Critical Natural Frequencies Research Articles

Optimizing plastic shredder rotor design through structural finite element analysis: A comprehensive approach using experimental design and response surface methodology

Shredder machines are essential for recycling plastic waste. They are used to shred plastic materials into smaller pieces, which can then be processed into new products. The shaft and rotary blades of the plastic shredder are its most crucial parts since they directly influence how effectively the machine shreds or recycles material. The shredder’s rotor is optimized based on the design of experiments and the response surface method. The natural frequencies and mode shapes are identified by modal analysis, and the critical natural frequencies that must be avoided during operation are identified through harmonic response analysis. The shredder’s rotor is optimized by determining its critical areas through a transient structural analysis. The optimization goals are attained by using the response surface method and experiment design in the ANSYS WORKBENCH DESIGN EXPLORATION module. The rotor of the optimized shredder is investigated, and its results are contrasted with the nominal design. The study of the optimum structure leads to a slight increase in mass of 2.43% in addition to reductions in equivalent stress and total deformation by about 9.84% and 42.86% respectively, as well as a 21.4%, 4.35%, and 4.48% increase in the first three natural frequencies, respectively.

Critical Natural Frequencies for Seismic Design of Latticed Domes Under Multi-component Earthquake Excitations

Critical Natural Frequencies for Seismic Design of Latticed Domes Under Multi-component Earthquake Excitations

Research on stability monitoring and early warning methods for cantilevered rocks

It is difficult to monitor the change of rock stability effectively and warn of the damage of rocks by using external deformation indicators. The article analyzed the change of the cantilevered rock’s natural frequency during its stability decline and proved that the rock’s natural frequency can reflect the rock’s stability. The article analyzed the motion characteristics of cantilevered rocks and gave the calculation method of the natural frequency of cantilevered rocks. Using the formula, the natural frequency value within each stage of the rock can be calculated, and the critical natural frequency value before rock damage can be determined. Based on the theoretical equations’ calculation results, the monitoring of dynamic changes in cantilevered rocks’ stability and early warning of rock collapse can be accomplished using vibration sensors.

Critical natural frequency: an improved empirical effectiveness criterion in vibration stress relief of rectangle welded plates

Decreasing of natural frequency of the treated structure is the most frequently used empirical effectiveness criteria in vibration stress relief (VSR). However, dependability and reliability of this criteria is still far from sufficient. In this study, a covert negative treatment phenomenon was investigated, i.e. natural frequency of welded structures decreased after VSR but residual stress in one direction increased. Relationship between natural frequency and residual stresses was studied by mathematical deduction and finite element method. “Natural Frequency Function” and “Natural Frequency Surface (NFS)” was proposed to describe that relationship. “Critical Natural Frequency” (CNF) was proposed to depict possible situations after VSR. A quantitative natural frequency criterion for VSR effectiveness estimation was proposed.

Stability Diagram, Hysteresis, and Critical Time Delay and Frequency for the Kuramoto Model with Heterogeneous Interaction Delays

We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the bifurcations in the system. Of particular interest is the onset of hysteresis where both the incoherent and partially synchronized states are stable for a range of coupling strengths — this occurs at a codimension-two point at the intersection between a Hopf bifurcation and saddle node bifurcation of cycles. By studying this codimension-two point we find the full set of characteristic time delays and natural frequencies where bistability exists and identify the critical time delay and critical natural frequency below which bistability does not exist. Finally, we examine the dynamics of the more general system where time delays are drawn from a Gamma distribution, finding that more homogeneous time delay distributions tend to both promote the onset of synchronization and inhibit the presence of hysteresis.

Failure criterion of titanium alloy irregular sheet specimens for vibration-based bending fatigue testing

The failure moments of vibration-based fatigue tests are usually defined based on the natural frequency drops of specimens. But the selections of the critical values of the frequency drop have been very arbitrary in the previous tests, lacking of convincing reasons. The present paper aims to propose a failure criterion of titanium alloy irregular sheet specimens tested in a vibration-based bending fatigue experiment. A novel three-dimensional finite element model of the specimen is built, with a cohesive zone model employed to simulate the fatigue dangerous zone (FDZ) and the semi-elliptic crack propagation process of the specimen. A failure criterion to define the critical natural frequency drop is subsequently proposed based on the obtained computational results. Furthermore, a vibration-based bending fatigue test for the specimens is conducted to verify the computational model and the proposed failure criterion. After comparing the present testing results with the results of a similar bending fatigue test, the two types of the testing results are found very close. The vibration-based bending fatigue test with the proposed failure criterion provides an effective way for obtaining accurate fatigue life of irregular specimens.

Dynamic Response Of Tower Structures

The present study focuses on the tower type structures response to the dynamic loads. The study analyzes the possible mode shapes regarding to tower structure. The estimation of mode shapes and their dependence from structural changes was made for an existing tower structure. To get an acceptable tower’s vibration level and avoid possibility of resonance effect from usual serviceability loads it was evaluated options to change natural frequencies of the structure. It is performed existing 36m high sightseeing tower dynamic analysis and proposed potential solutions to increase critical natural frequencies of the structure. In this study to obtain dynamic parameters of the sightseeing tower structure have been used finite element models and calculation techniques.

Dynamic Behavior of the Hydraulic Press for Free Forging

Work on hydraulic presses is defined by a static forging force. This force may have in special cases of forging properties of dynamic and shock load. Commonly used hydraulic presses can use speed-forging with speed up to 180 strokes per minute. Our goal is to compare different types of frame designs used for hydraulic forging presses. Result is determination of the suitability of each supporting structures for these special operations. Comparing is made using FEM modal analysis. The performed modal analysis show needs for lowering of first critical natural frequency. An overview of these frequencies is shown in attached tables.

Tuning of the natural frequency spectrum of a circular plate by in-plate stress

Initial stresses are often introduced deliberately into centrally clamped, peripherally free circular plates to increase the plate natural frequencies. Increased natural frequencies in the critical modes extend the range of stable rotation speed. Current axisymmetric initial stressing schemes increase the natural frequencies of the zero nodal circle, two and higher nodal diameter vibration modes, but the zero and one nodal diameter natural frequencies decrease. For sufficiently large initial stress, the zero nodal diameter natural frequency vanishes and the plate experiences divergence buckling, thereby limiting the initial stress that can be induced. In this paper a new initial stressing method is presented whereby the natural frequencies of all zero nodal circle modes increase simultaneously, thus avoiding buckling of the plate through excessive initial stress. The stress field is induced by applying uniform pressure to the boundaries of eccentric interior holes. Through proper location of the holes, the critical natural frequencies increase monotonically with increased pressure, and the magnitudes of the frequency shifts increase with the introduction of additional stressed holes. The initial stressing schemes can be directed towards optimal increases in specific vibration modes. Calculations predict natural frequency increases between 35% and 90% depending on the vibration mode. Experimental measurements are consistent with the model predictions.