Initial Compression Force Research Articles

Mechanical properties of homogeneous and functionally graded spinodal structures

This paper investigates the compressive mechanical behavior of spinodoid metamaterials in a quasi-static state through experimental and numerical analysis at the macroscopic level. This homogeneous structure exhibits weak strain hardening, resulting in a lower initial peak compression force and higher specific absorption energy compared to other mechanical metamaterials. The homogeneous model has multiple low-density regions uniformly distributed within the three-dimensional space due to the random nature of the Gaussian field. Thus, the transition from low-density to high-density regions is described as a gradual process, implying that the deformation of metamaterial shifts to region-by-region compaction. Besides, the functionally graded spinodoid structure shows strong strain hardening, whose deformation mainly tends to collapse layer by layer along a positive graded direction. The graded structures with low densities have a lower energy absorption capacity than the corresponding homogeneous structure, while higher-density structures show a reverse trend. This phenomenon originates from the superimposed effect of two kinds of strain hardening.

Energy absorption characteristics of aluminum foam-filled corrugated tube under axial compression loading

To improve the energy absorption characteristics of thin-walled structures and reduce the initial peak compression force and load fluctuation, a novel aluminum foam-filled corrugated tube was proposed in this study. Finite element model validated by quasi-static compression experiments was adopted to investigate the crashworthiness performances of aluminum foam-filled corrugated tubes and their combined energy-absorbing structures. The effects of structure parameters including corrugation radius, wall thickness, corrugation length and corrugation radius increments on axial compression characteristics were investigated through finite element analysis. The results showed that compared with aluminum foam-filled straight tubes, the initial peak compression force of aluminum foam filled corrugated tube was reduced by 22.87 %, the compression force efficiency was increased by 6.69 % and the load fluctuation was reduced by 17.94 %. The smaller the values of corrugation radius, wall thickness and corrugation length, the smaller the initial peak compression force; Because the corrugation radius had a great effect on the peak compression force, the order that the corrugations were compressed into folds can be controlled by designing the corrugation radius; In view of the peak and valley values of compression force, an innovative combination of single tubes with different △H was obtained, which had better energy absorption performance. Compared with a single aluminum foam-filled corrugated tube, the compression force efficiency of the combined structure (△H: 0–5–10) was increased by 18.15 % and the load fluctuation was reduced by 33.60 %. The research results can provide a reference for the design and optimization of energy-absorbing devices.

Influence of density gradient and hybrid effect on quasi-static axial crushing behavior of lattice cylindrical structures

Uniform/gradient lattice cylindrical structures (ULCS/GLCS) and hybrid uniform/gradient lattice cylindrical structures (HULCS/HGLCS) are innovatively designed and fabricated. The axial crushing behaviors of these four-type cylindrical structures are investigated by the quasi-static axial compression experiments and numerical simulations. The influence of the density gradient and the hybrid effect (metal skin+ABS core) on the deformation mode, loading capacity, and energy absorption of the lattice cylindrical structures are elaborated systematically. The results show that the gradient design realizes the function of regulation and controllability of the structural deformation. The softer layers (with smaller relative density) in GLCS begin to deform first and then gradually extend to the harder layers (with larger relative density). And it effectively reduces the initial peak compression force (PCF), and makes the load more stable on the premise of energy absorption. However, unstably catastrophic failures are observed before the final densification in both ULCS and GLCS during the compression due to the brittleness of the ABS material and the compression–expansion​ deformation of structure. For HULCS/HGLCS, it presents progressive crushing mode and overcome the unstably catastrophic failure due to the ductility and constraint of the metal skins. The effect of “1 ＋ 1 > 2” on energy absorption from hybrid effect is achieved in HULCS/HGLCS, in which the EA of HULCS and HGLCS increases by 74.62% and 100.78% comparing the sum of all components individually compressed. Moreover, the progressive peak with increasing trend of HGLCS demonstrated that the hybrid design enhances the advantages of gradient design in sandwich structures.

Tensile strength and thermal cycle analysis of AA6061 friction weld joints with different diameters and various friction times

The paper reports measurement of tensile strength and the thermal cycle of AA6061 aluminum alloy circular bar friction weld with different diameters and various friction times. A continuous drive friction welding (CDFW) of AA6061 was conducted to weld the AA6061 circular bar with different diameters of 30 mm for the rotating part and 15 mm for the stationary part. The CDFW process was carried out with the revolution speed of 1,600 rpm, the initial compressive force of 2.8 kN during the friction stage for various friction times of 10, 12, and 14 seconds, and an upset force of 28 kN for 60 seconds. The flash temperature was measured using a digital infrared thermometer gun. Computer simulation using the finite element method was also done by coupling transient thermal and static structural methods. The flash temperature becomes higher along with increasing friction time based on the digital infrared thermometer gun measurement and finite element analysis. The results of tensile strength testing show that the specimen with a friction time of 12 seconds has the highest tensile strength. Based on the hardness testing result, it is found that the specimen with a friction time of 10 seconds has higher hardness, but it has an incomplete joint flash so that the tensile strength is lower than that of the specimen with a friction time of 12 seconds. Besides, the hardness of the specimen with a friction time of 12 seconds is higher than that of the specimen with a friction time of 14 seconds. The flash size becomes bigger along with the increase of the friction time based on the macrostructure observation on the longitudinal section of the CDFW specimen. It is confirmed by the temperature measurement and finite element analysis that the specimen with a friction time of 12 seconds has heat input to form the CDFW joint that has a maximum tensile strength in the range of this study

Numerical Analysis of the Die Forging of Porous Blanks in a Die with the Implementation of Active Friction Forces

This paper provides the results of simulating the hot die forging of porous powder preforms with active friction forces applied along the lateral surface of the blank under deformation due to internal cohesion in the die–material system. The study covers the evolution of the distribution of the relative density over the blank cross section at different stages of deformation, the stress-strain state, and the total strain force while varying the boundary loading conditions by changing the initial compression force applied to elastic elements that prevent the die from displacement. It is shown that the active friction forces that act on the periphery of the forged piece adjacent to the die inner side result in areas with a significantly higher deformation intensity compared to deformations in the center of the blank volume. In this case, the volume of the high deformation intensity area and the maximum values of deformation increase with a decrease in the initial compression force of the springs and, accordingly, with an increase in the die displacement value during the deformation. The automatic displacement of the die due to the internal cohesion in the die–deformed material system leads to a decrease in the total deformation force, and the deformation force increases with a decrease in the die displacement value during deformation.

Numerical analysis of porous blank die forging in the die with the implementation of active friction forces

The paper provides the results of simulating the hot die forging of porous powder preforms with active friction forces applied along the lateral surface of the deformable blank by means of internal cohesion in the die-material system. The study covers the evolution of relative density distribution over the blank cross section at different stages of deformation, stress-strain state and total strain force while varying the loading boundary conditions by changing the initial compression force applied to elastic elements that prevent the die from displacement. It is shown that active friction forces acting on the periphery of the forging adjacent to the die inner side result in areas with a significantly higher deformation intensity compared to deformations in the center of the blank volume. At the same time, the volume of the high deformation intensity area and maximum values of deformation increase with a decrease in the spring initial compression force and, accordingly, with an increase in the die displacement value during deformation. Automatic die displacement due to internal cohesion in the die-deformable material system leads to a decrease in the total deformation force, and with a decrease in the die displacement value during deformation, the deformation force increases.

Numerical simulation of the operation of the disc shredder

The purpose of the work is to model the performance of the disk grain shredder by numerical methods of determining the performance of the device and its components, and to establish the existing trends in the influence of the size of the initial particles on the components of the shredder performance. The increase in the initial particle size leads to an increase in the initial angular velocity of the particle movement, which increases as the particle is compressed, while the increase in particle size does not significantly reduce the productivity of the shredder due to the worsening conditions of particle capture by the disks as they increase in size. The increase in the initial spring compression force ensures a reduction in the thickness of the resulting flattened particles and at the same time reduces the productivity.

Tensile strength and fatigue crack growth rate of chamfered and clamped A6061 friction weld joints

Friction welding is a solid-state joining technique. It is suitable to be used to join a round bar of aluminum that has problems in joining. This paper reports measurements of the tensile strength and fatigue crack growth rate of a continuous drive friction welding (CDFW) joint of aluminum alloys A6061. The CDFW process was conducted by using the round bar A6061 machined to form a chamfer angle and applying a clamping process before the upset stage. Various chamfer angles of 0, 30, 45, and 60 degrees were machined on the stationary round bar. In order to increase the tensile strength and to reduce the fatigue crack growth rate of the CDFW joint, round clamps were applied on the CDFW joint. CDFW process was conducted with the revolution speed of 1,100 rpm, the initial compression force of 3.9 kN during friction stage for 4 seconds, and an upset force of 28 kN for 60 seconds. The specimens of friction weld joints were machined to shape the specimens of tensile strength testing and fatigue crack growth testing. Fatigue crack growth testing was performed using a cantilever rotary bending machine. The testing results show that using a small chamfer angle together with the round clamp produced a CDFW joint that exhibited higher tensile strength than the joint without chamfer or clamping. The specimen created with a chamfer angle of 30 degrees and the clamping method had the highest tensile strength and the lowest fatigue crack growth rate among the samples studied. This result was caused by smaller heat input as a result of using a small one-sided chamfer together with two stages of plastic deformation from the clamping process and upset process during CDFW. The fatigue crack growth rate is also confirmed by macro and scanning electron microscope imaging of the fracture surfaces. The area of fatigue crack growth of the specimen with high tensile strength is wider than the specimen with lower tensile strength. The striations are also observed more clearly in the fracture surface of the specimen with the highest tensile strength and the lowest fatigue crack growth rate, namely the specimen, which has a chamfer angle of 30 degrees with clamping

Biomechanics of common fixation devices for first tarsometatarsal joint fusion\u2014a comparative study with synthetic bones

BackgroundHallux valgus disease is a common deformity of the forefoot. There are currently more than 100 surgical approaches for operative treatment. Because hypermobility of the first tarsometatarsal joint is considered to be causal for hallux valgus disease, fusion of the tarsometatarsal joint is an upcoming surgical procedure. Despite the development of new and increasingly stable fixation devices like different locking plates, malunion rates have been reported in 5 to 15% of cases.MethodsBiomechanical comparison of three commonly used fixation devices (a dorsal locking plate, a plantar locking plate, and an intramedullary fixation device) was performed by weight-bearing simulation tests on synthetic bones. Initial compression force and stiffness during simulation of postoperative weight-bearing were analysed.ResultsFixation of the first tarsometatarsal joint with the plantar plate combination demonstrated a higher stiffness compared to fixation with the intramedullary implant or the medial locking plate. The intramedullary device provided the highest initial compression force. Failure was detected in the following ranking: (1) the angle-stable intramedullary fixation device, (2) the medial located plate, and (3) the plantar locking plate.ConclusionThe intramedullary device demonstrated the highest initial compression force of the three tested implants. The plantar locking plate showed the best overall stability during weight-bearing simulation. Further clinical research is necessary to analyse if the intramedullary fixation device needs a longer period of non-weight-bearing to reach a better non-union rate compared to the plantar locking plate.

Gripping characteristics of an electromagnetically activated magnetorheological fluid-based gripper

The design and test of a magnetorheological fluid (MRF)-based universal gripper (MR gripper) are presented in this study. The MR gripper was developed to have a simple design, but with the ability to produce reliable gripping and handling of a wide range of simple objects. The MR gripper design consists of a bladder mounted atop an electromagnet, where the bladder is filled with an MRF, which was formulated to have long-term stable sedimentation stability, that was synthesized using a high viscosity linear polysiloxane (HVLP) carrier fluid with a carbonyl iron particle (CIP) volume fraction of 35%. Two bladders were fabricated: a magnetizable bladder using a magnetorheological elastomer (MRE), and a passive (non-magnetizable) silicone rubber bladder. The holding force and applied (initial compression) force of the MR gripper for a bladder fill volume of 75% were experimentally measured, for both magnetizable and passive bladders, using a servohydraulic material testing machine for a range of objects. The gripping performance of the MR gripper using an MRE bladder was compared to that of the MR gripper using a passive bladder.

TORSION STRENGTH OF ROUND BAR A6061 FRICTION WELD JOINT INFLUENCED BY FRICTION TIME, UPSET FORCE AND ONE-SIDE CONE GEOMETRY

ABSTRACT Effect of friction time, upset force and one-side cone geometry on torsion strength of A6061 round bar friction weld joint was studied. Round bar commercial A6061 was friction welded with initial compression force of 2.5 kN on stationary part and the rotated part had revolution speed of 1600 rpm with variation of friction time of 45, 50 and 55 minutes. In the upset stage, the variation of upset force of 5 kN, 7.5 kN and 10 kN with the same upset holding time of 110 seconds. The stationary part of the specimen had friction area with variation of cone geometry that represented with ratio of upper diameter, D 1 and lower diameter, D 2 , D 1 / D 2 . It was found friction time and the ratio of D 1 / D 2 affected torsion strength in the upset force below 10 kN. In case of the higher upset force of 10 kN, the upset force more dominant to affect torsion strength of the continuous drive friction weld (CDFW) joint. The specimen with maximum torsion strength has more precipitates in grains of microstructures compared to that of specimen with lower torsion strength. Keywords : Continuous drive friction welding, aluminum, friction time, upset force, one-sdie cone geometry, torsion strength .

Feasibility Study of a Gripper with Thermally Controlled Stiffness of Compliant Jaws

This paper proposes a simple and compact compliant gripper, whose gripping stiffness can be thermally controlled to accommodate the actuation inaccuracy to avoid or reduce the risk of breaking objects. The principle of reducing jaw stiffness is that thermal change can cause an initial internal compressive force along each compliant beam. A prototype is fabricated with physical testing to verify the feasibility. It has been shown that when a voltage is applied, the gripping stiffness effectively reduces to accommodate more inaccuracy of actuation, which allows delicate or small-scale objects to be gripped.

Compressive Deformation Characteristics of Logging Residues by Tree Species

The aim of this study was to provide the basic design parameters for developing logging residue compression machines by investigating compressive deformation characteristics of different types of logging residues. To achieve these objectives, Pinus rigida, Pinus koraensis and Quercus mongolica were selected as specimens, and compression-deformation tests by UTM(universial testing machine) were conducted. The experimental dataset were used to set up the model based on the compression-deformation ratio in the form of exponential function. The results showed that stress coefficient in terms of mechanical properties of logging residues was decreased, whereas strain coefficient tended to be increased as the number of compression increased at target density of and . The model presented that the required stress was decreased as the number of compression increased, and the stress growth rate was swelled compared to the change of the deformation rate. Therefore, it showed that proper initial compression force was a significant variable in order to achieve the target density of logging residue.

Mechanical Effect Characterization in Posterior Monosegmental Instrumentation in Burst Fractures: Biomechanical Analysis

Introduction Different treatment options and approaches have been applied to treat thoracolumbar burst fractures. From an anterior to a combine 360-degree approach, none has proven to be a gold standard for this type of fracture. Considering the four principles for proper spinal patient management (stability, function, alignment, and biology), different treatment options arouse to treat thoracolumbar bust fractures. Short posterior instrumentations with an intermediate pedicle screw, which acts as an anchorage point, counterbalancing anterior forces and favoring the lumbar lordosis strength. And monosegmental instrumentation are been applied to preserve as much spine segments as possible, allowing mobility and maintaining spine stability. The objective of this study is to determine the biomechanical effects of posterior monosegmental constructs in burst fractures by a characterization analysis. Material and Methods Otherwise healthy swine thoracolumbar vertebrae were used to apply an axial load to simulate a burst fracture. Initial force, end force, and total displacement were analyzed. Posterior monosegmental instrumentation was performed in the thoracolumbar segment. Healthy swine vertebrae were used as control group. A CT scan was done in the instrumented segment. The images then were converted for biomechanical analysis using meshing and reconstruction software. Results Initial compression force: 34.92 N. End force: 1.44 kN. Total displacement: 11.27 mm. Healthy and instrumented specimens initial compression force: 2.311 and 2.657 kN, respectively. Young module in healthy and instrumented specimens was 123,276 versus 159.749 MPa. Maximum load applied 2.126 kN/m. Mean displacement was 5.30272 mm. Discussion There is much more resistance against deformation, even when the specimen is fractured. SolidWorks software is a useful tool for biomechanical testing. When comparing simulated results with live compression tests there is a 17.3% chance of error during the maximum load test

Influence of the screw augmentation technique and a diameter increase on pedicle screw fixation in the osteoporotic spine: pullout versus fatigue testing.

For posterior spinal stabilization, loosening of pedicle screws at the bone-screw interface is a clinical complication, especially in the osteoporotic population. Axial pullout testing is the standard pre-clinical testing method for new screw designs although it has questioned clinical relevance. The aim of this study was to determine the fixation strength of three current osteoporotic fixation techniques and to investigate whether or not pullout testing results can directly relate to those of the more physiologic fatigue testing. Thirty-nine osteoporotic, human lumbar vertebrae were instrumented with pedicle screws according to four treatment groups: (1) screw only (control), (2) prefilled augmentation, (3) screw injected augmentation, and (4) unaugmented screws with an increased diameter. Toggle testing was first performed on one pedicle, using a cranial-caudal sinusoidal, cyclic (1.0 Hz) fatigue loading applied at the screw head. The initial compressive forces ranged from 25 to 75 N. Peak force increased stepwise by 25 N every 250 cycles until a 5.4-mm screw head displacement. The contralateral screw then underwent pure axial pullout (5 mm/min). When compared to the control group, screw injected augmentation increased fatigue force (27 %, p = 0.045) while prefilled augmentation reduced fatigue force (-7 %, p = 0.73). Both augmentation techniques increased pullout force compared to the control (ps < 0.04). Increasing the screw diameter by 1 mm increased pullout force (24 %, p = 0.19), fatigue force (5 %, p = 0.73), and induced the least stiffness loss (-29 %) from control. For the osteoporotic spine, screw injected augmentation showed the best biomechanical stability. Although pullout testing was more sensitive, the differences observed were not reflected in the more physiological fatigue testing, thus casting further doubt on the clinical relevance of pullout testing.

MAGNAMOSIS IV: magnetic compression anastomosis for minimally invasive colorectal surgery

MAGNAMOSIS forms a compression anastomosis using self-assembling magnetic rings that can be delivered via flexible endoscopy. The system has proven to be effective in full-thickness porcine small-bowel anastomoses. The aim of this study was to show the feasibility of the MAGNAMOSIS system in hybrid endoscopic colorectal surgery and to compare magnetic and conventional stapled anastomoses. A total of 16 swine weighing 35 - 50 kg were used following animal ethical committee approval. The first animal was an acute model to establish the feasibility of the procedure. The subsequent 15 animals were survival models, 10 of which underwent side-to-side anastomoses (SSA) and 5 of which underwent end-to-side (ESA) procedures. Time to patency, surveillance endoscopy, burst pressure, compression force, and histology were assessed. Histology was compared with conventional stapled anastomoses. Magnetic compression forces were measured in various anastomosis configurations. Colorectal anastomoses were performed in all cases using a hybrid NOTES technique. The mean operating time was 71 minutes. Mean time to completion of the anastomosis was similar between the SSA and ESA groups. Burst pressure at 10 days was greater than 95 mmHg in both groups. One complication occurred in the ESA group. Compression force among various configurations of the magnetic rings was significantly different (P < 0.05). Inflammation and fibrosis were similar between magnetic SSA and conventional stapled anastomoses. MAGNAMOSIS was feasible in performing a hybrid NOTES colorectal anastomosis. It has the advantage over circular staplers of precise endoscopic delivery throughout the entire colon. SSA was reliable and effective. A minimum initial compression force of 4 N appears to be required for reliable magnetic anastomoses.

Reduction and fixation capabilities of different plate designs for pubic symphysis disruption: A biomechanical comparison

BackgroundTypical stabilisation of pelvic open book injuries consists in plate fixation of the symphysis, leading to many different plate designs and procedures that have evolved. However, implant loosening and development of chronic instability are still evident and represent major complications after plate fixation of the symphysis. The aim of this study was to analyse reduction and fixation capabilities of different classical plate techniques with dynamic compression (DC), prebending or modern interlocking screws. MethodsCompression injuries (OTA B1.1) were simulated on synthetic composite pelvises. Sensor films placed in the disrupted symphysis allowed assessment of reduction and compression forces, as well as contact characteristics by implants at defined time points under static non loaded conditions. The commercially available steel plates used in our study differed in curved design, prebending and DC- or locking screw capabilities, as narrow large fragment (4.5) or small fragment plates (3.5). ResultsDC procedure clearly increased the compressive force in the symphysis and improved the reduction by enhanced contact areas. These effects were preserved to the end of the experiments only when the plates were prebended (10°). Anatomically contoured and prebended 3.5 plates had a similar effect, but the contact area was even more pronounced. Best results were observed using the “3.5 symphyseal plate” with DC-effect medially and locking screws laterally. Purely interlocking screw plates by themselves allowed an optimal contact area, yet failed to preserve the initial compressive reduction force. ConclusionsThe experimental results suggest a biomechanical advantage in using prebended plates for symphysis fixation compared to non-bended plates. Best results with regard to compression and increased contact area can be achieved by anatomically contoured plates with combined DC and locking screw capabilities. These findings are of special interest in pelvic surgery for choosing the right implant in severe displacements, obese patients and symphysiodesis techniques.

Suture compression induced bone resorption with intensified MMP-1 and 13 expressions

Suture compression is a widely used approach to inhibit maxillary growth; however, biological responses in sutures to compressive force are still unclear. The objective of this pilot study was to investigate the matrix metalloproteinase (MMP) expression and osteoclast activities during the midpalatal suture compression. Methods: 56 six-week old male C57BL/6 mice were randomly assigned to the control and compression groups. The mice in the compression and control groups received helix springs bonded to the maxillary molars delivering initial compressive forces of 0.20 and 0N (no activation), respectively. On Days 1, 4, 7 and 14, animals were sacrificed and scanned using micro-computed tomography to quantify suture width and bone mineral density. Serial histological sections were stained with HE, TRAP, and immunohistochemistry to observe changes in bone resorption, osteoclast activities, and MMP-1, 8, and 13 expressions. Bone volume/total volume (Bv/Tv) ratio, osteoclast count, osteoclast covering area, and MMP expression intensity were measured. The Mann–Whitney and the Kruskal–Wallis tests with Bonferroni post-hoc corrections were performed to compare differences between groups and between time points in the same group at significant level of P<0.05. Results: Compared to the control, suture width in the compression group was significantly reduced on Day 1, but continuously widened with reduced bone mineral density afterwards. With MMP-1 and ‐13 evidently intensified expressions, osteoclast number and activities significantly increased, leading to reduced Bv/Tv ratio and progressive bone resorption from Days 4 to 14. Conclusions: Suture compression elevated the MMP-1 and 13 expressions, activated osteoclasts, reduced bone density, and induced bone resorption adjacent to the suture. It suggests that suture compression can be used for bone volume reduction.

Mechanistic characterization of bilayer tablet formulations

The interest in bilayer tablet as an oral immediate-release/controlled-release system has substantially increased in the past decade. However, during the production of such tablets, lack of sufficient bonding and adhesion at interfaces between adjacent layers is compromising the mechanical integrity and performance of the final solid dosage form. In this study, bilayer tablets of the widely used excipient microcrystalline cellulose in the form of Avicel 102 and pregelatinized starch were formed with different pre-compression (2 kN, 4 kN, 6 kN, 8 kN) and final compression (6 kN, 10 kN, 14 kN, 18 kN) forces to quantitatively characterize the strength (σ) of the interface and the compacted adjacent layers. Bilayer tablets were axially debonded (i.e., separation of adjacent layers that are subjected to axial loading) until fracture and axial tensile strength values were determined. It was observed that when the first layer was compressed to a low porosity, the bonding with the second layer became difficult and it was not possible to produce intact bilayer tablets (σlayer > σinterface). It has been demonstrated that the material response of the constrained MCC particles to an applied initial compression force within the initial compacted layer have a detrimental effect on the resistance to fracture of a bilayer tablet. The mechanism of failure at the interface or at the individual layers was also studied. Different fracture patterns, namely, clear layer break, half–half break, cap-shape break, and clear interface break were observed as a function of various initial and final compression forces. X-ray micro-computed tomography (μCT) was utilized to examine the influence of localized density distribution on the delamination (layer separation) phenomena of bilayer tablets. It has been shown that once the magnitude of the applied final layer compaction stress greatly exceeds the initial layer compaction stress, the tablet catastrophically fails at the initial layer not at the interface (σlayer < σinterface). The results of this study point out that the measurement of the interfacial strength provides insight into some of the major complications of bilayer tablets.

Vibration Analysis of Axially Compressed Nanobeams and its Critical Pressure Using a New Nonlocal Stress Theory

The transverse vibration of a nanobeam subject to initial axial compressive forces based on nonlocal elasticity theory is investigated. The effects of a small nanoscale parameter at molecular level unavailable in classical mechanics theory are presented and analyzed. Explicit solutions for natural frequency, vibration mode shapes are derived through two different methods: separation of variables and multiple scales. The respective numerical solutions are in close agreement. Validity of the models and approaches presented in the work are verified. Unlike the previous studies for a nonlocal nanostructure, this paper adopts the effective nonlocal bending moment instead of the pure traditional nonlocal bending moment. The analysis yields an infinite-order differential equation of motion which governs the vibrational behaviors. For practical analysis and as examples, an eight-order governing differential equation of motion is solved and the results are discussed. The paper presents a complete nonlocal nanobeam model and the results may be helpful for the application and design of various nano-electro-mechanical devices, e.g. nano-drivers, nano-oscillators, nano-sensors, etc., where a nanobeam acts as a basic element.