Theoretical and Numerical Vibration Study of Continuous Beam with Crack Size and Location Effect

Abstract:In this research the natural frequency of a cracked beam with different supported, simply and clamped beam, is investigated analytically and numerically by finite element method with using of ANSYS program ver. 14 with different crack depth and location effect and the results are compared. The analytical results of the effect of a crack in a continuous beam are calculated the equivalent stiffness, EI, for a rectangular beam to involve an exponential function with depth and location of crack effect, with solution of assuming equivalent stiffness beam (EI) by using of Fourier series method. And, The beam materials studied are low carbon steel, Alloys Aluminium, and Bronze materials with different beam length and depth. A comparison made between analytical results from theoretical solution of general equation of motion of beam with crack effect with numerical by ANSYS results, where the biggest error percentage is about (1.8 %). Also it is found that the frequency of beam when the crack is in the middle position is less than the frequency with crack near the end position and the natural frequency of beam decreasing with increasing of crack depth due to decreasing of beam stiffness at any location of crack in beam. Keywords:Vibration beam, crack beam, health monitoring, theoretical vibration crack beam, frequency of beam with crack effect. I. INTRODUCTION Many engineering components used in the aeronautical, aerospace and naval construction industries are considered by designers as vibrating structures, operating under a large number of random cyclic stresses. Consequently, it is natural to expect that fatigue crack initiation and propagation in critically stressed zones of such structures, in particular when local or general resonance occurs

An Analytical Investigation of Thermal Buckling Behavior of Composite Plates Reinforced by Carbon Nano Particles

The research used analytical and numerical methods to test thermal buckling activity for a composite plate structure with a range of Nano fractions. Experimental program with mechanical properties for the Nano composites were carried out and have been validated from previous work. In addition, both mechanical and thermal expansions were tested from previous work experimentally and used in numerical and analytical methods by the Nano composite. The general motion equation for thermal buckling load was derived and then, the results were compared with the numerical results. The analysis showed that the average outcome error was not greater (2.49%). Ultimately, the results showed that the thermal effect results in a buckling of Nano particle strengthening (1%) volume fraction for the adjusted structure of the plate leads to increase thermal buckling strength (63,4%). This achievement modified a high thermal buckling strength with low percentage of Nano volume fraction compared to the previous work in this field

Studying the Thermal Effect and Nano Zinc Oxide Load Level on the Adhesion Between Rubber Compound and Steel Tire Cords

في هذا البحث، عينات التلاصق T تحسب عند °C (100,75, 50, 25) . درس تأثير تحميل أوكسيد الزنك النانوي على سطح اسلاك الإطار مع المطاط بتبديل أوكسيد الزنك الاعتيادي باوكسيد الزنك النانوي كمنشط. احدى العجنات تحتوي على أوكسيد الزنك الاعتيادي كمنشط بتركيز8pphr (جزء من مائة من وزن المطاط) . ثمان عجنات تحتوي أوكسيد الزنك النانوي بتركيز(4, 2.75, 2.2, 1.8, 1.4, 1, 0.6, 0.2pphr) لزيادة قوة التلاصق وتقليل كمية أوكسيد الزنك داخل العجنات.   بينت النتائج ان زيادة درجة الحرارة تؤدي الى نقصان التلاصق عند سطح اسلاك الإطار مع المطاط. أعظم قيمة لقوة التلاصق عند 2.2pphr أوكسيد زنك نانوي. استبدال أوكسيد الزنك الاعتيادي باوكسيد الزنك النانوي يؤدي الى تحسين قوة السحب ب 12%. كذلك تقلل من أوكسيد الزنك ب 72.5%. بالإضافة الى ذلك تؤدي الى تقليل الكلفة للعجنات. اخيرا يقلل من التأثير السلبي لأوكسيد الزنك على البيئة وذلك بتقليل كمية أوكسيد الزنك داخل العجنات.In this research, T-adhesion of samples were evaluated at (25,50,75 and 100) °C temperature. The effect of nano-zinc oxide loading on rubber-tire cords interface is investigated by replacing of conventional zinc oxide by nano-zinc oxide as an activator. One compound has conventional zinc oxide as an activator with 8pphr (part per hundred rubber). Eight compounds have nano-zinc oxide with (0.2, 0.6, 1, 1.4, 1.8, 2.2, 2.6 and 4) pphr so as to improve adhesion force and reduce the amount of zinc oxide inside the compounds. The results show that the increasing temperature leads to decrease the adhesion in the rubber-tire cords interface. The maximum value of adhesion force with nano-zinc oxide is occurred at 2.2 pphr. The replacement of conventional zinc oxide by nano-zinc oxide leads to improve the pull-out force by 12%. Also, it reduces the amount of zinc oxide by 72.5%. Furthermore, it leads to reduce the cost of compounds. Finally, it reduces the negative effect of zinc oxide on the environment by reduction in the amount of zinc oxide inside the compounds

Free Vibration Analysis of Composite Cylindrical Shell Reinforced with Silicon Nano-Particles: Analytical and FEM Approach

Previous research presented the effect of nanomaterials on the mechanical properties of composite materials with various volume fraction effects; in addition, their research presented the effect of nanomaterials on the same mechanical characteristics for a composite plate structure, such as vibration and thermal buckling behavior. Therefore, since the use of shell structures is for large applications, it is necessary to investigate the modification of the vibration characteristics of its design with the effect of nanomaterials and study the influence of other reinforced nanoparticle types on its features. Therefore, in this work, silicon nanoparticles were selected to investigate their effect on the vibration behavior of a shell structure. As a result, this work included studying the vibration behavior by testing the shell structure with a vibration test machine. In addition, after manufacturing the composite material shell with various silicon volume fractions, the mechanical properties were evaluated. In addition, the finite element technique with the Ansys program was used to assess and compare the vibration behavior of the shell structure using the numerical technique. The comparison of the results gave an acceptable percentage error not exceeding 10.93%. Finally, the results evaluated showed that the modification with silicon nanomaterials gave very good results since the nanomaterials improved about 65% of the shell's mechanical properties and vibration characteristics

EFFECT OF NANO ZINC OXIDE ON TENSILE PROPERTIES OF NATURAL RUBBER COMPOSITE

This study investigates the effect of Nano-zinc oxide on tensile properties of natural rubber composites by replacing the conventional zinc oxide by Nano-zinc oxide as an activator. It has a small particle size and large surface area in comparison with conventional zinc oxide. In this paper, one compound has a conventional zinc oxide as an activator with concentration 8phr (part per hundred rubber) and eight compounds have Nano-zinc oxide as an activator with concentrations (0.2, 0.6, 1, 1.4, 1.8, 2.2, 2.6, 4) phr. The tensile test sample carried out by using the Monsanto T10 Tensometer. Results show that maximum values of tensile strength and elastic modulus at 300% are found with Nano-zinc oxide at 1.8 phr. Replacing the conventional zinc oxide by Nano-zinc oxide decreases the price of the compounds due to reducing the amount of zinc oxide inside the compounds by 77.5%. It also reduces the contamination of the environment and improves the tensile strength by 38.31%. http://dx.doi.org/10.30572/2018/kje/090105

Free vibration analysis of composite face sandwich plate strengthens by Al2O3 and SiO2 nanoparticles materials

The main novelty of the paper is that analytical, experimental, and numerical analyses are used to investigate the free vibration problem of a sandwich structure in which Nanocomposites skins (SiO2/epoxy and Al2O3/epoxy) at different densities are used as the face sheet. The volume fraction's of nanoparticle addition varies (0% to 2.5%). The present free vibration was derived based on Kirchhoff's theory and aspiration to obtain the natural frequency. The results show that in structures with SiO2 nanoparticles with a density of 1180 kg⁄m3, the optimum increase (VF = 2.5%) is 50% in Young's modulus and 22% in natural frequency, while at a density of 1210 kg⁄m3 is 56 % in Young's modulus and 24.5% in natural frequency. Furthermore, the same structures reinforced with Al2O3 Nano-particles show that at the density of 1180 kg⁄m3, the optimum (VF=2.5%) parentage increase in Young's modulus is 41% and 19% in natural frequency, while at the density of 1210 kg⁄m3 is 46% in Young's modulus and 21% in natural frequency. A numerical investigation was used to validate the obtained results of the analytical solution. The findings also show an acceptable convergence between analytical and numerical techniques with a maximum discrepancy not exceeding 3%

Sandwiched Plate Vibration Analysis with Open and Closed Lattice Cell Core

This work attempts to replace the sandwich core's traditional shape and material with a cellular pattern, where the cells have a regular shape, distribution, and size. The contribution of this paper is to design two structures, one open-celled and the other closed, and to evaluate the performance of sandwich plates with lattice cell core as it is used for many industrial applications, particularly in automobile engineering. The new theoretical formulations are constructed for two structures to find the free vibration characteristics. The results of the new design are compared with the traditional shape. Derivation of equations to predict mechanical properties based on relative density with the chosen shapes, specific vibration equation of three-layer sandwich plate, and substitution by equation using excel sheet. Results are promising, and the effectiveness of cellular pattern theoretical analysis estimation. Limitations and error rates for the mechanical properties come through the empirical equations, and their ratio to the relative density values are higher depending on the behavior of the core material. Findings reveal, with open cell decrease in modulus of elasticity by (PLA: -90.4%) and (TPU: -90.4%), increases natural frequency by (PLA: 44.5%) and (TPU: 46.4%), as for closed-cell decreases in the modulus of elasticity by (PLA: -66.9%) and (TPU: -64.4%), increases natural frequency by (PLA: 36%) and (TPU: 37.7%). Converting a solid substance or replacing a foam form with a cellular pattern is one way to better performance and save weight through the selected cell pattern in absorbing the energy of the vibration wave