Second-order Natural Frequency Research Articles

The study of the natural frequency evolution and numerical simulation of retrogressive landslides

A retrogressive landslide is influenced by the cyclical fluctuations in reservoir water levels is considered a common natural disaster. Tension cracks are important indicators for assessing landslide status in the case of retrogressive landslides. Displacement monitoring is a commonly used method and provides an intuitive reflection of the landslide deformation; however, it does not directly indicate the depth of the tension cracks. Based on the principles of vibrational dynamics, a retrogressive landslide is proposed to be initially classified as a single-mass spring oscillator model before the development of cracks. Following the development of tension cracks, the model can be classified as a double-mass spring oscillator model. The model patterns are verified through numerical simulations using ABAQUS. Based on the numerical simulations, with an increase in the number of reservoir water cycle fluctuations, the displacement and stress of the landslide exhibit periodic growth. However, during displacement growth, the tension cracks do not necessarily increase. As the tension cracks deepen, the landslide transitions from a single-mass spring oscillator model to a double-mass spring oscillator model, with the appearance of a second-order natural frequency. Moreover, as the tension cracks deepen, the numerical values of the natural frequency change. The maximum change in first-order natural frequency is 3.5 Hz. The maximum change in second-order natural frequency is 4.5 Hz. The variation in the natural frequency can reflect the depth of development of the landslide's tension cracks and, consequently, indicate changes in the stability state of the landslide.

Research on the vibration mechanism of compressor complex exhaust pipeline based on transient flow

The periodic exhaust of the compressor often induces gas flow fluctuations within the pipeline, leading to vibrations. Excessive vibration can lead to fatigue, cracks, loosening of components, and resulting in local leakage, which may easily lead to fire, explosion, and secondary hazards. Therefore, in this paper, a computational model for the transient flow field of the compressor exhaust pipeline was established, using the pulse excitation method and Fluent software, the natural frequencies of the gas column in the pipeline were calculated, and the patterns of oscillation decay of the gas column wave propagating back and forth within three exhaust pipes were researched. The mechanism behind the pipeline pressure pulsation and the influence of pipeline structural parameters on the natural frequencies of the gas column were explored. The calculation results show that the first-order natural frequency of the gas column is very close to the double frequency of the compressor excitation frequency at 3.33Hz, and the second-order natural frequency of the gas column is very close to the quadruple frequency of the compressor excitation frequency at 3.33Hz, which may cause significant pipeline vibrations. Altering the pipeline structure, especially when influenced by airflow branching after a tee junction, results in complex changes in the natural frequencies of the gas column. Furthermore, the structural natural frequencies of the pipeline were obtained through the finite element. It has been observed that resonance phenomena exist among the structural natural frequencies and their harmonics of the pipeline and the natural frequencies of the gas column and their harmonics, as well as multiples of the excitation frequency. These results lay the foundation for understanding the vibration mechanism of the pipeline and finding ways to reduce vibration.

Design and Experimental Evaluation of a Dual-Cantilever Piezoelectric Film Sensor with a Broadband Response and High Sensitivity.

Cantilever-beam-type PVDF (Polyvinylidene Fluoride) piezoelectric film sensors are commonly utilized for vibration signal detection due to their simple structures and ease of processing. Traditional cantilevered PVDF piezoelectric film sensors are susceptible to the influence of the second-order vibration mode and have a low lateral stress distribution at the free end, which limit their measurement bandwidth and sensitivity. This study is on the design of a dual-cantilever PVDF piezoelectric film sensor based on the principle of cantilevered piezoelectric film sensors. The results of the experiments indicate that, compared to a typical single-arm piezoelectric cantilever beam vibration sensor, the developed sensor has a longer second-order natural frequency that ranges from 112 Hz to 453 Hz, while the first-order natural frequency is maintained at around 12 Hz. This leads to a better ratio of the second-order natural frequency to the first-order natural frequency and a wider frequency response range. At the same time, the sensitivity is increased by a factor of 3.48.

An investigation into the modal effect mechanism of multi-mode coupled flutter with modality-driven method

Modal coupled effects concealed in the semblance of flutter dominated by torsional modes have an uncertain impact on the flutter characteristics of long-span bridges, making it challenging to fully comprehend the underlying physics of three-dimensional flutter. Consequently, this research has investigated the composition of flutter modality and its related modal effect mechanism through experimental and theoretical analyses. Initially, the actual flutter modality and its compositions were ascertained through full-bridge aeroelastic tests on four suspension bridges with main spans exceeding 1750 m. Subsequently, the practical modality-driven flutter analysis was developed to measure the impact of each natural mode, particularly the higher-order mode, on the flutter performance through modal-generated aerodynamic damping. Next, the genetic algorithm was introduced in this method to enhance the convergence robustness. Finally, a systematic investigation was conducted to examine the evolution of modal effects with changes in the main spans. The results of full-bridge aeroelastic tests indicate that the flutter pattern is predominantly formed by the first-order symmetric torsional mode, the first-order symmetric heaving mode, and the second-order symmetric heaving mode. In terms of modal participation and modal aerodynamic damping contribution, the second-order mode governs the flutter heaving modality but has a smaller impact on the flutter performance compared to the first-order mode. The first-order torsional mode and the first-order heaving mode provide continuously increasing positive damping and continuously decreasing negative damping respectively, while the aerodynamic damping provided by the second-order heaving mode exhibits a turning phenomenon as wind velocities increase due to the system frequency approaching the second-order natural frequency. The genetic algorithm can effectively address potential occurrences of non-convergence or switching phenomena in numerical calculations.

Field Measurements of Wind-Induced Responses of the Shanghai World Financial Center during Super Typhoon Lekima.

In this paper, the wind-induced responses of the Shanghai World Financial Center (SWFC) under Super Typhoon Lekima are measured using the health monitoring system. Based on the measurements, the characteristics of vibration, including probability density distribution of accelerations, power spectra, and mode shapes are studied. The curve method and the standard deviation method are used to analyze the relationship of the first- and second-order natural frequencies and damping ratios with amplitudes and the mean wind speed. The results show the following: (1) The structural wind-induced responses in the X and Y directions have high consistencies, and the vibration signals exhibit a peak state; moreover, response amplitudes and acceleration signals disperse when the floor height increases. (2) The first- and second-order natural frequencies in the X and Y directions decrease with the increasing amplitudes and are negatively correlated with mean wind speed; the maximum decrease in natural frequency is 5.794%. The first- and second-order damping ratios in the X and Y directions increase with the increasing amplitudes and are positively correlated with the mean wind speed; the maximum increase in damping ratio is 95.7%. (3) The curve method and the standard deviation method are similar in identifying dynamic characteristic parameters, but the discreteness of the natural frequencies obtained by the curve method is lesser. (4) Under excitations of various typhoons, the mode shapes of SWFC are basically the same, and the mode shapes in the X and Y directions increase with the height and have nonlinearity.

Prestress Modal Analysis under Assembling Error of Diaphragm Disc Coupling

The high-speed and high-torque diaphragm disc coupling used in coal machine-driven systems is the critical power transmission component, especially in high-speed and heavy-duty shafting. The dynamic rotor characteristics are significant. In the case of external excitation in the installation or working process of diaphragm coupling, it is inevitable to have axial deviation, angular misalignment, and radial misalignment error. Therefore, analyzing the prestress mode under the assembly error of diaphragm disc coupling is crucial. The finite element model of diaphragm plate coupling was established using ABAQUS software. The accessible way under critical speed, the mode under axial dislocation, and radial dislocation were analyzed. The results show that the assembly error of the diaphragm disc coupling will affect the first and second-order natural frequencies in a specific range but will not cause resonance.

Research on Dynamic Characteristics Analysis Method of Spindle-Flywheel Rotor System of Inertia Friction Welding Machine

A rotor is a special vibration system whose mechanical characteristics change with rotating speed. Taking the spindle-flywheel rotor system of inertia friction welding machine as the research object, in order to explore the variation law of critical speed and the unbalanced response of rotor system at different node positions, according to the special form of the spindle-flywheel rotor system, the combined flywheel set is simplified as a node of a lumped mass model, and the Riccati transfer matrix method and finite element method are used to calculate respectively. The error of the Riccati transfer matrix method is less than 4% compared with the finite element method, which proves the rationality of an equivalent flywheel node. Compared with the finite element method, the Riccati transfer matrix method, which simplifies the flywheel model, not only ensures accuracy but also shortens the calculation time. This method is obviously more suitable for calculating the spindle-flywheel rotor system model of an inertial friction welding machine. In addition, this method can also calculate the unbalanced response. When the unbalanced mass distribution is closer to the head end of the spindle, the unbalanced response vibrates more strongly at the second-order natural frequency, and the rotor response during vibration can be predicted.

Analysis of the influence of piston–cylinder friction on the torsional vibration characteristics of compressor crankshaft system

With the development of compressors toward high speed and multiple columns, the torsional vibration phenomenon has become a major factor affecting the service life and reliability of the shaft system. Therefore, this paper considers the influence of friction between piston and cylinder on the instantaneous inertia of the crank connecting rod mechanism, establishes a nonlinear torsional vibration mechanics model of shale gas compressor shaft system, solves the natural frequency of the shaft system under undamped and damped conditions using the eigenvector method, and investigates the influence of the friction coefficient between piston and cylinder and the operating speed on the torsional vibration response of the shaft system under the self-excitation of the shaft system and the action of and excitation moment by the Runge–Kutta methods. The results show that after considering the friction between the piston and the cylinder, the second-order natural frequency of the shaft system shows a "high-low–high" fluctuation pattern. As the friction coefficient increases, the amplitude of the shaft system and the peak vibration speed show a rising trend. Meanwhile, when the speed increases, the vibration of the shaft system changes from chaotic \ period to the proposed periodic state, but the amplitude shows a decreasing trend. The research in this paper aims to improve the theory of nonlinear dynamics of compressor shaft systems, and the determined nonlinear parameters can be used to guide the operation and maintenance of compressors in engineering.

A Preliminary Top-Down Parametric Design of Electromechanical Actuator Position Control

A top-down process is proposed and virtually validated for the position control of electromechanical actuators (EMA) that use conventional cascade controllers. It aims at facilitating the early design phases of a project by providing a straightforward mean that requires simple algebraic calculations only, from the specified performance and the top-level EMA design parameters. This makes it possible to include realistic control considerations in the preliminary sizing and optimisation phase. The position, speed and current controllers are addressed in sequence. This top-down process is based on the generation and use of charts that define the optimal position gain, speed loop second-order damping factor and natural frequency with respect to the specified performance of the position loop. For each loop, the control design formally specifies the required dynamics and the digital implementation of the following inner loop. A noncausal flow chart summarises the equations used and the interdependencies between data. This potentially allows changing which ones are used as inputs. The process is virtually validated using the example of a flight control actuator. This is achieved with resort to the simulation of a realistic lumped-parameter model, which includes any significant functional and parasitic effects. The virtual tests are run following a bottom–up approach to highlight the pursuit and rejection performance. Using low-, medium- and high-excitation magnitudes, they show the robustness of the controllers against nonlinearities. Finally, the simulation results confirm the soundness of the proposed process.

Coupling Characteristics of Creep Fracture of Rock Foundation on Wind Turbine under Wind-Induced Vibration

In view of the nonlinear mechanical characteristics of rock foundation creep fracture and its influence on the stability of wind turbine under wind load, based on the influence of wind load, this paper proposed the elastoplastic creep fracture and rock foundation bearing capacity on wind turbine. Considering the superstructure concrete with rock foundation and its boundary conditions, the wind load standard value was obtained and wind turbine system composition was constructed. The two grades of freedom system of viscous damping vibration model was proposed. Furthermore, the frequency characteristic equations and the relations of the first- and second-order natural frequencies were obtained. Considering plastic yield theory on power hard rock base material, the analytical expressions of principal stress distribution, plastic zone, and plastic state of I-II composite crack were obtained and used for coupling Mohr–Coulomb plastic yield condition and creep fracture characteristics. Furthermore, the nonlinear creep model equation and accelerated creep fracture time were also obtained, to be used for the modified Kelvin nonlinear accelerated creep model. Combined with the calculation examples, it is verified that the accelerated creep displacement and crack propagation of rock foundation are obvious, taking full account of the wind bracing and creep characteristics of rock foundation. Final, the failure mode of rock foundation is of compressive shear, local shear, and bending-shear; so, it is necessary to reinforce the interface of the rock foundation in a timely manner.

Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation

The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.

Natural characteristics analysis and experimental test of spiral bevel gear pair in the tractor transmission system

Spiral bevel gear is widely used in various mechanical transmission systems, such as tractor transmission system. Because it is mainly used in the heavy-load conditions, it would most likely resonate within the rated speed, resulting in tooth fatigue damage. In this paper, based on the principle of meshing and gear tooth machining, the spherically involute tooth profile equation of spiral bevel gear is deduced and the precise modeling method based on the CATIA is studied. The natural frequency and modal shape under free vibration are obtained by the finite element method (FEM), the influence of web thickness and web hole on the natural frequency of driven gear plate is analyzed as well. In addition, the experimental modal of bevel gear pair is carried out based on a multiple-reference impact test, Modal Assurance Criterion (MAC) is calculated, the three-dimensional modeling accuracy and the finite element analysis reliability are verified. The results show that the error between the measured frequency of bevel gear pair and the calculated frequency of the finite element simulation are both within 5%, and the MAC is above 0.8. The fourth-order natural frequency is the most sensitive to the web thickness, the second-order natural frequency is the most sensitive to the web hole.

Modal Analysis of Three-point Contact Outside Diameter On-line Measuring Device Based on ANSYS Workbench*

In the grinding process, because the grinding wheel will wear, it is difficult to control the grinding accuracy of the workpiece by the grinder itself. Using radial measuring instrument to measure workpiece size in real time, detect the change of workpiece size and guide the adjustment of grinding parameters can improve the production efficiency of grinder and reduce the machining cost, which is an important link in the machining process of grinder. Different from the traditional two-point contact on-line measurement technology of outer diameter, this paper designs and develops a set of three-point contact on-line measurement device of outer diameter based on the principle of bow height and chord length. In the measuring process, two fixed probes and one displacement sensing probe are in contact with the outer diameter of the workpiece at the same time, and the on-line measurement of the outer diameter of the workpiece is realized by solving the positional relationship among the three probes. In order to avoid resonance in the measuring process of the three-point contact external diameter online measuring device, In this paper, the modal analysis of the device is carried out in the environment of ANSYS Workbench 17.0, and the results show that the first-order and second-order natural frequencies of the free mode of the three-point contact on-line outer diameter measuring device are 648.57 Hz. When the measuring claw of the device is prestressed, the first-order and second-order natural frequencies of the device are 398.5 Hz and 403.94 Hz, respectively, which meet the requirements for on-line measurement of workpieces with rotational speeds in the range of 0-150rpm.

Deflection test and modal analysis of lightweight timber floors

In order to meet the objective requirements of the safety and comfort of the modern lightweight timber floors, and strengthen the research on the coupling performance of the lightweight timber floors vibration characteristics and the building comfort, this article discusses the floor of a two-story prefabricated lightweight timber building demonstration house. In this paper, the floor structure of a two-story light-weight wooden house has been carried out on structural calculation modal and experimental modal, static uniform load and concentrated load deflection value testing. The evaluation of the deflection value of the floor structure, the mode shape, the coupling of the fundamental frequency mode parameters, and the vibration comfort were also studied. The results show that the fundamental frequency simulation value, one-way modal test value and two-way modal test value of the floor structure all meet the requirements of BS-6472 (BS6472-1:2008). That is, the floor structure is not lower than 8 Hz design requirements, and meets the frequency of BS-6472(BS6472-1:2008). The weighted root mean square acceleration is lower than the requirement of 0.45 m/s2; the first three natural frequencies of the floor structure calculated by the finite element simulation are 16.413, 31.847 and 48.921 Hz, and the fundamental frequency mode is the bending vibration in the length and width directions. The second order is the bending mode in the length direction, and the third order is the bending mode in the width direction. The fundamental frequency of the two-way modal test of the floor structure is the first-order bending mode in the X direction; and the second-order natural frequency is the second-order bending vibration shape in the X direction. when the uniform load is mainly the weight of floor own, the simulated maximum deflection value is 1.0658 mm; the simulation is performed according to the standard value of 0.566 kN/m for the uniform load of the floor design, and the simulation is the largest. The maximum deflection value of the simulated floor is 1.47383 mm at its midpoint, which meets the requirements of National Building Code of Canada-2015 (NBCC). The maximum deflection limit of the light wood structure floor system is lower than 3 m and the maximum deflection limit is 2 mm; the six deflection value test lines simulated under a concentrated load of 1 kN all present a parabolic distribution and are symmetrical. The above results has engineering application value for promoting the research on the vibration characteristics of the fabricated lightweight timber floors structure and its optimization design.

Dynamics modeling and analysis of feed drive system for a frame saw machine considering time-varying load

Frame saw machine is one of machine tools that is used to process dimension stone. The velocity fluctuation of traditional feed drive system (FDS) lead to excessive wear of diamond particles. The dynamic performance of the FDS has time-varying characteristics during the processing of stone with a large material removal rate. In this paper, a novel FDS was proposed. Firstly, the dynamic modeling of FDS was set up on account of lumped parameter method (LPM). Then the speed of the new FDS was compared with that of the traditional FDS. Finally, the frequency response characteristics of the system were solved by Lagrange and state space method. Results showed that the new FDS has a faster response feed and less velocity fluctuation. The natural frequency and the amplitude of acceleration increase with decreasing load. With the time-varying load, the range of the second-order natural frequency increased by 50 Hz, which was larger than that of the first-order. The modal test verified that the first two natural frequencies of the saw blade are within the range of the natural frequencies of FDS. The proposed FDS can guide for design, reduce the wear of diamond, and improve processing quality.

Multi-Objective Optimization Design of Natural Frequency of Two-Degree-of-Freedom Fast Steering Mirror System

In the design of two-degree-of-freedom (2-DOF) fast steering mirror (FSM) system, in order to improve the control bandwidth of the system, the low-order natural frequency in the working direction should be reduced as much as possible, and the high-order natural frequency in the non-working direction should be increased. In this paper, a deep-cut flexure hinge mirror system was studied. Firstly, the motion direction of the first to third order natural vibration mode of the system was analyzed. Next, the working stiffness in the third vibration mode direction was deduced to solve the problem that the traditional stiffness calculation method is not suitable for the third vibration mode direction. Then, the energy method and the Castigliano’s second theorem were used to analyze the working stiffness of the deep-cut flexure hinge. Next, the formula for calculating the relationship between the thickness of the mirror and the moment of inertia in the direction of the vibration mode was derived. Combined with the calculation formula of working stiffness in the vibration mode direction, the formula of the first to third order natural frequencies was derived, and the finite element verification and sensitivity analysis of structural parameters were carried out. Finally, by using NSGA-II, a multi-objective optimization design was carried out on the first to third natural frequencies of the system with hinge structure parameters and reflector thickness as independent variables, and the optimization results were analyzed by theoretical calculation and finite element simulation verification. The results show that the first and second-order natural frequencies of fast steering mirror system are reduced by 7.8% and 7.11%, and the third-order natural frequencies are increased by 139.8%. It proves that the optimized structure is much better than the original structure, and the optimal calculation can effectively increase the control bandwidth of the system

Impact of sustained load on damage characteristics of reinforced concrete beams under the combined action of salt freeze-thaw cycles and corrosion

A large number of reinforced concrete (RC) structures in cold regions are attacked by the combined action of sustained load, freeze-thaw cycles and steel corrosion. The combined effects accelerate the deterioration process of RC and significantly reduce the service life of RC structures. This paper presents an investigation of the damage characteristics of RC beams under combined action of salt freeze-thaw cycles (SFTCs), load and corrosion. By using the large artificial climate chamber and the RC beam reverse loading device, three RC beams were subjected to SFTCs and corrosion tests under different load levels, and one beam was subjected to corrosion tests under normal temperature without load. The test results showed that the second-order natural frequency can be used as an index to evaluate the freeze-thaw damage of RC beams. The higher the load level, the greater the amount of concrete spalling and the faster the second-order natural frequency decreases. Affected by the freeze-thaw damage, the surface of test beams is not prone to rust crack, but the stress cracks become wider with the increase of SFTCs. In addition, freeze-thaw damage aggravates the non-uniformity of longitudinal reinforcement corrosion, accelerates the corrosion ratio of reinforcement. With the increase of load level, the average corrosion ratios of longitudinal rebar and stirrups increase, and the local corrosion of longitudinal reinforcement is more serious. The coupling effect is obvious when the load, SFTCs and corrosion work together, and the evaluation of the damage characteristics of concrete members should pay attention to the interaction between various factors.

Experimental investigation on vortex-induced vibrations of a hang-off evacuated drilling riser

A model experiment has been conducted for a hang-off evacuation riser considering the lower marine riser package (LMRP) based on the strain gauge test technology. The finite element eigenvalue method is used to analyze the natural frequency and mode shapes of the hang-off riser considering the axial tension force and the weight of LMRP. The modal analysis method is used to restructure the motion and analyze the vortex-induced vibration characteristics of the hang-off riser. Then, the influence of evacuation velocity is discussed. Results indicate that the mode shapes amplitude of the experimental riser with LMRP is significantly larger than that of the ordinary cantilever. The dominant frequency of each measuring point is the same, and the end-cell-induced vibration small frequency is observed near the bottom end. The vortex shedding in the cross-flow (CF) direction produced a large lift force, which resulted in the vibration frequency of in-line direction dominated by the CF direction. When the reduced velocity (Vr) is less than 40, the frequency response of the hang-off riser model increased with the evacuation velocity, which was subjected to the Karman vortex shedding frequency. When the frequency response of the riser model reached, the second-order natural frequency with Vr exceeds 40. Consequently, the “lock-in” phenomenon was observed and the riser exhibited vibrations with the second-order model.

Experimental and numerical investigation of the frequency-domain characteristics of impact load for AUV during water entry

Autonomous underwater vehicles (AUVs) are subjected to a very large impact load during the water-entry process, which may damage the structure of the vehicle and affect its motion trajectory. In this paper, five kinds of models with different nose shapes are tested under different water-entry velocities and angles, and the impact acceleration signals are obtained by a sensor. First, the accuracy of the experimental data is verified by comparison with the velocity obtained by the high-speed camera. Then, the ensemble empirical mode decomposition (EEMD) method combined with modal analysis is used to analyse the acceleration signal composition. Subsequently, a numerical simulation model based on the arbitrary Lagrangian Eulerian (ALE) method to describe the water-entering process of the vehicle is established, and the accuracy and capability of the numerical algorithm is verified by comparison with the experimental data. Finally, the frequency-domain characteristics of the impact load are analysed through the shock response spectrum (SRS) method. The result shows that the maximum acceleration shock spectrum of the impact load is related to the peak pulse width of the impact load and independent of the peak value. The smaller the pulse width is, the larger the inflection point frequency and magnification of the shock response spectrum are. The inflection point frequency of the shock response spectrum usually corresponds to the second-order bending natural frequency of the vehicle. The conclusions in this paper will be useful for the design and analysis of the water-entry impact structure of AUVs.

Dynamic responses of a piezoelectric cantilever plate under high–low excitations

In this paper, the nonlinear dynamic responses of a piezoelectric cantilever plate near the first-order and second-order natural frequencies under the action of electromechanical coupling are studied by experiments and finite element (FE) methods. The influence of different excitation frequencies on the dynamical characteristics of piezoelectric cantilever plates is analyzed with the fixed excitation amplitude. First, an experimental setup is built, including a carbon fiber cantilever plate attached to a macro fiber composite (MFC) sheet. Then, the electromechanical coupling excitations are subjected to the plate with different frequencies, which are chosen near the first and second-order natural frequencies of the plate. The piezoelectric cantilever plate has periodical motions under a lower frequency excitation, and the motions of the plate become more complex after another high frequency excitation added in the physical field. The experimental results show that the motion of the piezoelectric cantilever plate changes from stable to unstable with high–low coupled resonant frequencies. At last, the FE study is carried out to compare and verify the experimental results and the effects of isotropic and orthotropic materials on the accuracy of natural frequencies results are also compared.