transfer between the Internal Resonance modes and the saturation-like phenomena in the steady-state responses is presented.
Marco Amabili - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear vibrations of a circular cylindrical shell with multiple Internal Resonances under multi-harmonic excitation
Nonlinear Dynamics, 2018Co-Authors: Ivan D. Breslavsky, Marco AmabiliAbstract:The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two Internal Resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the Resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to Resonance and each one is in a one-to-one Internal Resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincaré maps and time responses.
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nonlinear vibrations of a circular cylindrical shell with multiple Internal Resonances under multi harmonic excitation
Nonlinear Dynamics, 2018Co-Authors: Ivan D. Breslavsky, Marco AmabiliAbstract:The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two Internal Resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the Resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to Resonance and each one is in a one-to-one Internal Resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincare maps and time responses.
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Identification of Non-Linear Damping of Nuclear Reactor Components in Case of One-to-One Internal Resonance
Volume 4A: Dynamics Vibration and Control, 2016Co-Authors: Joachim Delannoy, Marco Amabili, Brett Matthews, Brian Painter, Kostas KarazisAbstract:In Pressurized Water Reactors (PWR) assemblies are exposed to challenging thermal, mechanical, and irradiation loads during operation. Global core and local fuel assembly flow fields coupled with seismic excitation result in fuel assembly and fuel rod vibrations. The fact that vibrations may become excessive in certain conditions has consequences on operational safety margins in fuel assemblies designs.In order to understand how the fuel assembly responds dynamically to an external excitation, it is important to identify the main characteristics of the structures. Among them, the fuel assembly system damping is a fundamental parameter that is usually identified by a number of experiments involving fluid-structure interaction. Recent studies have shown that the damping ratio increases with the excitation force when the structure is entering large-amplitude vibrations, in which case the geometric non-linearities have to be taken into account.The present paper presents an advanced identification procedure developed to identify the system characteristics from experimental non-linear response curves obtained from forced vibration tests, accounting for fluid-structure interaction, at different excitation levels. Furthermore, the numerical tool developed in this analysis is capable of working with systems presenting one-to-one Internal Resonance, i.e. systems with symmetry such as circular tubes and circular cylindrical shells. The method relies on a harmonic decomposition of the displacement to cope with the data usually available by vibration measurements.Copyright © 2016 by ASME
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nonlinear dynamics of an axially moving timoshenko beam with an Internal Resonance
Nonlinear Dynamics, 2013Co-Authors: Mergen H Ghayesh, Marco AmabiliAbstract:This paper investigates the nonlinear forced dynamics of an axially moving Timoshenko beam. Taking into account rotary inertia and shear deformation, the equations of motion are obtained through use of constitutive relations and Hamilton’s principle. The two coupled nonlinear partial differential equations are discretized into a set of nonlinear ordinary differential equations via Galerkin’s scheme. The set is solved by means of the pseudo-arclength continuation technique and direct time integration. Specifically, the frequency-response curves of the system in the subcritical regime are obtained via the pseudo-arclength continuation technique; the bifurcation diagrams of Poincare maps are obtained by means of direct time integration of the discretized equations. The resonant response is examined, for the cases when the system possesses a three-to-one Internal Resonance and when not. Results are shown through time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The results indicate that the system displays a wide variety of rich dynamics.
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coupled longitudinal transverse dynamics of an axially moving beam with an Internal Resonance
Mechanism and Machine Theory, 2012Co-Authors: Mergen H Ghayesh, Siavash Kazemirad, Marco AmabiliAbstract:Abstract The forced nonlinear dynamics of an axially moving beam with coupled longitudinal and transverse displacements is numerically investigated in this paper with special consideration to the case with a three-to-one Internal Resonance. The two coupled nonlinear partial differential equations for the longitudinal and transverse motions are discretized via the Galerkin technique, and the resulting set of nonlinear ordinary differential equations is solved either by means of the pseudo-arclength continuation method or via direct time integration. Specifically, the frequency–response curves of the system are obtained using the pseudo-arclength continuation technique, and the bifurcation diagrams of Poincare maps via direct time integration. The effect of system parameters on the above-mentioned diagrams is examined and the results are presented in the form of time histories, phase-plane portraits, Poincare maps, and fast Fourier transforms (FFTs). It is shown that depending on the system parameters, the system displays a wide variety of rich dynamics.
Tianyi Zhang - One of the best experts on this subject based on the ideXlab platform.
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Internal Resonance between the extensional and flexural modes in micromechanical resonators
Journal of Applied Physics, 2019Co-Authors: Tianyi Zhang, Chaowei Guo, Zhuangde Jiang, Xueyong WeiAbstract:Internal Resonance between different vibration modes in micromechanical devices has been widely studied due to its promising application prospects in microelectromechanical systems (MEMS) resonators and oscillators. In this paper, we investigated the 2:1 Internal Resonance between the extensional and flexural modes in a micromechanical cantilever beam resonator using open and closed loop testing methods. In the open loop test, energy transfer from the extensional mode to the flexural mode induced by Internal Resonance is directly observed. Amplitude saturation and Internal Resonance bandwidth change in the extensional mode are experimentally studied and theoretically verified with numerical simulation. In the closed loop system, Internal Resonance produces a bistable self-oscillation frequency. The oscillation frequency of the extensional mode will be locked to one of the two peaks induced by Internal Resonance. In addition, obvious improvement in short-term frequency stability of the closed loop system is observed with the help of Internal Resonance. The dynamic characteristics studied in this research can be potentially used to enhance the performance of MEMS vibration devices by Internal Resonance.
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sensitivity enhancement of a resonant mass sensor based on Internal Resonance
Applied Physics Letters, 2018Co-Authors: Tianyi Zhang, Zhuangde JiangAbstract:There exist numerous vibration modes in a resonant structure, and these modes can interact with each other. Here, the Internal Resonance between the fundamental mode and higher order modes is observed in a polyvinylidene fluoride piezoelectric membrane as a resonant mass sensor. Higher order modes draw energy from the fundamental one and vibrate at integer times of the fundamental mode's frequency. The Resonance frequency shift of the fundamental mode can thus be magnified integer times through Internal Resonance. The sensitivity of the resonant mass sensor, defined by the Resonance frequency shift caused by mass change, is enhanced based on this mechanism. The sensing characteristics are experimentally studied with a concentrated mass load attached to the sensor. The sensitivity improvement of directly using higher order modes and detecting the Internal Resonance response is tested and compared in our experiment. An 11 times sensitivity magnification is achieved with the Internal Resonance method, which has an obvious advantage over the higher order method.There exist numerous vibration modes in a resonant structure, and these modes can interact with each other. Here, the Internal Resonance between the fundamental mode and higher order modes is observed in a polyvinylidene fluoride piezoelectric membrane as a resonant mass sensor. Higher order modes draw energy from the fundamental one and vibrate at integer times of the fundamental mode's frequency. The Resonance frequency shift of the fundamental mode can thus be magnified integer times through Internal Resonance. The sensitivity of the resonant mass sensor, defined by the Resonance frequency shift caused by mass change, is enhanced based on this mechanism. The sensing characteristics are experimentally studied with a concentrated mass load attached to the sensor. The sensitivity improvement of directly using higher order modes and detecting the Internal Resonance response is tested and compared in our experiment. An 11 times sensitivity magnification is achieved with the Internal Resonance method, which ...
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sensitivity enhancement of a resonant mass sensor based on Internal Resonance
Applied Physics Letters, 2018Co-Authors: Tianyi Zhang, Zhuangde Jiang, Xueyong Wei, Tianhong CuiAbstract:There exist numerous vibration modes in a resonant structure, and these modes can interact with each other. Here, the Internal Resonance between the fundamental mode and higher order modes is observed in a polyvinylidene fluoride piezoelectric membrane as a resonant mass sensor. Higher order modes draw energy from the fundamental one and vibrate at integer times of the fundamental mode's frequency. The Resonance frequency shift of the fundamental mode can thus be magnified integer times through Internal Resonance. The sensitivity of the resonant mass sensor, defined by the Resonance frequency shift caused by mass change, is enhanced based on this mechanism. The sensing characteristics are experimentally studied with a concentrated mass load attached to the sensor. The sensitivity improvement of directly using higher order modes and detecting the Internal Resonance response is tested and compared in our experiment. An 11 times sensitivity magnification is achieved with the Internal Resonance method, which has an obvious advantage over the higher order method.
A E Koshelev - One of the best experts on this subject based on the ideXlab platform.
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alternating dynamic state self generated by Internal Resonance in stacks of intrinsic josephson junctions
Physical Review B, 2008Co-Authors: A E KoshelevAbstract:Intrinsic Josephson-junction stacks realized in high-temperature superconductors provide a very attractive base for developing coherent sources of electromagnetic radiation in the terahertz frequency range. A promising way to synchronize phase oscillations in all the junctions is to excite an Internal cavity Resonance. We demonstrate that this Resonance promotes the formation of an alternating coherent state, in which the system spontaneously splits into two subsystems with different phase-oscillation patterns. There is a static phase shift between the oscillations in the two subsystems, which changes from 0 to 2 in a narrow region near the stack center. The oscillating electric and magnetic fields are almost homogeneous in all the junctions. The formation of this state promotes efficient pumping of the energy into the cavity Resonance leading to strong Resonance features in the current-voltage dependence.
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alternating dynamic state self generated by Internal Resonance in stacks of intrinsic josephson junctions
Physical Review B, 2008Co-Authors: A E KoshelevAbstract:Intrinsic Josephson-junction stacks realized in high-temperature superconductors provide a very attractive base for developing coherent sources of electromagnetic radiation in the terahertz frequency range. A promising way to synchronize phase oscillations in all the junctions is to excite an Internal cavity Resonance. We demonstrate that this Resonance promotes the formation of an alternating coherent state, in which the system spontaneously splits into two subsystems with different phase-oscillation patterns. There is a static phase shift between the oscillations in the two subsystems, which changes from 0 to $2\ensuremath{\pi}$ in a narrow region near the stack center. The oscillating electric and magnetic fields are almost homogeneous in all the junctions. The formation of this state promotes efficient pumping of the energy into the cavity Resonance leading to strong Resonance features in the current-voltage dependence.
Hu Ding - One of the best experts on this subject based on the ideXlab platform.
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dynamic effect of Internal Resonance caused by gravity on the nonlinear vibration of vertical cantilever beams
Journal of Sound and Vibration, 2020Co-Authors: Guoxu Wang, Hu Ding, Li-qun ChenAbstract:Abstract Although the transverse vibration of the cantilever structure is of great interest, the Internal Resonance of the vertical cantilever structure is always ignored. In this paper, nonlinear free vibration and 1/3 super-harmonic Resonance of a hanging cantilever beam are firstly presented with 3:1 Internal Resonance caused by gravity. By employing the temporal multi-scale method, mode responses in these two vibrations are obtained. The harmonic balanced method is used for solving the excitation component and the whole deflection in super-harmonic Resonance. For nonlinear free vibration, beat phenomenon is found and the effect of mode interaction is determined by gravity, damping and initial perturbation. For super-harmonic Resonance, the amplitude of the first two modes can be quite large and exceed the excitation component if damping is not strong. Besides, the softening-type frequency curves are predominated by the inertia nonlinearity. Compared with the excitation component and the whole deflection, the mode responses are more easily affected by gravity. If the value of gravity parameter is a little bit lower than the one in the condition of strict Internal Resonance, the energy transmission, multiple solutions and bifurcations and three complex types of frequency curves can be found in mode responses. Hysteresis and saturation phenomena in mode responses can be discovered as well. Results from analytical methods are almost identical to those from numerical ways. In summary, the Internal Resonance of slender hanging cantilever structures should be aroused more attention, for hanging cantilevers are common in practical engineering and considerable mode responses can be induced by large initial perturbation in weakly damped free vibration or by low excitation frequency and large excitation amplitude in super-harmonic Resonance. In addition, the complex dynamics can be worthwhile to judge the occurrence of Internal Resonance and its impact on structures. Since gravity has tensile effects on hanging cantilevers, these phenomena may also occur in beams with axial tension.
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Resonance response interaction without Internal Resonance in vibratory energy harvesting
Mechanical Systems and Signal Processing, 2019Co-Authors: Hu Ding, Li-qun ChenAbstract:Abstract Resonance response interaction in nonlinear multiple degrees of freedom vibration systems has always involved Internal Resonance. In this article, bubble shaped response curve is uncovered without pre-designated Resonances relationship that is a necessary condition for Internal Resonance. The objective of this article is twofold: first to explore the connection between the Resonance response interaction and bubble shaped response curve that may appear in the forced response of a nonlinear magnetoelectric coupled system; and, second, to exploit Resonance response interaction to enhance the vibratory energy harvesting bandwidth. A nonlinear magnetoelectric oscillator coupled linearly to an additional oscillator is used to demonstrate the phenomena and the enhanced performance. The lateral springs could produce the geometrical nonlinear stiffness and its stiffness to adjust the two Resonance responses such that the bubble shaped response curve appears in the power-frequency response plot. The method of harmonic balance is well established method for the analysis of such the power-frequency response. The results are also validated by some numerical work. The power-frequency response curves are generated for distinct harvesting mass, manifesting the Resonance response interaction could increase the bandwidth and output power. At last, the Resonance response interaction designed energy harvesting from Gaussian white noise excitation is numerically addressed to illustrate positive effects of geometrical nonlinearity.
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forced vibration of axially moving beam with Internal Resonance in the supercritical regime
International Journal of Mechanical Sciences, 2017Co-Authors: Xiao-ye Mao, Hu Ding, Li-qun ChenAbstract:Abstract Local and global Resonances under the condition of 3:1 Internal Resonance of a super-critically axially moving beam, subjected to a harmonic exciting force, are investigated in the present work. The governing equation is derived from the generalized Hamilton's principle and discreted into a multiple-degrees-of-freedom system by the Galerkin's method. In the super-critical regime, the axially moving beam becomes a bistable system with two symmetrical non-trivial equilibrium configurations. Based on the transformation around one of them, natural frequencies and the condition of Internal Resonance are obtained. By employing the method of multiple scales, Resonances for first-two modes and harmonics under the condition of Internal Resonance are discussed analytically. Total displacement at the middle of the beam is composed by them and confirmed by direct numerical method. Internal Resonance is found to have a big effect on the phase angle of and the amplitude. Coupling ship between the first-two modes is verified to be produced by the cubic nonlinearity and the 3:1 commensurability together. The effect of moving speed acting on the Internal Resonance is discussed and an energy transmission region is found. Different with the Internal Resonance in the sub-critical regime, most of the transferred energy is absorbed by the quadratic nonlinearity in the super-critical regime. The critical excitation of the local response is predicted by the analytical method and certified by simulations. The global response for the primary Resonance has two stable focal points. However, the global response for the secondary Resonance only has one stable focal point for the non-trivial equilibrium configuration is counteracted.
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primary Resonance of traveling viscoelastic beam under Internal Resonance
Applied Mathematics and Mechanics-english Edition, 2017Co-Authors: Hu Ding, Linglu Huang, Xiao-ye Mao, Li-qun ChenAbstract:Under the 3:1 Internal Resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the Internal Resonance, the energy transfer between the Internal Resonance modes and the saturation-like phenomena in the steady-state responses is presented.
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steady state response of a fluid conveying pipe with 3 1 Internal Resonance in supercritical regime
Nonlinear Dynamics, 2016Co-Authors: Xiao-ye Mao, Hu Ding, Li-qun ChenAbstract:The forced vibration response of the pipe conveying fluid, with 3:1 Internal Resonance, is studied here for the first time. The straight equilibrium configuration becomes bent while the velocity of the fluid exceeds the critical value. As a result, the original mono-stable system transforms to a bi-stable system. Critical excitation which can cause global responses is solved out from the potential equation of the unperturbed system. The condition of 3:1 Internal Resonance is established after the partial differential equation is discretized. Global bifurcations are studied in simulation ways. By the method of multiple scales, local responses around the bent configuration are investigated. The analytical results are verified by simulations. Responses at the second mode bifurcate out another branch near the Resonance frequency. It is very different with the triply harmonic responses without Internal Resonance. The triply harmonic response is a resonant excitation to the second mode. Responses will change largely with the detuning relationship between these two modes. Influences of the excited amplitude are also studied. Based on the analytical method, critical excited conditions of jumping and hysteretic phenomena are determined. The responses will have up- and down-bifurcations in the special region.