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The dynamic behaviour of an Euler–Bernoulli beam resting on the fractionally damped viscoelastic foundation subjected to a moving point load is investigated. The fractional-order derivative-based Kelvin–Voigt model describes the rheological properties of the viscoelastic foundation. The Riemann–Liouville fractional derivative model is applied for a fractional derivative order. The modal superposition method and Triangular strip matrix approach are applied to solve the fractional differential equation of motion. The dependence of the modal convergence on the system parameters is studied. The influences of (a) the fractional order of derivative, (b) the speed of the moving point load and (c) the foundation parameters on the dynamic response of the system are studied and conclusions are drawn. The damping of the beam-foundation system increases with increasing the order of derivative, leading to a decrease in the dynamic amplification factor. The results are compared with those using the classical integer-order derivative-based foundation model. The classical foundation model over-predicts the damping and under-predicts the dynamic deflections and stresses. The results of the classical (integer-order) foundation model are verified with literature.

The coupled horizontal-torsional-warping vibration of a thin-walled open-section 7800 TEU container ship bare-hull, modelled as a non-uniform girder, is analysed by the efficient energy-based Rayleigh-Ritz method, in order to generate the dry asymmetric vibration frequencies. Since the centre of gravity is within the hull and the shear centre is below the keel, the horizontal and torsional modes of vibration are highly coupled. An open section is also prone to warping. In a novel attempt, the bare-hull geometry is generated mathematically, using section-wise closed-form semi super-ellipses (Lame’s curves). The main dimensions, weight distributions, and fineness ratios are preserved, and closed-form expressions of sectional properties become available in the process. The hull has arbitrarily (non-mathematically) varying mass, bending stiffness, warping stiffness, and shear stiffness distributions along the length. The non-uniform beam modeshape in horizontal/torsional vibration is assumed to be a weighted sum of the uniform beam horizontal/torsional modeshapes. Several benchmark cases of simpler geometry have been analysed first, for both torsion-warping vibration, and coupled horizontal-torsional-warping vibration. Pontoon approximation of the containership has been analysed and validated. Subsequently, the coupled dry vibration frequencies are obtained for the open deck non-uniform girder, and compared with published results.

This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin–Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

A semi-analytical approach to free dry and wet vibration of a trapezoidal, 2-way tapered, pivoted hollow spade rudder is presented. The rudder is modeled as a hollow Kirchhoff’s plate, with a NACA0018 profile chord section. The rudder pivot is modeled as a combination of a translational spring and a rotational spring. The span-wise and chord-wise non-uniform beam vibration is first analyzed by the Rayleigh-Ritz method, to establish the non-uniform beam modeshapes, which act as admissible functions to the Galerkin’s method for plate vibration. Eigenvalue analysis generates the plate natural frequencies and the plate modeshapes. Alternately, uniform beam modeshapes themselves are used as admissible functions into the Galerkin’s method. Frequencies are analyzed for various pivot positions, taper ratios, and NACA sections. For the wet vibration, constant strength source distribution technique is used to generate the added mass of a 2D aerofoil. Also, 3D panel method is used to generate the modal added masses, and hence the wet natural frequencies. The added mass coefficient is generated for various aerofoil fineness ratios, pivot fixities, taper ratios, aspect ratios.

Parathyroid hormone-related peptide (PTHrP) is well-known to play a role in bone formation, and abaloparatide, an analog of PTHrP(1-34), is approved for the treatment of osteoporosis in post-menopausal women. PTHrP has also been reported to have cardiovascular effects, with recent data demonstrating that exogenously administered PTHrP can limit the death of isolated cardiomyocytes subjected to oxidative stress via upregulation of classic ‘survival kinase’ signaling. Our aim in the current study was to extend this concept and, employing both in vitro and in vivo models, establish whether PTHrP(1-36) and abaloparatide are cardioprotective in the setting of lethal myocardial ischemia-reperfusion injury. We report that preischemic administration of PTHrP(1-36) and abaloparatide attenuated cell death in HL-1 cardiomyocytes subjected to simulated ischemia-reperfusion, an effect that was accompanied by the augmented expression of phospho-ERK and improved preservation of phospho-Akt, and blocked by co-administration of the MEK-ERK inhibitor PD98059. Moreover, using the translationally relevant swine model of acute coronary artery occlusion-reperfusion, we make the novel observation that myocardial infarct size was significantly reduced in pigs pretreated with PTHrP(1-36) when compared with placebo-controls (13.1 ± 3.3% versus 42.0 ± 6.6% of the area of at-risk myocardium, respectively; p < 0.01). Taken together, these data provide the first evidence in support of the concept that pretreatment with PTHrP(1-36) and abaloparatide renders cardiomyocytes resistant to lethal myocardial ischemia-reperfusion injury.

A compliant tower is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with parallel linear and torsional dampers (Kelvin-Voigt model). The superstructure adds to the kinetic energy of the system without affecting the potential energy, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its natural frequencies further. The empty space factor due to the truss-type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes satisfying the end condition. The weights are evaluated by the Rayleigh-Ritz (RR) method, and verified using finite element method (FEM). The weight of the superstructure acts as an axial compressive load on the beam. Kelvin-Voigt model of structural damping is included. A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. A parametric study is done for various magnitudes of tip mass and various levels of submergence. The computational efficiency and accuracy of the Rayleigh-Ritz method, as compared to the FEA, has been demonstrated. The advantage of using closed-form trial functions is clearly seen in the efficacy of calculating the various energy components in the RR method.

A closed-form approach is proposed to scrutinize and study the prominence of rigid-body modes (RBM) of a translationally edge-restrained thin plate. Accurate vibrational analysis of an elastically edge-supported plate is not possible without the inclusion of degenerate rigid-body beam-wise admissible functions. The trivial solution(s) of the beam frequency equation produce(s) a non-trivial modeshape, which satisfies the boundary conditions, has zero curvature, and is orthogonal to other modeshapes. The frequency parameters, waveform coefficients, orthogonality, and potential energies of the RBM have been studied for a wide range of edge restraints, asymptotically leading to the classical edge beam vibration characteristics. The second trivial frequency parameter is seen to transform from a RBM to a flexural mode at a certain range of edge spring constant. The first several (20) non-trivial modeshapes of a fully free (FFFF) square plate have been semi-analytically generated and are seen to match well with published experimental work. The nature of the frequencies has been scrutinized using Eigenvectors, with respect to the participation of the RBM functions, which are seen to dominate the plate modeshape even in higher-order frequencies. However, they are mutually exclusive: the translational RBM influences the odd flexural modes, while the rotational RBM influences the even flexural modes. The confusions in literature, especially about the identical frequencies, have been clarified.

The free vibration of a low-aspect cantilever wing is studied by semianalytical, numerical, and experimental means. The wing is modeled as a two-way tapered, hollow Kirchhoff's plate, with the chord-wise section as symmetrical NACA0018 aerofoil. The chord length and the thickness taper from root to tip, over the span. The semianalytical approach is based on Galerkin's method, which includes the modal superposition of two orthogonal beam modeshapes (free-free beam in chord-wise direction and cantilever beam in span-wise direction). The free vibration is also studied numerically using ANSYS. The results have been compared with an experimental study, performing the dry impact hammer test. A model scale wing has been constructed from a 3-mm-thick metal sheet, with a length-scale ratio of 1:10. Comparative studies have been done among the three methods. The feasibility of modeling a low-aspect-ratio wing as a plate has been investigated. 1. Introduction Lifting surfaces commonly occur in engineering structures: fans, steam and gas turbine blades, impeller blades, wind turbine blades, helicopter fans, airplane wings, marine propeller blades, marine rudders and skegs, and other control surfaces like hydrofoils and wings in high-speed marine crafts. The lifting surface is typically a cantilever, with one edge welded to the main structure (root), and the other end free (tip). The span-wise geometry is tapered, for greater strength at the root and lighter weight at the tip. The chord-wise cross section is an aerofoil, which acts as a lifting surface to the incoming flow at varying angles of attack. The aspect ratio of the lifting surface, i.e., the ratio of the span length to the mean chord length, may vary from 0.4 to 0.6 in a turbine blade to 12 to 15 in an airplane wing/wind turbine. This work focuses on a low-aspect-ratio lifting surface, whose usual span-to-chord ratio is 1.5–2.

A semi-analytical approach to understand the manifestation of plate modeshapes associated with twin frequencies has been presented. Square Mindlin’s plate, clamped on all sides, has been considered here. It highlights the importance of efficacy of the beam-wise trial functions in an energy-based plate vibration analysis method, in terms of (a) accuracy, (b) orthogonality, (c) sense (plus/minus) and (d) interference. The inconsistency in the modeshapes of repeated frequencies, seen extensively in literature, has been attempted to be removed, through superior closed-form orthogonal set of Timoshenko admissible functions into the Rayleigh-Ritz method. The constructive/destructive interferences of the admissible functions, which are the products of the beam-wise modeshapes, give the final nodal patterns and the prominence of the anti-nodes. Also, the pairs of ‘very close’ but distinct frequencies, which were often considered as ‘numerical errors’, have been counter-intuitively justified through their Eigenvectors, which are either symmetric or skew-symmetric in the matrix form. Nodal patterns for CCCC plate modeshapes are accurately investigated; i.e. chess-board and diagonal nodal patterns.

A theoretical hydroelastic analysis of an axially loaded uniform Timoshenko beam, with intermediate end fixities, undergoing hydrodynamic impact-induced bottom slamming, is presented. The underwater part of a marine craft is modeled as a lightly damped flexible beam, which rises out of the water in rough seas, and slams against it at a very large vertical velocity. This causes highly intense, localized hydrodynamic impact pressure sweeping across the beam at high velocities, setting it into high-frequency vibrations, predisposing it to plastic deformation and/or fatigue failure. The natural frequencies of the structure depend on the slenderness ratio, axial load, and end fixities. The natural frequencies and modeshapes are generated through the Eigen analysis. The changing wetted surface is the prime complexity of the problem. The relative velocity between fluid and structure is considered to establish the hydrodynamic pressure (radiation and impact). Normal mode summation method is used to analyze the transient structural vibration, for various impact speeds, deadrise angles, end fixities, and axial loads on the beam. The primary aim is to establish the zone of prominence of hydroelasticity, study the maximum dynamic stress magnitudes under various loading conditions and structural parameters; and draw conclusions leading to insights into sound structural designs.

Previous attempts to solve for vibration of non-uniform hull girder have used Finite Element Analysis (FEA). This work utilizes the Rayleigh–Ritz (R–R) method to analyze the vertical vibration of a non-prismatic mathematical hull, with arbitrary longitudinal distribution of sectional properties. It is shown that (a) the R-R method provides reasonably accurate results for the actual natural frequency; and (b) the R–R method offers significant computational advantages over FEA. This computational supremacy can be exploited in the initial design stages when several designs are to be iteratively tested for its structural characteristics. The natural frequencies and modeshapes are obtained by the Rayleigh–Ritz method. The non-uniform beam modeshape is a weighted series sum of the (closed-form) uniform beam modeshapes. Only a few uniform beam modes are necessary to generate the non-uniform beam modeshape and a convergent hull girder frequency. Thus, the method is very effective in the low-frequency domain like ship-structure. The proposed method is compared with FEA for two illustrative structures : (a) a containership and (b) a tanker; and also with several hulls from established literature. Modal convergence studies have also been included. The distortions of the non-uniform modeshapes have been studied in the light of the loading conditions of the hull.

The free vibration of a continuous, elastic model of a mono-piled ocean tower is studied. The tower, partially submerged in water, is undergoing free transverse vibration in a plane. It is modeled as a non-uniform Timoshenko beam which has an eccentric tip mass on one end and is supported by a mono-piled foundation on the other. Effects of shear deformation and rotary inertia are included in the beam. The problem of interaction of soil with the pile is solved by adopting the Winkler Foundation model. The viscoelastic character of the soil is included using the Kelvin–Voigt model. Equation of motion of the tower is derived using Hamilton׳s variational principle and approximate analytical solution is found using the Rayleigh Ritz Method (RRM). The solution is compared with that obtained from a conventional Finite Element Method (FEM) which shows a good agreement. The trial function of RRM is assumed as uniform beam mode-shapes satisfying the boundary and continuity conditions of the ocean tower. At the end, an extensive parametric study is carried out which provides an insight into the dependence of natural frequency on different configurations of the tower.

In this review, we have highlighted work that has clearly demonstrated that mitogen-activated protein kinase (MAPK) phosphatase-1 (MKP-1), a negative regulator of MAPKs, is an important signaling mediator in bone, muscle, and fat tissue homeostasis and differentiation. Further, we examined recent studies with particular focus on MKP-1 overexpression or deletion and its impact on tissues connected to bone. We also summarized regulation of MKP-1 by known skeletal regulators like parathyroid hormone (PTH)/PTH-related peptide (PTHrP) and bone morphogenic proteins. MKP-1's integration into the pathophysiological state of osteoporosis, osteoarthritis, rheumatoid arthritis, obesity, and muscular dystrophy are examined to emphasize possible involvement of MKP-1 both at the molecular level and in disease complications such as sarcopenia- or diabetes-related osteoporosis. We predict that understanding the mechanism of MKP-1-mediated signaling in bone-muscle-fat crosstalk will be a key in coordinating their activities and developing therapeutics to improve clinical outcomes for diseases associated with advanced age.

This paper studies a continuous, elastic model of an ocean tower, partially submerged in water, undergoing free transverse vibration in a plane. The tower is modeled as a non-uniform Timoshenko beam which is supported by an eccentric tip mass on one end and a non-classical damped foundation on the other. The foundation is modeled as a combination of translational and rotational springs and dampers. The effect of shear deformation and rotary inertia is included in the analysis. The free vibration equation is derived using Hamilton׳s variational principle based on two approaches, Rayleigh Ritz Method (RRM) and Finite Element Method (FEM), which show a good agreement in results. The computational efficiency of RRM over FEM is shown using a convergence study. Finally, a parametric study is done to demonstrate the dependence of natural frequency on different configurations of the tower.

Bone mass is dependent on osteoblast proliferation, differentiation and life-span of osteoblasts. Parathyroid hormone (PTH) controls osteoblast cell cycle regulatory proteins and suppresses mature osteoblasts apoptosis. Intermittent administration of PTH increases bone mass but the mechanism of action are complex and incompletely understood. Cell Cycle and Apoptosis Regulatory Protein (CARP)-1 (aka CCAR1) is a novel transducer of signaling by diverse agents including cell growth and differentiation factors. To gain further insight into the molecular mechanism, we investigated involvement of CARP-1 in PTH signaling in osteoblasts. Immunostaining studies revealed presence of CARP-1 in osteoblasts and osteocytes, while a minimal to absent levels were noted in the chondrocytes of femora from 10 to 12-week old mice. Treatment of 7-day differentiated MC3T3-E1 clone-4 (MC-4) mouse osteoblastic cells and primary calvarial osteoblasts with PTH for 30min to 5h followed by Western blot analysis showed 2- to 3-fold down-regulation of CARP-1 protein expression in a dose- and time-dependent manner compared to the respective vehicle treated control cells. H-89, a Protein Kinase A (PKA) inhibitor, suppressed PTH action on CARP-1 protein expression indicating PKA-dependent mechanism. PMA, a Protein Kinase C (PKC) agonist, mimicked PTH action, and the PKC inhibitor, GF109203X, partially blocked PTH-dependent downregulation of CARP-1, implying involvement of PKC. U0126, a Mitogen-Activated Protein Kinase (MAPK) Kinase (MEK) inhibitor, failed to interfere with CARP-1 suppression by PTH. In contrast, SB203580, p38 inhibitor, attenuated PTH down-regulation of CARP-1 suggesting that PTH utilized an Extracellular Signal Regulated Kinase (ERK)-independent but p38 dependent pathway to regulate CARP-1 protein expression in osteoblasts. Immunofluorescence staining of differentiated osteoblasts further revealed nuclear to cytoplasmic translocation of CARP-1 protein following PTH treatment. Collectively, our studies identified CARP-1 for the first time in osteoblasts and suggest its potential role in PTH signaling and bone anabolic action.

Activation of G protein-coupled receptors by agonists leads to receptor phosphorylation, internalization of ligand receptor complexes, and desensitization of hormonal response. The role of parathyroid hormone (PTH) receptor 1, PTHR1, is well characterized and known to regulate cellular responsiveness in vitro. However, the role of PTHR1 phosphorylation in bone formation is yet to be investigated. We have previously demonstrated that impaired internalization and sustained cAMP stimulation of phosphorylation-deficient (PD) PTHR1 leads to exaggerated cAMP response to subcutaneous PTH infusion in a PD knockin mouse model. To understand the physiological role of receptor internalization on PTH bone anabolic action, we examined bone parameters of wild-type (WT) and PD knockin female and male mice following PTH treatment. We found a decrease in total and diaphyseal bone mineral density in female but not in male PD mice compared with WT controls at 3–6 mo of age. This effect was attenuated at older age groups. PTH administration displayed increased bone volume and trabecular thickness in the vertebrae and distal femora of both WT and PD animals. These results suggest that PTHR1 phosphorylation does not play a major role in the anabolic action of PTH.

Phosphorylation, internalization, and desensitization of G protein-coupled receptors, such as the parathyroid hormone (PTH) and PTH-related peptide (PTHrP) receptor (PTH1R), are well characterized and known to regulate the cellular responsiveness in vitro. However, the role of PTH1R receptor phosphorylation in bone formation and osteoblast functions has not yet been elucidated. In previous studies, we demonstrated impaired internalization and sustained cAMP stimulation of a phosphorylation-deficient (pd) PTH1R in vitro, and exaggerated cAMP and calcemic responses to s.c. PTH infusion in pdPTH1R knock-in mouse model. In this study, we examined the impact of impaired PTH1R phosphorylation on the skeletal phenotype of mice maintained on normal, low, and high calcium diets. The low calcium diet moderately reduced (P1/S phase cyclin, in vitro. In contrast to WT osteoblasts, down-regulation of cyclin D1 was sustained for longer periods of time in osteoblasts isolated from the pd mice. Our results suggest that adaptive responses of intracellular signaling pathways in the pd mice may be important for maintaining bone homeostasis.

Objective This study was undertaken to address the involvement of CDK activating kinase (CAK), p53, and MDM2 proteins in the mitotic arrest associated with the acquisition of a polyploid DNA content during megakaryocyte differentiation of human erythroleukemia (HEL) cells. Methods To evaluate this mechanism we investigated HEL cells as a model system in which there is a marked increase in DNA content during megakaryocyte differentiation induced by phorbol-diesters. Specific cell-cycle phases were separated by centrifugal elutriation and SDS PAGE and Western analysis were performed to determine the relative abundance of these proteins. Kinase assays were carried out following immunoprecipitation of cellular lysates with the antibodies to the proteins. Results Polyploid HEL cells show an increase in the abundance of the CAK complex proteins, CDK7 and cyclin H, and a sixfold increase in CAK-specific activity. Increased CAK activity in polyploid HEL cells follows both the downregulation of p53 protein and its decreased association with CAK complex. Consistent with the reduction of p53, polyploid HEL cells undergo a dramatic increase in MDM2 protein abundance that in turn facilitates increased interaction of this protein with p53. Conclusion These observations demonstrate that deregulated expression of MDM2 and p53 during megakaryocyte differentiation allow a relaxation of the control over genomic stability, allowing further replicative rounds of DNA synthesis.

The role of MAPKs in osteogenesis and in Parathyroid hormone (PTH) signaling has been shown in vitro and in vivo previously. However, the role of MAPK phosphatase-1 (MKP-1) in bone formation remains unclear. We observed age dependent sexual dimorphism in bone phenotype of MKP-1 knock out (KO) mice showing osteopenia in females and osteopetrosis in males. We investigate the involvement of MKP-1 on b-catenin, a key mediator of the canonical Wnt signaling pathway and an important regulator of bone forming cells, the osteoblasts. Signal transduction through b-catenin requires inhibition of GSK-3b which is also inhibited via phosphorylation by AKT upon insulin-like growth factor-1 (IGF-1) signaling. Real-time PCR analysis of primary calvarial osteoblasts revealed significant down-regulation of IGF-1 mRNA expression in osteoblasts isolated from MKP-1 KO female mice in contrast to KO osteoblasts from males. Inhibition of P-ERK and P-p38 with pharmacological inhibitors showed disparate regulation of IGF-1 express...

Metabolic bone disease occurs when there is a net loss in bone density. Osteoporosis, the most common metabolic bone disease, is a devastating problem and an increasingly major public health issue. A substantial body of evidence in the elderly population indicates that a relationship exists between the components of body weight and various measures of bone/mass, density, and function. Both muscle and fat contribute to the body’s total weight and the intimate associations of muscle, fat, and bone are known. But the close functional interactions between muscle and bone or fat and bone are largely unidentified and have drawn much attention in recent years. Each of these tissues not only responds to afferent signals from traditional hormone systems and the central nervous systems but also secretes factors with important endocrine functions. Studies suggest that during growth, development, and aging, the relationship of muscle and fat with the skeleton possibly governs bone homeostasis and turnover. A better understanding of the endocrine function and the cellular and molecular mechanisms and pathways linking muscle or adipose tissues with bone anabolism and catabolism is a new avenue for novel pathways for anabolic drug discovery. These in turn will likely lead to more rational therapy toward increasingly prevalent disorders like osteoporosis. In this review, some of the recent works on the interaction of bone with muscle and fat are highlighted, and in so doing the role of parathyroid hormone (PTH), and PTH-related peptide (PTHrP) is surveyed.

Cancer cells are able to proliferate at accelerated rates within the confines of a three-dimensional (3D) extracellular matrix (ECM) that is rich in type I collagen. The mechanisms used by tumor cells to circumvent endogenous antigrowth signals have yet to be clearly defined. We find that the matrix metalloproteinase, MT1-MMP, confers tumor cells with a distinct 3D growth advantage in vitro and in vivo. The replicative advantage conferred by MT1-MMP requires pericellular proteolysis of the ECM, as proliferation is fully suppressed when tumor cells are suspended in 3D gels of protease-resistant collagen. In the absence of proteolysis, tumor cells embedded in physiologically relevant ECM matrices are trapped in a compact, spherical configuration and unable to undergo changes in cell shape or cytoskeletal reorganization required for 3D growth. These observations identify MT1-MMP as a tumor-derived growth factor that regulates proliferation by controlling cell geometry within the confines of the 3D ECM.