Material Length Research Articles

On nonlinear buckling of microshells

Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells.

An enhanced strain gradient model for temperature-dependent sound transmission loss in double-walled functionally graded microplates

With the growing use of functionally graded (FG) microplates in structural acoustic metamaterials for aerospace and automotive applications, accurate modeling of sound transmission loss is critical for effective vibration and noise control engineering. In this study, a theoretical model is formulated based on the first-order shear deformation theory (FSDT) to estimate sound transmission loss (STL) through air-filled rectangular double-walled FG microplates with simply supported boundary conditions. The microplates are subjected to a nonlinear thermal environment, and the modified strain gradient theory (MSGT) is employed, incorporating three material length scale parameters to account for the size effect. The material properties are temperature-dependent and vary across the thickness following a power-law distribution. Size-dependent coupled vibroacoustic equations are derived utilizing the sound velocity potential, normal velocity continuity conditions, and Hamilton's principle, and are subsequently solved using the Galerkin method. Comparative analysis is performed by contrasting the results obtained from the MSGT model with those from the modified couple stress theory (MCST) and classical continuum theory (CCT) models, allowing for the assessment of the accuracy and precision of the proposed solution. Additionally, the influence of various parameters, such as gradient index, length scale parameters, temperature variation, incident angles, and acoustic cavity depth, on the STL is investigated. Key findings demonstrate that in the stiffness-controlled region, length scale parameters significantly enhance STL, while power-law index and temperature variation reduce it.

Genome integrity as a potential index of longevity in Ashkenazi Centenarian’s families

The aging process, or senescence, is characterized by age-specific decline in physical and physiological function, and increased frailty and genomic changes, including mutation accumulation. However, the mechanisms through which changes in genomic architecture influence human longevity have remained obscure. Copy number variants (CNVs), an abundant class of genomic variants, offer unique opportunities for understanding age-related genomic changes. Here we report the spectrum of CNVs in a cohort of 670 Ashkenazi Jewish centenarians, their progeny, and unrelated controls. The average ages of these groups were 97.4 ± 2.8, 69.2 ± 9.2, and 66.5 ± 7.0 respectively. For the first time, we compared different size classes of CNVs, from 1 kB to 100 MB in size. Using a high-resolution custom Affymetrix array, targeting 44,639 genomic regions, we identified a total of 12,166, 22,188, and 10,285 CNVs in centenarians, their progeny, and control groups, respectively. Interestingly, the offspring group showed the highest number of unique CNVs, followed by control and centenarians. While both gains and losses were found in all three groups, centenarians showed a significantly higher average number of both total gains and losses relative to their controls (p < 0.0327, 0.0182, respectively). Moreover, centenarians showed a lower total length of genomic material lost, suggesting that they may maintain superior genomic integrity over time. We also observe a significance fold increase of CNVs among the offspring, implying greater genomic integrity and a putative mechanism for longevity preservation. Genomic regions that experienced loss or gains appear to be distributed across many sites in the genome and contain genes involved in DNA transcription, cellular transport, developmental pathways, and metabolic functions. Our findings suggest that the exceptional longevity observed in centenarians may be attributed to the prolonged maintenance of functionally important genes. These genes are intrinsic to specific genomic regions as well as to the overall integrity of the genomic architecture. Additionally, a strong association between longer CNVs and differential gene expression observed in this study supports the notion that genomic integrity could positively influence longevity.

Optimisation of printing parameters of fused filament fabrication and uniaxial compression failure analysis for four-point star-shaped structures

PurposeThe purpose of this paper is to present an optimisation of four-point star-shaped structures produced through additive manufacturing (AM) polylactic acid (PLA). The study also aims to investigate the compression failure mechanism of the structure.Design/methodology/approachA Taguchi L9 orthogonal array design of the experiment is adopted in which the input parameters are resolution (0.06, 0.15 and 0.30 mm), print speed (60, 70 and 80 mm/s) and bed temperature (55°C, 60°C, 65°C). The response parameters considered were printing time, material usage, compression yield strength, compression modulus and dimensional stability. Empirical observations during compression tests were used to evaluate the load–response mechanism of the structures.FindingsThe printing resolution is the most significant input parameter. Material length is not influenced by the printing speed and bed temperature. The compression stress–strain curve exhibits elastic, plateau and densification regions. All the samples exhibit negative Poisson’s ratio values within the elastic and plateau regions. At the beginning of densification, the Poisson’s ratios change to positive values. The metamaterial printed at a resolution of 0.3 mm, 80 mm/s and 60°C exhibits the best mechanical properties (yield strength and modulus of 2.02 and 58.87 MPa, respectively). The failure of the structure occurs through bending and torsion of the unit cells.Practical implicationsThe optimisation study is significant for decision-making during the 3D printing and the empirical failure model shall complement the existing techniques for the mechanical analysis of the metamaterials.Originality/valueTo the best of the authors’ knowledge, for the first time, a new empirical model, based on the uniaxial load response and “static truss concept”, for failure mechanisms of the unit cell is presented.

Teaching and Learning English Literature Through Multimedia

Reading and understanding English literature can be quite challenging for students if English is not their native language. Thus, somehow students do not feel motivated in reading literature because of the high language proficiency the texts require and the length of the teaching materials. The conventional “Chalk and Talk” teaching method is not enough to convey the complexity of English literature effectively. The use of multimedia might be a precious medium in the teaching of literature and to increase students’ motivation to read literary texts. Research indicates that multimedia helps students to understand literature, to focus on the target language but also on its culture, new terminologies, new phraseology and their proper usage. The use of multimedia has many advantages as it is a great facilitator in transmitting knowledge. However, there are many questions about the use of digital tools, some think that they interfere with the teaching process and the student’s concentration, whereas others think that digital media can be effectively integrated into the teaching and learning process. In this paper, we will focus on how the multimedia content helps to vary and enhance the learning process and to lead to a better understanding and memorising. Multimedia elements help learners to be more engaged and active at learning. It makes studying literature more exciting because some students are visual learners and use visual senses in the process of learning. I used tests, observation and questionaries to analyse my research questions. Received: 10 February 2024 / Accepted: 11 April 2024 / Published: 5 May 2024

An investigation on the torsional vibration of a FG strain gradient nanotube

AbstractIn this work, an attention is paid to the prediction of torsional vibration frequencies of functionally graded porous nanotubes based on the Lam strain gradient elasticity theory. The nanotubes are formed of functionally graded porous nanomaterials that vary in the radial direction. This study also aims to obtain the analytical solution of the strain gradient model presented by Lam for torsional vibration response, in a simple manner, for different rigid or restrained boundary conditions. The torsion angle of a functionally graded nanotube is defined by an infinite Fourier series. Then, the Stokes’ transformation is applied to force the boundary conditions to the desired state. An eigenvalue problem is established with the help of the two systems of equations obtained. This eigenvalue problem, which includes deformable springs at both ends of the nanotube, appears as a general analytical solution that can find torsional vibration frequencies. It is shown that the vibrational responses can be significantly influenced by the through‐radius gradings of material, material length scale parameters and deformable springs of the functionally graded nanotubes and consequently can be predicted by giving proper values to torsional spring parameters.

Nonlinear oscillation of microscale fiber-reinforced composite laminated beams under a thermal loading

The work analyzes the nonlinear dynamic response of fiber-reinforced composite laminated microbeams in thermal environment, accounting for the dependence of the material properties on temperature. The governing equations of the nonlinear partial differential equations are based on the Euler-Bernoulli beam theory, and the modified couple stress theory involving the von Kármán geometrical nonlinearity. The governing nonlinear equations are reduced to a single equation by neglecting the axial inertia, which is discretized in the form of nonlinear ordinary differential equation, according to the Galerkin method, and it is solved analytically using the multiple time scales (MTS) method. A systematic investigation checks for the effect of the material length scale parameter, temperature increase, and damping parameter of the microscale beam on its time history and phase plane trajectory. Different stacking sequences are also considered within the parametric investigation. Based on results, it is noticed that the system is in a damped period-doubling bifurcation for four cycle oscillation states. It is also noticed that the stacking sequence affects significantly the nonlinear dynamic behavior of the system. It is found that the microscale composite laminated beam with [0/0/0] lay-ups has the highest dynamical deflection and the highest nonlinear frequency, followed by [0/90/0], [30/-30/30] (angle ply), [90/0/90], [45/-45/45] (angle ply) and [60/-60/60] (angle ply). However, the microscale composite laminated beam with [90/90/90] lay-ups has the lowest dynamical deflection and the lowest nonlinear frequency.

Dynamic stability of the euler nanobeam subjected to inertial moving nanoparticles based on the nonlocal strain gradient theory

This research studied the dynamic stability of the Euler-Bernoulli nanobeam considering the nonlocal strain gradient theory (NSGT) and surface effects. The nanobeam rests on the Pasternak foundation and a sequence of inertial nanoparticles passes above the nanobeam continuously at a fixed velocity. Surface effects have been utilized using the Gurtin-Murdoch theory. Final governing equations have been gathered implementing the energy method and Hamilton's principle alongside NSGT. Dynamic instability regions (DIRs) are drawn in the plane of mass-velocity coordinates of nanoparticles based on the incremental harmonic balance method (IHBM). A parametric study shows the effects of NSGT parameters and Pasternak foundation constants on the nanobeam's DIRs. In addition, the results exhibit the importance of 2T-period DIRs in comparison to T-period ones. According to the results, the Winkler spring constant is more effective than the Pasternak shear constant on the DIR movement of nanobeam. So, a 4 times increase of Winkler and Pasternak constants results in 102 % and 10 % of DIR movement towards higher velocity regions, respectively. Furthermore, the effect of increasing nonlocal and material length scale parameters on the DIR movement are in the same order regarding the magnitude but opposite considering the motion direction. Unlike nonlocal parameter, an increase in material length scale parameter shifts the DIR to the more stable region.

On the stability analysis of a restrained functionally graded nanobeam in an elastic matrix with neutral axis effects

Abstract In this work, a general eigenvalue solution of an arbitrarily constrained nonlocal strain gradient nanobeam made of functionally graded material is presented for the first time for the stability response by the effect of the Winkler foundation. Elastic springs at the ends of the nanobeam are considered in the formulation, which have not been considered in most studies. In order to analyze deformable boundary conditions, linear equation systems are derived in terms of infinite power series by using the Fourier sine series together with the Stokes’ transform. The higher-order force boundary conditions are used to obtain a coefficient matrix including different end conditions, power-law index, elastic medium, and small-scale parameters. A general eigenvalue problem of technical interest, associated with nonlocal strain gradient theory, is mathematically evaluated and presented in detail. Parametric results are obtained to investigate the effects of material length scale parameter, Winkler stiffness, power-law index, nonlocal parameter, and elastic springs at the ends. In addition, the effects of the other higher-order elasticity theories simplified from nonlocal strain gradient theory are also investigated and some benchmark results are presented.

Examining the critical speed and electro-mechanical vibration response of a spinning smart single-walled nanotube via nonlocal strain gradient theory

In this study, the stability and vibration analyses of a spinning smart nanotube under electrical loads are examined for the first time. The smart nanotube structure is made from a single-walled zinc oxide nanotube (SWZnONT) due to its extraordinary piezoelectric and magnetic properties, which have great potential for use as a rotating component in nanoelectromechanical systems (NEMS). To achieve this aim, nonlocal strain gradient theory and Maxwell’s electrostatic equations are used to capture the structure’s small-scale and piezoelectric effects, respectively. In addition, the nanotube’s structural model is based on the Euler–Bernoulli beam theory, deriving governing equations and boundary conditions via the Hamilton principle. A technique employing Galerkin-based closed-form solutions is utilized to solve the equations of motion and get the vibration response of the spinning smart nanotube. Finally, the effects of the material length scale, nonlocal parameter, rotating speed, external voltage, and boundary conditions on natural frequency and critical rotational speed are investigated. The study results indicate that applying an external voltage to spinning SWZnONT effectively adjusts the critical speed and enhances structural stability.

Symmetric/Asymmetric Vibrational Characteristics of Bi-Directional Functionally Graded Annular Microplates

In this study, a free vibration model of bi-directional functionally graded (BD-FG) annular microplates is established based on the modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT), and the corresponding governing equations are derived from Hamilton’s principle. The annular microplates are assumed to be composed of metal and ceramic materials, and the equivalent material properties are a combination of power-law function and exponential ones. The generalized differential quadrature method (GDQM) is used to obtain the vibration frequencies and mode displacements for the C–C, S–C, C–S, and S–S (S: simply supported; C: clamped) annular microplates. The convergence and validity of the proposed model are verified through selective numerical examples. Further, the effects of gradient index, material length scale parameter, boundary conditions, and geometrical dimensions on the symmetric/asymmetric vibration frequencies of the annular microplate are explored. The modal assurance criterion is applied to estimate the influence of the radial gradient index and material length scale parameter on different-order mode displacements of the annular microplate. The results show that: (1) the vibration frequencies of the annular microplate are sensitive to changes in the geometry and boundary conditions; (2) compared with the axial gradient index, the radial gradient index not only affects the vibration frequencies of the annular microplate, but also impacts the distribution of the highest and lowest points of the vibration mode displacements as well as the vibration mode nodal lines; (3) as the material length scale parameter increases, the vibration frequencies are significantly increased, and the higher-order vibration modes of the annular microplate also change.

The influence of borehole lengths on a numerical model of a double-tube vertical ground heat exchanger

GHEs are underground pipes that transmit heat between the earth and pipes. ANSYS Fluent was used to numerically investigate the thermal and hydraulic performance of a vertical twin tube ground-linked heat exchanger in a pile foundation in cooling mode. The CFD analysis uses three borehole length models—M1-10 m, M2-15 m, and M3-20 m—with flow rates from 1-100 lit/min and Reynolds numbers from 162 to 1625. The numerical results show that the average heat transfer rate of the Model M1 was 13% higher than that of the Model M2, 32% higher than that of the Model M3, and 95% higher than that of the Model M2. The pressure drop was minimal for 1 to 5 lit/min (laminar flow condition) but very high for 10 to 100 lit/min. The bore cavity length increased the pressure drop and decreased the average output temperature. These two-tube vertical GHEs with optimized length and selection of pipe materials can improve natural convection heat transfer by contacting ground waters.

Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions

PurposeIn the present study, the nonlinear vibration analysis of a nanoscale beam with different boundary conditions named as simply supported, clamped-clamped, clamped-simple and clamped-free are investigated numerically.MethodsNanoscale beam is considered as Euler-Bernoulli beam model having size-dependent. This non-classical nanobeam model has a size dependent incorporated with the material length scale parameter. The equation of motion of the system and the related boundary conditions are derived using the modified couple stress theory and employing Hamilton’s principle. Multiple scale method is used to obtain the approximate analytical solution.ResultNumerical results by considering the effect of the ratio of beam height to the internal material length scale parameter, h/l and with and without the Poisson effect, υ are graphically presented and tabulated.ConclusionWe remark that small size effect and poisson effect have a considerable effect on the linear fundamental frequency and the vibration amplitude. In order to show the accuracy of the results obtained, comparison study is also performed with existing studies in the literature.

Free Vıbratıon of a Carbon Nanotube-Reınforced Nanowıre/Nanobeam wıth Movable Ends

ObjectiveThe purpose of this work is to investigate the size-dependent free vibrations of carbon nanotube-reinforced nanowires/nanobeams with movable ends. For this purpose, two movable end conditions are considered for carbon nanotube-reinforced nanowires/nanobeams with different carbon nanotube distributions. The size effect is addressed with the modified couple stress theory, which includes a material length scale parameter.MethodsIn this study, a solution approach based on the Fourier sine series and Stokes' transformation is used. With the help of this approach, both rigid and movable end conditions can be investigated. Firstly, equation sets consisting of infinite series and movable end parameters are derived. Then, eigenvalue problems are obtained for the free vibration of carbon nanotube-reinforced nanowires/nanobeams. The eigenvalues of these problems give the frequencies of the carbon nanotube-reinforced nanowires/nanobeams with movable ends.ConclusionsThe eigenvalue problems obtained in this study can be used to examine both rigid and movable end conditions. The accuracy of the problems obtained for solution is proven by various comparison studies. Then, a series of analyses are carried out for nanowire/nanobeam reinforced with carbon nanotubes, including both the size effect and the rotary inertia effect. When the frequencies of nanowire/nanobeams reinforced with carbon nanotubes are examined, it is understood that the material length scale parameter, carbon nanotube distribution, carbon nanotube volume fraction, rotational and lateral spring parameters can cause significant changes in free vibration.

Elastostatics of nonuniform miniaturized beams: Explicit solutions through a nonlocal transfer matrix formulation

A mathematically well-posed nonlocal model is formulated based on the variational approach and the transfer matrix method to investigate the size-dependent elastostatics of nonuniform miniaturized beams. The beams are composed of an arbitrary number of sub-beams with diverse material and geometrical properties, as well as small-scale size dependency. The model adopts a stress-driven nonlocal approach, a well-established framework in the Engineering Science community. The curvature of a sub-beam is defined through an integral convolution, considering the bending moments across all cross-sections of the sub-beam and a kernel function. The governing equations are solved and the deflections are derived in terms of some constants. The formulation uses local and interfacial transfer matrices, incorporating continuity conditions at cross-sections where sub-beams are joined, to define relations between constants in the solution of a generic sub-beam and those of the first sub-beam at the left end. The boundary conditions are then imposed to derive an explicit, closed-form solution for the deflection. The solution significantly simplifies the study of nonuniform beams with multiple sub-beams. The predictions of the model for two limiting cases, namely local nonuniform and nonlocal uniform beams, are in excellent agreement with the available literature data. The flexural behavior of nonuniform miniaturized beams, composed of two to five different sub-beams and subjected to different boundary conditions, is studied. The results are presented and discussed, emphasizing the effects of the material properties, nonlocalities, and lengths of the sub-beams on the deflection. It is demonstrated that the flexural response of nonlocal nonuniform beams is more complex than local counterparts. Unlike the local beams, dividing a nonlocal uniform beam into multiple sub-beams and then reconnecting them changes the overall stiffness of the beam. The study highlights the potential to design nonuniform miniaturized beams with specific configurations to control their flexural response effectively.

Vibration analysis of a smart viscoelastic porous sandwich micro-shell with magnetorheological fluid core using the modified couple stress theory

In the current study, for the first time, the size-dependent vibration of a functionally graded (FG) porous sandwich cylindrical microshell with magnetorheological fluid core is investigated using modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT). The microshell is made of FG porous material and for investigating the material properties, two types of porous distributions are considered. Based on FSDT and the MCST, the governing equations are derived using Hamilton’s principle regarding the energy dissipation due to the shear deformation of the magnetorheological core layer and the interaction between all layers. Different assumptions, based on the continuity in transverse shear stresses and slope of in-plane displacements, are considered in the theoretical formulation. The natural frequency and loss factor of the microshell with sliding simply supported boundary conditions are determined using Navier’s solution method. Finally, the influence of some parameters such as material length scale(l/h: 0-1), types of porous distributions (symmetric-asymmetric), porosity volume fraction (e0: 0-1), magnetic field intensity (B: 0-800) and aspect ratio (L/R: 1-8, R/h: 10-100) on the vibration damping characteristics of microshell, is investigated and validity of the results is studied.

Vibration frequency and mode localization characteristics of strain gradient variable-thickness microplates

Based on the modified strain gradient theory and Kirchhoff–Love assumptions, a free vibration model is established for variable-thickness microplates with three material length scale parameters, and the corresponding Euler–Lagrange equation is derived. Keeping the microplate volume constant, three kinds of thickness variations along the X-direction are considered: linear, parabolic, and cubic variations. Further, a C2-type four-node 36-degree-of-freedom variable-thickness differential quadrature finite element is developed to solve the resulting variable-coefficient boundary value problem by combining the Gauss–Lobatto and differential quadrature rules. Galerkin approximate solution for fully simply supported microplates is provided as a benchmark for numerical method verification. The convergence and accuracy of the model are verified through several examples. Finally, the vibration frequencies of the microplates under different thickness variation types, taper ratios, thickness ratios, material length scale parameters, and boundary conditions are examined through parametric analysis. Also, the influence of each factor on the mode localization of the microplates is quantitatively characterized by the modal assurance criterion (MAC) for the first time. The numerical results show that the thickness variation has a minor effect on the vibration frequency but a significant influence on the mode shape when the volume of the microplate is constant. The strain gradient, taper ratio, and discontinuous boundary have a remarkable effect on the distribution of higher-order mode shape contour lines and the regions where vibration localization occurs.

On the variable length scale parameter in functionally graded non-porous and porous microplate/nanoplate

In this article, the solution for free vibration and static bending of nonporous and porous square microplate/nanoplate is studied by practicing the modified couple stress theory (MCST). The impact of incorporating the length scale parameter of MCST is confirmed by comparing the results to that of molecular dynamics simulations. This study is aimed at investigating the influence of implementing a variable length scale parameter on the static and dynamic behavior of the small-scaled plates. Results are obtained adopting the analytical technique and compared to cases of presupposing constant numerical values of material length scale throughout each plate. The novelty of this theoretical study is the approach employed to achieve the formulation of the material length scale parameter, which varies along the thickness of both porous and nonporous plates. The results indicate that the inclusion of the variable length scale parameter increases the fundamental frequency and stiffness of plates. When comparing two cases of variable length scale parameter, one approximating the scale parameter of each constituent based on the bending parameter and Poisson’s ratio of the material, and the other adopting the numerical values estimated by prior experimental studies, reveals that the latter gives higher results and is chosen correspondingly.

Static and free vibration responses of nanobeams considering flexoelectricity and surface effect

In this paper, the electro-mechanical behavior of a flexoelectric nanobeam, considering the surface effect, is studied with an induced electric potential. Based on the modified strain gradient theory and Hamilton’s variational principle, the governing differential equations of the nanobeam and the corresponding boundary conditions are obtained. The exact deflection solution of the flexoelectric nanobeam is derived from static bending. The relationship between the induced electric potential, including the surface effect, and the angle of the end of the cantilever beam is presented. Moreover, the characteristic equation of natural frequency is obtained by using a separate variable method under an open circuit with surface electrodes and an induced electric potential condition (OCI). The simulated results indicate the electro-mechanical response of the cantilever beam can be controlled by adjusting the flexoelectric coefficient, residual surface stress, and material length scale parameters of strain gradient theory. The free end of the beam with a platform phenomenon is also found by setting the appropriate parameters. The results also show that the residual surface stress and the ratio of beam thickness to material length scale parameters have a more significant effect on the effective frequency shift of the flexoelectric nanobeam. Therefore, considering the induced electric potential and surface effect is of great significance for the study of flexoelectric nanobeam sensors.

The Physiological Basis of Alfalfa Plant Height Establishment.

Plant height plays an important role in crop yield, product quality, and cultivation management. However, the physiological mechanisms that regulate the establishment of plant height in alfalfa plants remain unclear. Herein, we measured plant height traits, leaf characteristics, photosynthetic physiology, cell wall composition, and endogenous hormone contents of tall- and short-stalked alfalfa materials at different reproductive periods. We analyzed the physiology responsible for differences in plant height. The results demonstrated that the number of internodes in tall- and short-stalked alfalfa materials tended to converge with the advancement of the fertility period. Meanwhile, the average internode length (IL) of tall-stalked materials was significantly higher than that of short-stalked materials at different fertility periods, with internode length identified as the main trait determining the differences in alfalfa plant height. Leaf characteristics, which are closely related to photosynthetic capacity, are crucial energy sources supporting the expression of plant height traits, and we found that an increase in the number of leaves contributed to a proportional increase in plant height. Additionally, a significant positive correlation was observed between plant height and leaf dry weight per plant during the branching and early flowering stages of alfalfa. The leaves of alfalfa affect plant height through photosynthesis, with the budding stage identified as the key period for efficient light energy utilization. Plant height at the budding stage showed a significant positive correlation with soluble sugar (SS) content and a significant negative correlation with intercellular CO2 concentration. Moreover, we found that alfalfa plant height was significantly correlated with the contents of indole-3-acetic acid in stem tips (SIAA), gibberellin A3 in leaves (LGA3), zeatin in stem tips (SZT), and abscisic acid in leaves (LABA). Further investigation revealed that SS, SIAA, and LGA3 contents were important physiological indicators affecting alfalfa plant height. This study provides a theoretical basis for understanding the formation of alfalfa plant height traits and for genetic improvement studies.